use workspaces

sbp/Cargo.toml

@@ -0,0 +1,21 @@
+[package]
+name = "sbp"
+version = "0.1.1"
+authors = ["Magnus Ulimoen <flymagnus@gmail.com>"]
+edition = "2018"
+
+[dependencies]
+ndarray = { version = "0.13.0", features = ["approx"] }
+approx = "0.3.2"
+packed_simd = "0.3.3"
+
+[dev-dependencies]
+criterion = "0.3.0"
+
+[[bench]]
+name = "maxwell"
+harness = false
+
+[[bench]]
+name = "euler"
+harness = false

sbp/benches/euler.rs

@@ -0,0 +1,56 @@
+use criterion::{black_box, criterion_group, criterion_main, Criterion};
+use sbp::euler::System;
+use sbp::operators::{SbpOperator, Upwind4, UpwindOperator, SBP4};
+
+fn advance_system<SBP: SbpOperator>(universe: &mut System<SBP>, n: usize) {
+    for _ in 0..n {
+        universe.advance(1.0 / 40.0 * 0.2);
+    }
+}
+
+fn advance_system_upwind<UO: UpwindOperator>(universe: &mut System<UO>, n: usize) {
+    for _ in 0..n {
+        universe.advance_upwind(1.0 / 40.0 * 0.2);
+    }
+}
+
+fn performance_benchmark(c: &mut Criterion) {
+    let mut group = c.benchmark_group("EulerSystem");
+    group.sample_size(25);
+
+    let w = 40;
+    let h = 26;
+    let x = ndarray::Array1::linspace(-10.0, 10.0, w);
+    let x = x.broadcast((h, w)).unwrap();
+    let y = ndarray::Array1::linspace(-10.0, 10.0, h);
+    let y = y.broadcast((w, h)).unwrap().reversed_axes();
+
+    let mut universe = System::<Upwind4>::new(x.into_owned(), y.into_owned());
+    group.bench_function("advance", |b| {
+        b.iter(|| {
+            universe.init_with_vortex(0.0, 0.0);
+            advance_system(&mut universe, black_box(20))
+        })
+    });
+
+    let mut universe = System::<Upwind4>::new(x.into_owned(), y.into_owned());
+    group.bench_function("advance_upwind", |b| {
+        b.iter(|| {
+            universe.init_with_vortex(0.0, 0.0);
+            advance_system_upwind(&mut universe, black_box(20))
+        })
+    });
+
+    let mut universe = System::<SBP4>::new(x.into_owned(), y.into_owned());
+    group.bench_function("advance_trad4", |b| {
+        b.iter(|| {
+            universe.init_with_vortex(0.0, 0.0);
+            advance_system(&mut universe, black_box(20))
+        })
+    });
+
+    group.finish();
+}
+
+criterion_group!(benches, performance_benchmark);
+criterion_main!(benches);

sbp/benches/maxwell.rs

@@ -0,0 +1,54 @@
+use criterion::{black_box, criterion_group, criterion_main, Criterion};
+use sbp::maxwell::System;
+use sbp::operators::{SbpOperator, Upwind4, UpwindOperator, SBP4};
+
+fn advance_system<SBP: SbpOperator>(universe: &mut System<SBP>, n: usize) {
+    for _ in 0..n {
+        universe.advance(0.01);
+    }
+}
+
+fn advance_system_upwind<UO: UpwindOperator>(universe: &mut System<UO>, n: usize) {
+    for _ in 0..n {
+        universe.advance_upwind(0.01);
+    }
+}
+
+fn performance_benchmark(c: &mut Criterion) {
+    let mut group = c.benchmark_group("MaxwellSystem");
+    group.sample_size(25);
+
+    let w = 40;
+    let h = 26;
+    let x = ndarray::Array2::from_shape_fn((h, w), |(_, i)| i as f32 / (w - 1) as f32);
+    let y = ndarray::Array2::from_shape_fn((h, w), |(j, _)| j as f32 / (h - 1) as f32);
+
+    let mut universe = System::<Upwind4>::new(x.clone(), y.clone());
+    group.bench_function("advance", |b| {
+        b.iter(|| {
+            universe.set_gaussian(0.5, 0.5);
+            advance_system(&mut universe, black_box(20))
+        })
+    });
+
+    let mut universe = System::<Upwind4>::new(x.clone(), y.clone());
+    group.bench_function("advance_upwind", |b| {
+        b.iter(|| {
+            universe.set_gaussian(0.5, 0.5);
+            advance_system_upwind(&mut universe, black_box(20))
+        })
+    });
+
+    let mut universe = System::<SBP4>::new(x, y);
+    group.bench_function("advance_trad4", |b| {
+        b.iter(|| {
+            universe.set_gaussian(0.5, 0.5);
+            advance_system(&mut universe, black_box(20))
+        })
+    });
+
+    group.finish();
+}
+
+criterion_group!(benches, performance_benchmark);
+criterion_main!(benches);

sbp/src/euler.rs

@@ -0,0 +1,695 @@
+use super::grid::Grid;
+use super::integrate;
+use super::operators::{SbpOperator, UpwindOperator};
+use ndarray::azip;
+use ndarray::prelude::*;
+
+pub const GAMMA: f32 = 1.4;
+
+// A collection of buffers that allows one to efficiently
+// move to the next state
+pub struct System<SBP: SbpOperator> {
+    sys: (Field, Field),
+    wb: WorkBuffers,
+    grid: Grid<SBP>,
+}
+
+impl<SBP: SbpOperator> System<SBP> {
+    pub fn new(x: ndarray::Array2<f32>, y: ndarray::Array2<f32>) -> Self {
+        let grid = Grid::new(x, y).expect(
+            "Could not create grid. Different number of elements compared to width*height?",
+        );
+        let nx = grid.nx();
+        let ny = grid.ny();
+        Self {
+            sys: (Field::new(ny, nx), Field::new(ny, nx)),
+            grid,
+            wb: WorkBuffers::new(ny, nx),
+        }
+    }
+
+    pub fn advance(&mut self, dt: f32) {
+        integrate::rk4(
+            RHS_trad,
+            &self.sys.0,
+            &mut self.sys.1,
+            dt,
+            &self.grid,
+            &mut self.wb.k,
+            &mut self.wb.tmp,
+        );
+        std::mem::swap(&mut self.sys.0, &mut self.sys.1);
+    }
+
+    #[allow(clippy::many_single_char_names)]
+    pub fn init_with_vortex(&mut self, x0: f32, y0: f32) {
+        // Should parametrise such that we have radius, drop in pressure at center, etc
+        let rstar = 1.0;
+        let eps = 3.0;
+        #[allow(non_snake_case)]
+        let M = 0.5;
+
+        let p_inf = 1.0 / (GAMMA * M * M);
+        let t = 0.0;
+
+        let nx = self.grid.nx();
+        let ny = self.grid.ny();
+
+        for j in 0..ny {
+            for i in 0..nx {
+                let x = self.grid.x[(j, i)];
+                let y = self.grid.y[(j, i)];
+
+                let dx = (x - x0) - t;
+                let dy = y - y0;
+                let f = (1.0 - (dx * dx + dy * dy)) / (rstar * rstar);
+
+                use std::f32::consts::PI;
+                let u =
+                    1.0 - eps * dy / (2.0 * PI * p_inf.sqrt() * rstar * rstar) * (f / 2.0).exp();
+                let v =
+                    0.0 + eps * dx / (2.0 * PI * p_inf.sqrt() * rstar * rstar) * (f / 2.0).exp();
+                let rho = f32::powf(
+                    1.0 - eps * eps * (GAMMA - 1.0) * M * M
+                        / (8.0 * PI * PI * p_inf * rstar * rstar)
+                        * f.exp(),
+                    1.0 / (GAMMA - 1.0),
+                );
+                assert!(rho > 0.0);
+                let p = p_inf * rho.powf(GAMMA);
+                assert!(p > 0.0);
+                let e = p / (GAMMA - 1.0) + rho * (u * u + v * v) / 2.0;
+                assert!(e > 0.0);
+
+                self.sys.0[(0, j, i)] = rho;
+                self.sys.0[(1, j, i)] = rho * u;
+                self.sys.0[(2, j, i)] = rho * v;
+                self.sys.0[(3, j, i)] = e;
+            }
+        }
+    }
+
+    pub fn field(&self) -> &Field {
+        &self.sys.0
+    }
+}
+
+impl<UO: UpwindOperator> System<UO> {
+    pub fn advance_upwind(&mut self, dt: f32) {
+        integrate::rk4(
+            RHS_upwind,
+            &self.sys.0,
+            &mut self.sys.1,
+            dt,
+            &self.grid,
+            &mut self.wb.k,
+            &mut self.wb.tmp,
+        );
+        std::mem::swap(&mut self.sys.0, &mut self.sys.1);
+    }
+}
+
+#[derive(Clone, Debug)]
+/// A 4 x ny x nx array
+pub struct Field(pub(crate) Array3<f32>);
+
+impl std::ops::Deref for Field {
+    type Target = Array3<f32>;
+    fn deref(&self) -> &Self::Target {
+        &self.0
+    }
+}
+
+impl std::ops::DerefMut for Field {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        &mut self.0
+    }
+}
+
+impl Field {
+    pub fn new(ny: usize, nx: usize) -> Self {
+        let field = Array3::zeros((4, ny, nx));
+
+        Self(field)
+    }
+
+    pub fn nx(&self) -> usize {
+        self.0.shape()[2]
+    }
+    pub fn ny(&self) -> usize {
+        self.0.shape()[1]
+    }
+
+    pub fn rho(&self) -> ArrayView2<f32> {
+        self.slice(s![0, .., ..])
+    }
+    pub fn rhou(&self) -> ArrayView2<f32> {
+        self.slice(s![1, .., ..])
+    }
+    pub fn rhov(&self) -> ArrayView2<f32> {
+        self.slice(s![2, .., ..])
+    }
+    pub fn e(&self) -> ArrayView2<f32> {
+        self.slice(s![3, .., ..])
+    }
+
+    pub fn rho_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![0, .., ..])
+    }
+    pub fn rhou_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![1, .., ..])
+    }
+    pub fn rhov_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![2, .., ..])
+    }
+    pub fn e_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![3, .., ..])
+    }
+
+    #[allow(unused)]
+    pub fn components(
+        &self,
+    ) -> (
+        ArrayView2<f32>,
+        ArrayView2<f32>,
+        ArrayView2<f32>,
+        ArrayView2<f32>,
+    ) {
+        (self.rho(), self.rhou(), self.rhov(), self.e())
+    }
+    #[allow(unused)]
+    pub fn components_mut(
+        &mut self,
+    ) -> (
+        ArrayViewMut2<f32>,
+        ArrayViewMut2<f32>,
+        ArrayViewMut2<f32>,
+        ArrayViewMut2<f32>,
+    ) {
+        let mut iter = self.0.outer_iter_mut();
+
+        let rho = iter.next().unwrap();
+        let rhou = iter.next().unwrap();
+        let rhov = iter.next().unwrap();
+        let e = iter.next().unwrap();
+        assert_eq!(iter.next(), None);
+
+        (rho, rhou, rhov, e)
+    }
+
+    fn north(&self) -> ArrayView2<f32> {
+        self.slice(s![.., self.ny() - 1, ..])
+    }
+    fn south(&self) -> ArrayView2<f32> {
+        self.slice(s![.., 0, ..])
+    }
+    fn east(&self) -> ArrayView2<f32> {
+        self.slice(s![.., .., self.nx() - 1])
+    }
+    fn west(&self) -> ArrayView2<f32> {
+        self.slice(s![.., .., 0])
+    }
+    fn north_mut(&mut self) -> ArrayViewMut2<f32> {
+        let ny = self.ny();
+        self.slice_mut(s![.., ny - 1, ..])
+    }
+    fn south_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![.., 0, ..])
+    }
+    fn east_mut(&mut self) -> ArrayViewMut2<f32> {
+        let nx = self.nx();
+        self.slice_mut(s![.., .., nx - 1])
+    }
+    fn west_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![.., .., 0])
+    }
+}
+
+fn pressure(gamma: f32, rho: f32, rhou: f32, rhov: f32, e: f32) -> f32 {
+    (gamma - 1.0) * (e - (rhou * rhou + rhov * rhov) / (2.0 * rho))
+}
+
+#[allow(non_snake_case)]
+pub(crate) fn RHS_trad<SBP: SbpOperator>(
+    k: &mut Field,
+    y: &Field,
+    grid: &Grid<SBP>,
+    tmp: &mut (Field, Field, Field, Field, Field, Field),
+) {
+    let ehat = &mut tmp.0;
+    let fhat = &mut tmp.1;
+    fluxes((ehat, fhat), y, grid);
+    let dE = &mut tmp.2;
+    let dF = &mut tmp.3;
+
+    SBP::diffxi(ehat.rho(), dE.rho_mut());
+    SBP::diffxi(ehat.rhou(), dE.rhou_mut());
+    SBP::diffxi(ehat.rhov(), dE.rhov_mut());
+    SBP::diffxi(ehat.e(), dE.e_mut());
+
+    SBP::diffeta(fhat.rho(), dF.rho_mut());
+    SBP::diffeta(fhat.rhou(), dF.rhou_mut());
+    SBP::diffeta(fhat.rhov(), dF.rhov_mut());
+    SBP::diffeta(fhat.e(), dF.e_mut());
+
+    azip!((out in &mut k.0,
+                    eflux in &dE.0,
+                    fflux in &dF.0,
+                    detj in &grid.detj.broadcast((4, y.ny(), y.nx())).unwrap()) {
+        *out = (-eflux - fflux)/detj
+    });
+
+    let boundaries = BoundaryTerms {
+        north: Boundary::This,
+        south: Boundary::This,
+        west: Boundary::This,
+        east: Boundary::This,
+    };
+
+    SAT_characteristics(k, y, grid, &boundaries);
+}
+
+#[allow(non_snake_case)]
+pub(crate) fn RHS_upwind<UO: UpwindOperator>(
+    k: &mut Field,
+    y: &Field,
+    grid: &Grid<UO>,
+    tmp: &mut (Field, Field, Field, Field, Field, Field),
+) {
+    let ehat = &mut tmp.0;
+    let fhat = &mut tmp.1;
+    fluxes((ehat, fhat), y, grid);
+    let dE = &mut tmp.2;
+    let dF = &mut tmp.3;
+
+    UO::diffxi(ehat.rho(), dE.rho_mut());
+    UO::diffxi(ehat.rhou(), dE.rhou_mut());
+    UO::diffxi(ehat.rhov(), dE.rhov_mut());
+    UO::diffxi(ehat.e(), dE.e_mut());
+
+    UO::diffeta(fhat.rho(), dF.rho_mut());
+    UO::diffeta(fhat.rhou(), dF.rhou_mut());
+    UO::diffeta(fhat.rhov(), dF.rhov_mut());
+    UO::diffeta(fhat.e(), dF.e_mut());
+
+    let ad_xi = &mut tmp.4;
+    let ad_eta = &mut tmp.5;
+    upwind_dissipation((ad_xi, ad_eta), y, grid, (&mut tmp.0, &mut tmp.1));
+
+    azip!((out in &mut k.0,
+                    eflux in &dE.0,
+                    fflux in &dF.0,
+                    ad_xi in &ad_xi.0,
+                    ad_eta in &ad_eta.0,
+                    detj in &grid.detj.broadcast((4, y.ny(), y.nx())).unwrap()) {
+        *out = (-eflux - fflux + ad_xi + ad_eta)/detj
+    });
+
+    let boundaries = BoundaryTerms {
+        north: Boundary::This,
+        south: Boundary::This,
+        west: Boundary::This,
+        east: Boundary::This,
+    };
+    SAT_characteristics(k, y, grid, &boundaries);
+}
+
+#[allow(clippy::many_single_char_names)]
+fn upwind_dissipation<UO: UpwindOperator>(
+    k: (&mut Field, &mut Field),
+    y: &Field,
+    grid: &Grid<UO>,
+    tmp: (&mut Field, &mut Field),
+) {
+    let n = y.nx() * y.ny();
+    let yview = y.view().into_shape((4, n)).unwrap();
+    let mut tmp0 = tmp.0.view_mut().into_shape((4, n)).unwrap();
+    let mut tmp1 = tmp.1.view_mut().into_shape((4, n)).unwrap();
+
+    for (
+        ((((((y, mut tmp0), mut tmp1), detj), detj_dxi_dx), detj_dxi_dy), detj_deta_dx),
+        detj_deta_dy,
+    ) in yview
+        .axis_iter(ndarray::Axis(1))
+        .zip(tmp0.axis_iter_mut(ndarray::Axis(1)))
+        .zip(tmp1.axis_iter_mut(ndarray::Axis(1)))
+        .zip(grid.detj.iter())
+        .zip(grid.detj_dxi_dx.iter())
+        .zip(grid.detj_dxi_dy.iter())
+        .zip(grid.detj_deta_dx.iter())
+        .zip(grid.detj_deta_dy.iter())
+    {
+        let rho = y[0];
+        assert!(rho > 0.0);
+        let rhou = y[1];
+        let rhov = y[2];
+        let e = y[3];
+
+        let u = rhou / rho;
+        let v = rhov / rho;
+
+        let uhat = detj_dxi_dx / detj * u + detj_dxi_dy / detj * v;
+        let vhat = detj_deta_dx / detj * u + detj_deta_dy / detj * v;
+
+        let p = pressure(GAMMA, rho, rhou, rhov, e);
+        assert!(p > 0.0);
+        let c = (GAMMA * p / rho).sqrt();
+
+        let alpha_u = uhat.abs() + c;
+        let alpha_v = vhat.abs() + c;
+
+        tmp0[0] = alpha_u * rho * detj;
+        tmp1[0] = alpha_v * rho * detj;
+
+        tmp0[1] = alpha_u * rhou * detj;
+        tmp1[1] = alpha_v * rhou * detj;
+
+        tmp0[2] = alpha_u * rhov * detj;
+        tmp1[2] = alpha_v * rhov * detj;
+
+        tmp0[3] = alpha_u * e * detj;
+        tmp1[3] = alpha_v * e * detj;
+    }
+
+    UO::dissxi(tmp.0.rho(), k.0.rho_mut());
+    UO::dissxi(tmp.0.rhou(), k.0.rhou_mut());
+    UO::dissxi(tmp.0.rhov(), k.0.rhov_mut());
+    UO::dissxi(tmp.0.e(), k.0.e_mut());
+
+    UO::disseta(tmp.1.rho(), k.1.rho_mut());
+    UO::disseta(tmp.1.rhou(), k.1.rhou_mut());
+    UO::disseta(tmp.1.rhov(), k.1.rhov_mut());
+    UO::disseta(tmp.1.e(), k.1.e_mut());
+}
+
+fn fluxes<SBP: SbpOperator>(k: (&mut Field, &mut Field), y: &Field, grid: &Grid<SBP>) {
+    let j_dxi_dx = grid.detj_dxi_dx.view();
+    let j_dxi_dy = grid.detj_dxi_dy.view();
+    let j_deta_dx = grid.detj_deta_dx.view();
+    let j_deta_dy = grid.detj_deta_dy.view();
+
+    let rho = y.rho();
+    let rhou = y.rhou();
+    let rhov = y.rhov();
+    let e = y.e();
+
+    for j in 0..y.ny() {
+        for i in 0..y.nx() {
+            let rho = rho[(j, i)];
+            assert!(rho > 0.0);
+            let rhou = rhou[(j, i)];
+            let rhov = rhov[(j, i)];
+            let e = e[(j, i)];
+            let p = pressure(GAMMA, rho, rhou, rhov, e);
+
+            assert!(p > 0.0);
+
+            let ef = [
+                rhou,
+                rhou * rhou / rho + p,
+                rhou * rhov / rho,
+                rhou * (e + p) / rho,
+            ];
+            let ff = [
+                rhov,
+                rhou * rhov / rho,
+                rhov * rhov / rho + p,
+                rhov * (e + p) / rho,
+            ];
+
+            for comp in 0..4 {
+                let eflux = j_dxi_dx[(j, i)] * ef[comp] + j_dxi_dy[(j, i)] * ff[comp];
+                let fflux = j_deta_dx[(j, i)] * ef[comp] + j_deta_dy[(j, i)] * ff[comp];
+
+                k.0[(comp, j, i)] = eflux;
+                k.1[(comp, j, i)] = fflux;
+            }
+        }
+    }
+}
+
+#[derive(Clone, Debug)]
+pub enum Boundary {
+    This,
+}
+
+#[derive(Clone, Debug)]
+pub struct BoundaryTerms {
+    pub north: Boundary,
+    pub south: Boundary,
+    pub east: Boundary,
+    pub west: Boundary,
+}
+
+#[allow(non_snake_case)]
+/// Boundary conditions (SAT)
+fn SAT_characteristics<SBP: SbpOperator>(
+    k: &mut Field,
+    y: &Field,
+    grid: &Grid<SBP>,
+    _boundaries: &BoundaryTerms,
+) {
+    /* // Whean using infinite boundaries, use this...
+    let steady_v = [1.0, 1.0, 0.0, {
+        let M = 0.1;
+        let p_inf = 1.0 / (GAMMA * M * M);
+        p_inf / (GAMMA - 1.0) + 0.5
+    }];
+    let steady_a = ndarray::Array1::from(steady_v.to_vec());
+    let steady = steady_a.broadcast((k.nx(), 4)).unwrap().reversed_axes();
+    assert_eq!(steady.shape(), [4, k.nx()]);
+    */
+    // North boundary
+    {
+        let hi = (k.ny() - 1) as f32 * SBP::h()[0];
+        let sign = -1.0;
+        let tau = 1.0;
+        let slice = s![y.ny() - 1, ..];
+        SAT_characteristic(
+            k.north_mut(),
+            y.north(),
+            y.south(), // Self South
+            //steady.view(),
+            hi,
+            sign,
+            tau,
+            grid.detj.slice(slice),
+            grid.detj_deta_dx.slice(slice),
+            grid.detj_deta_dy.slice(slice),
+        );
+    }
+    // South boundary
+    {
+        let hi = (k.ny() - 1) as f32 * SBP::h()[0];
+        let sign = 1.0;
+        let tau = -1.0;
+        let slice = s![0, ..];
+        SAT_characteristic(
+            k.south_mut(),
+            y.south(),
+            y.north(), // Self North
+            //steady.view(),
+            hi,
+            sign,
+            tau,
+            grid.detj.slice(slice),
+            grid.detj_deta_dx.slice(slice),
+            grid.detj_deta_dy.slice(slice),
+        );
+    }
+    /*let steady = ndarray::Array2::from_shape_fn((4, k.ny()), |(k, _)| match k {
+        0 => 1.0,
+        1 => 1.0,
+        2 => 0.0,
+        3 => {
+            let M = 0.1;
+            let p_inf = 1.0 / (GAMMA * M * M);
+            p_inf / (GAMMA - 1.0) + 0.5
+        }
+        _ => unreachable!(),
+    });*/
+    // West Boundary
+    {
+        let hi = (k.nx() - 1) as f32 * SBP::h()[0];
+        let sign = 1.0;
+        let tau = -1.0;
+        let slice = s![.., 0];
+        SAT_characteristic(
+            k.west_mut(),
+            y.west(),
+            y.east(), // Self East
+            //steady.view(),
+            hi,
+            sign,
+            tau,
+            grid.detj.slice(slice),
+            grid.detj_dxi_dx.slice(slice),
+            grid.detj_dxi_dy.slice(slice),
+        );
+    }
+    // East Boundary
+    {
+        let hi = (k.nx() - 1) as f32 * SBP::h()[0];
+        let sign = -1.0;
+        let tau = 1.0;
+        let slice = s![.., y.nx() - 1];
+        SAT_characteristic(
+            k.east_mut(),
+            y.east(),
+            y.west(), // Self West
+            //steady.view(),
+            hi,
+            sign,
+            tau,
+            grid.detj.slice(slice),
+            grid.detj_dxi_dx.slice(slice),
+            grid.detj_dxi_dy.slice(slice),
+        );
+    }
+}
+
+#[allow(non_snake_case)]
+#[allow(clippy::many_single_char_names)]
+#[allow(clippy::too_many_arguments)]
+/// Boundary conditions (SAT)
+fn SAT_characteristic(
+    mut k: ArrayViewMut2<f32>,
+    y: ArrayView2<f32>,
+    z: ArrayView2<f32>, // Size 4 x n (all components in line)
+    hi: f32,
+    sign: f32,
+    tau: f32,
+    detj: ArrayView1<f32>,
+    detj_d_dx: ArrayView1<f32>,
+    detj_d_dy: ArrayView1<f32>,
+) {
+    assert_eq!(detj.shape(), detj_d_dx.shape());
+    assert_eq!(detj.shape(), detj_d_dy.shape());
+    assert_eq!(y.shape(), z.shape());
+    assert_eq!(y.shape()[0], 4);
+    assert_eq!(y.shape()[1], detj.shape()[0]);
+
+    for (((((mut k, y), z), detj), detj_d_dx), detj_d_dy) in k
+        .axis_iter_mut(ndarray::Axis(1))
+        .zip(y.axis_iter(ndarray::Axis(1)))
+        .zip(z.axis_iter(ndarray::Axis(1)))
+        .zip(detj.iter())
+        .zip(detj_d_dx.iter())
+        .zip(detj_d_dy.iter())
+    {
+        let rho = y[0];
+        let rhou = y[1];
+        let rhov = y[2];
+        let e = y[3];
+
+        let kx_ = detj_d_dx / detj;
+        let ky_ = detj_d_dy / detj;
+
+        let (kx, ky) = {
+            let r = f32::hypot(kx_, ky_);
+            (kx_ / r, ky_ / r)
+        };
+
+        let u = rhou / rho;
+        let v = rhov / rho;
+
+        let theta = kx * u + ky * v;
+
+        let p = pressure(GAMMA, rho, rhou, rhov, e);
+        let c = (GAMMA * p / rho).sqrt();
+        let phi2 = (GAMMA - 1.0) * (u * u + v * v) / 2.0;
+
+        let phi2_c2 = (phi2 + c * c) / (GAMMA - 1.0);
+
+        let T = [
+            [1.0, 0.0, 1.0, 1.0],
+            [u, ky, u + kx * c, u - kx * c],
+            [v, -kx, v + ky * c, v - ky * c],
+            [
+                phi2 / (GAMMA - 1.0),
+                ky * u - kx * v,
+                phi2_c2 + c * theta,
+                phi2_c2 - c * theta,
+            ],
+        ];
+        let U = kx_ * u + ky_ * v;
+        let L = [
+            U,
+            U,
+            U + c * f32::hypot(kx_, ky_),
+            U - c * f32::hypot(kx_, ky_),
+        ];
+        let beta = 1.0 / (2.0 * c * c);
+        let TI = [
+            [
+                1.0 - phi2 / (c * c),
+                (GAMMA - 1.0) * u / (c * c),
+                (GAMMA - 1.0) * v / (c * c),
+                -(GAMMA - 1.0) / (c * c),
+            ],
+            [-(ky * u - kx * v), ky, -kx, 0.0],
+            [
+                beta * (phi2 - c * theta),
+                beta * (kx * c - (GAMMA - 1.0) * u),
+                beta * (ky * c - (GAMMA - 1.0) * v),
+                beta * (GAMMA - 1.0),
+            ],
+            [
+                beta * (phi2 + c * theta),
+                -beta * (kx * c + (GAMMA - 1.0) * u),
+                -beta * (ky * c + (GAMMA - 1.0) * v),
+                beta * (GAMMA - 1.0),
+            ],
+        ];
+
+        let res = [rho - z[0], rhou - z[1], rhov - z[2], e - z[3]];
+        let mut TIres = [0.0; 4];
+        #[allow(clippy::needless_range_loop)]
+        for row in 0..4 {
+            for col in 0..4 {
+                TIres[row] += TI[row][col] * res[col];
+            }
+        }
+
+        // L + sign(abs(L)) * TIres
+        let mut LTIres = [0.0; 4];
+        for row in 0..4 {
+            LTIres[row] = (L[row] + sign * L[row].abs()) * TIres[row];
+        }
+
+        // T*LTIres
+        let mut TLTIres = [0.0; 4];
+        #[allow(clippy::needless_range_loop)]
+        for row in 0..4 {
+            for col in 0..4 {
+                TLTIres[row] += T[row][col] * LTIres[col];
+            }
+        }
+
+        for comp in 0..4 {
+            k[comp] += hi * tau * TLTIres[comp];
+        }
+    }
+}
+
+pub struct WorkBuffers {
+    k: [Field; 4],
+    tmp: (Field, Field, Field, Field, Field, Field),
+}
+
+impl WorkBuffers {
+    pub fn new(nx: usize, ny: usize) -> Self {
+        let arr3 = Field::new(nx, ny);
+        Self {
+            k: [arr3.clone(), arr3.clone(), arr3.clone(), arr3.clone()],
+            tmp: (
+                arr3.clone(),
+                arr3.clone(),
+                arr3.clone(),
+                arr3.clone(),
+                arr3.clone(),
+                arr3,
+            ),
+        }
+    }
+}

sbp/src/grid.rs

@@ -0,0 +1,75 @@
+use ndarray::Array2;
+
+#[derive(Debug, Clone)]
+pub struct Grid<SBP>
+where
+    SBP: super::operators::SbpOperator,
+{
+    pub(crate) x: Array2<f32>,
+    pub(crate) y: Array2<f32>,
+
+    pub(crate) detj: Array2<f32>,
+    pub(crate) detj_dxi_dx: Array2<f32>,
+    pub(crate) detj_dxi_dy: Array2<f32>,
+    pub(crate) detj_deta_dx: Array2<f32>,
+    pub(crate) detj_deta_dy: Array2<f32>,
+
+    operator: std::marker::PhantomData<SBP>,
+}
+
+impl<SBP: super::operators::SbpOperator> Grid<SBP> {
+    pub fn new(x: Array2<f32>, y: Array2<f32>) -> Result<Self, ndarray::ShapeError> {
+        assert_eq!(x.shape(), y.shape());
+        let ny = x.shape()[0];
+        let nx = x.shape()[1];
+
+        let mut dx_dxi = Array2::zeros((ny, nx));
+        SBP::diffxi(x.view(), dx_dxi.view_mut());
+        let mut dx_deta = Array2::zeros((ny, nx));
+        SBP::diffeta(x.view(), dx_deta.view_mut());
+        let mut dy_dxi = Array2::zeros((ny, nx));
+        SBP::diffxi(y.view(), dy_dxi.view_mut());
+        let mut dy_deta = Array2::zeros((ny, nx));
+        SBP::diffeta(y.view(), dy_deta.view_mut());
+
+        let mut detj = Array2::zeros((ny, nx));
+        ndarray::azip!((detj in &mut detj,
+                        &dx_dxi in &dx_dxi,
+                        &dx_deta in &dx_deta,
+                        &dy_dxi in &dy_dxi,
+                        &dy_deta in &dy_deta) {
+            *detj = dx_dxi * dy_deta - dx_deta * dy_dxi;
+            assert!(*detj > 0.0);
+        });
+
+        let detj_dxi_dx = dy_deta;
+        let detj_dxi_dy = {
+            let mut dx_deta = dx_deta;
+            dx_deta.mapv_inplace(|v| -v);
+            dx_deta
+        };
+        let detj_deta_dx = {
+            let mut dy_dxi = dy_dxi;
+            dy_dxi.mapv_inplace(|v| -v);
+            dy_dxi
+        };
+        let detj_deta_dy = dx_dxi;
+
+        Ok(Self {
+            x,
+            y,
+            detj,
+            detj_dxi_dx,
+            detj_dxi_dy,
+            detj_deta_dx,
+            detj_deta_dy,
+            operator: std::marker::PhantomData,
+        })
+    }
+    pub fn nx(&self) -> usize {
+        self.x.shape()[1]
+    }
+    pub fn ny(&self) -> usize {
+        self.x.shape()[0]
+    }
+}

sbp/src/integrate.rs

@@ -0,0 +1,46 @@
+use super::grid::Grid;
+use super::operators::SbpOperator;
+use ndarray::{Array3, Zip};
+
+pub(crate) fn rk4<'a, F: 'a, SBP, RHS, WB>(
+    rhs: RHS,
+    prev: &F,
+    fut: &mut F,
+    dt: f32,
+    grid: &Grid<SBP>,
+    k: &mut [F; 4],
+    mut wb: &mut WB,
+) where
+    F: std::ops::Deref<Target = Array3<f32>> + std::ops::DerefMut<Target = Array3<f32>>,
+    SBP: SbpOperator,
+    RHS: Fn(&mut F, &F, &Grid<SBP>, &mut WB),
+{
+    assert_eq!(prev.shape(), fut.shape());
+
+    for i in 0..4 {
+        // y = y0 + c*kn
+        fut.assign(prev);
+        match i {
+            0 => {}
+            1 | 2 => {
+                fut.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
+            }
+            3 => {
+                fut.scaled_add(dt, &k[i - 1]);
+            }
+            _ => {
+                unreachable!();
+            }
+        };
+
+        rhs(&mut k[i], &fut, grid, &mut wb);
+    }
+
+    Zip::from(&mut **fut)
+        .and(&**prev)
+        .and(&*k[0])
+        .and(&*k[1])
+        .and(&*k[2])
+        .and(&*k[3])
+        .apply(|y1, &y0, &k1, &k2, &k3, &k4| *y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4));
+}

sbp/src/lib.rs

@@ -0,0 +1,5 @@
+pub mod euler;
+pub mod grid;
+pub mod integrate;
+pub mod maxwell;
+pub mod operators;

sbp/src/maxwell.rs

@@ -0,0 +1,575 @@
+use super::grid::Grid;
+use super::integrate;
+use super::operators::{SbpOperator, UpwindOperator};
+use ndarray::azip;
+use ndarray::prelude::*;
+
+#[derive(Clone, Debug)]
+pub struct Field(pub(crate) Array3<f32>);
+
+impl std::ops::Deref for Field {
+    type Target = Array3<f32>;
+    fn deref(&self) -> &Self::Target {
+        &self.0
+    }
+}
+
+impl std::ops::DerefMut for Field {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        &mut self.0
+    }
+}
+
+impl Field {
+    pub fn new(height: usize, width: usize) -> Self {
+        let field = Array3::zeros((3, height, width));
+
+        Self(field)
+    }
+
+    pub fn nx(&self) -> usize {
+        self.0.shape()[2]
+    }
+    pub fn ny(&self) -> usize {
+        self.0.shape()[1]
+    }
+
+    pub fn ex(&self) -> ArrayView2<f32> {
+        self.slice(s![0, .., ..])
+    }
+    pub fn hz(&self) -> ArrayView2<f32> {
+        self.slice(s![1, .., ..])
+    }
+    pub fn ey(&self) -> ArrayView2<f32> {
+        self.slice(s![2, .., ..])
+    }
+
+    pub fn ex_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![0, .., ..])
+    }
+    pub fn hz_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![1, .., ..])
+    }
+    pub fn ey_mut(&mut self) -> ArrayViewMut2<f32> {
+        self.slice_mut(s![2, .., ..])
+    }
+
+    pub fn components_mut(
+        &mut self,
+    ) -> (ArrayViewMut2<f32>, ArrayViewMut2<f32>, ArrayViewMut2<f32>) {
+        let mut iter = self.0.outer_iter_mut();
+
+        let ex = iter.next().unwrap();
+        let hz = iter.next().unwrap();
+        let ey = iter.next().unwrap();
+        assert_eq!(iter.next(), None);
+
+        (ex, hz, ey)
+    }
+}
+
+#[derive(Debug, Clone)]
+pub struct System<SBP: SbpOperator> {
+    sys: (Field, Field),
+    wb: WorkBuffers,
+    grid: Grid<SBP>,
+}
+
+impl<SBP: SbpOperator> System<SBP> {
+    pub fn new(x: Array2<f32>, y: Array2<f32>) -> Self {
+        assert_eq!(x.shape(), y.shape());
+        let ny = x.shape()[0];
+        let nx = x.shape()[1];
+
+        let grid = Grid::new(x, y).unwrap();
+
+        Self {
+            sys: (Field::new(ny, nx), Field::new(ny, nx)),
+            grid,
+            wb: WorkBuffers::new(ny, nx),
+        }
+    }
+
+    pub fn field(&self) -> &Field {
+        &self.sys.0
+    }
+
+    pub fn set_gaussian(&mut self, x0: f32, y0: f32) {
+        let (ex, hz, ey) = self.sys.0.components_mut();
+        ndarray::azip!(
+            (ex in ex, hz in hz, ey in ey,
+             &x in &self.grid.x, &y in &self.grid.y)
+        {
+            *ex = 0.0;
+            *ey = 0.0;
+            *hz = gaussian(x, x0, y, y0)/32.0;
+        });
+    }
+
+    pub fn advance(&mut self, dt: f32) {
+        integrate::rk4(
+            RHS,
+            &self.sys.0,
+            &mut self.sys.1,
+            dt,
+            &self.grid,
+            &mut self.wb.k,
+            &mut self.wb.tmp,
+        );
+        std::mem::swap(&mut self.sys.0, &mut self.sys.1);
+    }
+}
+
+impl<UO: UpwindOperator> System<UO> {
+    /// Using artificial dissipation with the upwind operator
+    pub fn advance_upwind(&mut self, dt: f32) {
+        integrate::rk4(
+            RHS_upwind,
+            &self.sys.0,
+            &mut self.sys.1,
+            dt,
+            &self.grid,
+            &mut self.wb.k,
+            &mut self.wb.tmp,
+        );
+        std::mem::swap(&mut self.sys.0, &mut self.sys.1);
+    }
+}
+
+fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 {
+    use std::f32;
+    let x = x - x0;
+    let y = y - y0;
+
+    let sigma = 0.05;
+
+    1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp()
+}
+
+#[allow(non_snake_case)]
+/// Solving (Au)_x + (Bu)_y
+/// with:
+///        A               B
+///  [ 0,  0,  0]    [ 0,  1,  0]
+///  [ 0,  0, -1]    [ 1,  0,  0]
+///  [ 0, -1,  0]    [ 0,  0,  0]
+///
+/// This flux is rotated by the grid metrics
+/// (Au)_x + (Bu)_y = 1/J [
+///          (J xi_x Au)_xi + (J eta_x Au)_eta
+///          (J xi_y Bu)_xi + (J eta_y Bu)_eta
+///      ]
+/// where J is the grid determinant
+///
+/// This is used both in fluxes and SAT terms
+fn RHS<SBP: SbpOperator>(
+    k: &mut Field,
+    y: &Field,
+    grid: &Grid<SBP>,
+    tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
+) {
+    fluxes(k, y, grid, tmp);
+
+    let boundaries = BoundaryTerms {
+        north: Boundary::This,
+        south: Boundary::This,
+        west: Boundary::This,
+        east: Boundary::This,
+    };
+    SAT_characteristics(k, y, grid, &boundaries);
+
+    azip!((k in &mut k.0,
+                    &detj in &grid.detj.broadcast((3, y.ny(), y.nx())).unwrap()) {
+        *k /= detj;
+    });
+}
+
+#[allow(non_snake_case)]
+fn RHS_upwind<UO: UpwindOperator>(
+    k: &mut Field,
+    y: &Field,
+    grid: &Grid<UO>,
+    tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
+) {
+    fluxes(k, y, grid, tmp);
+    dissipation(k, y, grid, tmp);
+
+    let boundaries = BoundaryTerms {
+        north: Boundary::This,
+        south: Boundary::This,
+        west: Boundary::This,
+        east: Boundary::This,
+    };
+    SAT_characteristics(k, y, grid, &boundaries);
+
+    azip!((k in &mut k.0,
+                    &detj in &grid.detj.broadcast((3, y.ny(), y.nx())).unwrap()) {
+        *k /= detj;
+    });
+}
+
+fn fluxes<SBP: SbpOperator>(
+    k: &mut Field,
+    y: &Field,
+    grid: &Grid<SBP>,
+    tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
+) {
+    // ex = hz_y
+    {
+        ndarray::azip!((a in &mut tmp.0,
+                        &dxi_dy in &grid.detj_dxi_dy,
+                        &hz in &y.hz())
+            *a = dxi_dy * hz
+        );
+        SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
+
+        ndarray::azip!((b in &mut tmp.2,
+                        &deta_dy in &grid.detj_deta_dy,
+                        &hz in &y.hz())
+            *b = deta_dy * hz
+        );
+        SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
+
+        ndarray::azip!((flux in &mut k.ex_mut(), &ax in &tmp.1, &by in &tmp.3)
+            *flux = ax + by
+        );
+    }
+
+    {
+        // hz = -ey_x + ex_y
+        ndarray::azip!((a in &mut tmp.0,
+                        &dxi_dx in &grid.detj_dxi_dx,
+                        &dxi_dy in &grid.detj_dxi_dy,
+                        &ex in &y.ex(),
+                        &ey in &y.ey())
+            *a = dxi_dx * -ey + dxi_dy * ex
+        );
+        SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
+
+        ndarray::azip!((b in &mut tmp.2,
+                        &deta_dx in &grid.detj_deta_dx,
+                        &deta_dy in &grid.detj_deta_dy,
+                        &ex in &y.ex(),
+                        &ey in &y.ey())
+            *b = deta_dx * -ey + deta_dy * ex
+        );
+        SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
+
+        ndarray::azip!((flux in &mut k.hz_mut(), &ax in &tmp.1, &by in &tmp.3)
+            *flux = ax + by
+        );
+    }
+
+    // ey = -hz_x
+    {
+        ndarray::azip!((a in &mut tmp.0,
+                        &dxi_dx in &grid.detj_dxi_dx,
+                        &hz in &y.hz())
+            *a = dxi_dx * -hz
+        );
+        SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
+
+        azip!((b in &mut tmp.2,
+                        &deta_dx in &grid.detj_deta_dx,
+                        &hz in &y.hz())
+            *b = deta_dx * -hz
+        );
+        SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
+
+        azip!((flux in &mut k.ey_mut(), &ax in &tmp.1, &by in &tmp.3)
+            *flux = ax + by
+        );
+    }
+}
+
+fn dissipation<UO: UpwindOperator>(
+    k: &mut Field,
+    y: &Field,
+    grid: &Grid<UO>,
+    tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
+) {
+    // ex component
+    {
+        ndarray::azip!((a in &mut tmp.0,
+                        &kx in &grid.detj_dxi_dx,
+                        &ky in &grid.detj_dxi_dy,
+                        &ex in &y.ex(),
+                        &ey in &y.ey()) {
+            let r = f32::hypot(kx, ky);
+            *a = ky*ky/r * ex + -kx*ky/r*ey;
+        });
+        UO::dissxi(tmp.0.view(), tmp.1.view_mut());
+
+        ndarray::azip!((b in &mut tmp.2,
+                    &kx in &grid.detj_deta_dx,
+                    &ky in &grid.detj_deta_dy,
+                    &ex in &y.ex(),
+                    &ey in &y.ey()) {
+            let r = f32::hypot(kx, ky);
+            *b = ky*ky/r * ex + -kx*ky/r*ey;
+        });
+        UO::disseta(tmp.2.view(), tmp.3.view_mut());
+
+        ndarray::azip!((flux in &mut k.ex_mut(), &ax in &tmp.1, &by in &tmp.3)
+            *flux += ax + by
+        );
+    }
+
+    // hz component
+    {
+        ndarray::azip!((a in &mut tmp.0,
+                        &kx in &grid.detj_dxi_dx,
+                        &ky in &grid.detj_dxi_dy,
+                        &hz in &y.hz()) {
+            let r = f32::hypot(kx, ky);
+            *a = r * hz;
+        });
+        UO::dissxi(tmp.0.view(), tmp.1.view_mut());
+
+        ndarray::azip!((b in &mut tmp.2,
+                        &kx in &grid.detj_deta_dx,
+                        &ky in &grid.detj_deta_dy,
+                        &hz in &y.hz()) {
+            let r = f32::hypot(kx, ky);
+            *b = r * hz;
+        });
+        UO::disseta(tmp.2.view(), tmp.3.view_mut());
+
+        ndarray::azip!((flux in &mut k.hz_mut(), &ax in &tmp.1, &by in &tmp.3)
+            *flux += ax + by
+        );
+    }
+
+    // ey
+    {
+        ndarray::azip!((a in &mut tmp.0,
+                        &kx in &grid.detj_dxi_dx,
+                        &ky in &grid.detj_dxi_dy,
+                        &ex in &y.ex(),
+                        &ey in &y.ey()) {
+            let r = f32::hypot(kx, ky);
+            *a = -kx*ky/r * ex + kx*kx/r*ey;
+        });
+        UO::dissxi(tmp.0.view(), tmp.1.view_mut());
+
+        ndarray::azip!((b in &mut tmp.2,
+                    &kx in &grid.detj_deta_dx,
+                    &ky in &grid.detj_deta_dy,
+                    &ex in &y.ex(),
+                    &ey in &y.ey()) {
+            let r = f32::hypot(kx, ky);
+            *b = -kx*ky/r * ex + kx*kx/r*ey;
+        });
+        UO::disseta(tmp.2.view(), tmp.3.view_mut());
+
+        ndarray::azip!((flux in &mut k.hz_mut(), &ax in &tmp.1, &by in &tmp.3)
+            *flux += ax + by
+        );
+    }
+}
+
+#[derive(Clone, Debug)]
+pub enum Boundary {
+    This,
+}
+
+#[derive(Clone, Debug)]
+pub struct BoundaryTerms {
+    pub north: Boundary,
+    pub south: Boundary,
+    pub east: Boundary,
+    pub west: Boundary,
+}
+
+#[allow(non_snake_case)]
+/// Boundary conditions (SAT)
+fn SAT_characteristics<SBP: SbpOperator>(
+    k: &mut Field,
+    y: &Field,
+    grid: &Grid<SBP>,
+    boundaries: &BoundaryTerms,
+) {
+    let ny = y.ny();
+    let nx = y.nx();
+
+    fn positive_flux(kx: f32, ky: f32) -> [[f32; 3]; 3] {
+        let r = (kx * kx + ky * ky).sqrt();
+        [
+            [ky * ky / r / 2.0, ky / 2.0, -kx * ky / r / 2.0],
+            [ky / 2.0, r / 2.0, -kx / 2.0],
+            [-kx * ky / r / 2.0, -kx / 2.0, kx * kx / r / 2.0],
+        ]
+    }
+    fn negative_flux(kx: f32, ky: f32) -> [[f32; 3]; 3] {
+        let r = (kx * kx + ky * ky).sqrt();
+        [
+            [-ky * ky / r / 2.0, ky / 2.0, kx * ky / r / 2.0],
+            [ky / 2.0, -r / 2.0, -kx / 2.0],
+            [kx * ky / r / 2.0, -kx / 2.0, -kx * kx / r / 2.0],
+        ]
+    }
+
+    {
+        let g = match boundaries.east {
+            Boundary::This => y.slice(s![.., .., 0]),
+        };
+        // East boundary
+        let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
+        for ((((mut k, v), g), &kx), &ky) in k
+            .slice_mut(s![.., .., nx - 1])
+            .gencolumns_mut()
+            .into_iter()
+            .zip(y.slice(s![.., .., nx - 1]).gencolumns())
+            .zip(g.gencolumns())
+            .zip(grid.detj_dxi_dx.slice(s![.., nx - 1]))
+            .zip(grid.detj_dxi_dy.slice(s![.., nx - 1]))
+        {
+            // East boundary, positive flux
+            let tau = -1.0;
+
+            let v = (v[0], v[1], v[2]);
+            let g = (g[0], g[1], g[2]);
+
+            let plus = positive_flux(kx, ky);
+
+            k[0] += tau
+                * hinv
+                * (plus[0][0] * (v.0 - g.0) + plus[0][1] * (v.1 - g.1) + plus[0][2] * (v.2 - g.2));
+            k[1] += tau
+                * hinv
+                * (plus[1][0] * (v.0 - g.0) + plus[1][1] * (v.1 - g.1) + plus[1][2] * (v.2 - g.2));
+            k[2] += tau
+                * hinv
+                * (plus[2][0] * (v.0 - g.0) + plus[2][1] * (v.1 - g.1) + plus[2][2] * (v.2 - g.2));
+        }
+    }
+    {
+        // West boundary, negative flux
+        let g = match boundaries.east {
+            Boundary::This => y.slice(s![.., .., nx - 1]),
+        };
+        let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
+        for ((((mut k, v), g), &kx), &ky) in k
+            .slice_mut(s![.., .., 0])
+            .gencolumns_mut()
+            .into_iter()
+            .zip(y.slice(s![.., .., 0]).gencolumns())
+            .zip(g.gencolumns())
+            .zip(grid.detj_dxi_dx.slice(s![.., 0]))
+            .zip(grid.detj_dxi_dy.slice(s![.., 0]))
+        {
+            let tau = 1.0;
+
+            let v = (v[0], v[1], v[2]);
+            let g = (g[0], g[1], g[2]);
+
+            let minus = negative_flux(kx, ky);
+
+            k[0] += tau
+                * hinv
+                * (minus[0][0] * (v.0 - g.0)
+                    + minus[0][1] * (v.1 - g.1)
+                    + minus[0][2] * (v.2 - g.2));
+            k[1] += tau
+                * hinv
+                * (minus[1][0] * (v.0 - g.0)
+                    + minus[1][1] * (v.1 - g.1)
+                    + minus[1][2] * (v.2 - g.2));
+            k[2] += tau
+                * hinv
+                * (minus[2][0] * (v.0 - g.0)
+                    + minus[2][1] * (v.1 - g.1)
+                    + minus[2][2] * (v.2 - g.2));
+        }
+    }
+
+    {
+        let g = match boundaries.north {
+            Boundary::This => y.slice(s![.., 0, ..]),
+        };
+        let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as f32);
+        for ((((mut k, v), g), &kx), &ky) in k
+            .slice_mut(s![.., ny - 1, ..])
+            .gencolumns_mut()
+            .into_iter()
+            .zip(y.slice(s![.., ny - 1, ..]).gencolumns())
+            .zip(g.gencolumns())
+            .zip(grid.detj_deta_dx.slice(s![ny - 1, ..]))
+            .zip(grid.detj_deta_dy.slice(s![ny - 1, ..]))
+        {
+            // North boundary, positive flux
+            let tau = -1.0;
+            let v = (v[0], v[1], v[2]);
+            let g = (g[0], g[1], g[2]);
+
+            let plus = positive_flux(kx, ky);
+
+            k[0] += tau
+                * hinv
+                * (plus[0][0] * (v.0 - g.0) + plus[0][1] * (v.1 - g.1) + plus[0][2] * (v.2 - g.2));
+            k[1] += tau
+                * hinv
+                * (plus[1][0] * (v.0 - g.0) + plus[1][1] * (v.1 - g.1) + plus[1][2] * (v.2 - g.2));
+            k[2] += tau
+                * hinv
+                * (plus[2][0] * (v.0 - g.0) + plus[2][1] * (v.1 - g.1) + plus[2][2] * (v.2 - g.2));
+        }
+    }
+
+    {
+        let g = match boundaries.south {
+            Boundary::This => y.slice(s![.., ny - 1, ..]),
+        };
+        let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as f32);
+        for ((((mut k, v), g), &kx), &ky) in k
+            .slice_mut(s![.., 0, ..])
+            .gencolumns_mut()
+            .into_iter()
+            .zip(y.slice(s![.., 0, ..]).gencolumns())
+            .zip(g.gencolumns())
+            .zip(grid.detj_deta_dx.slice(s![0, ..]))
+            .zip(grid.detj_deta_dy.slice(s![0, ..]))
+        {
+            // South boundary, negative flux
+
+            let tau = 1.0;
+            let v = (v[0], v[1], v[2]);
+            let g = (g[0], g[1], g[2]);
+
+            let minus = negative_flux(kx, ky);
+
+            k[0] += tau
+                * hinv
+                * (minus[0][0] * (v.0 - g.0)
+                    + minus[0][1] * (v.1 - g.1)
+                    + minus[0][2] * (v.2 - g.2));
+            k[1] += tau
+                * hinv
+                * (minus[1][0] * (v.0 - g.0)
+                    + minus[1][1] * (v.1 - g.1)
+                    + minus[1][2] * (v.2 - g.2));
+            k[2] += tau
+                * hinv
+                * (minus[2][0] * (v.0 - g.0)
+                    + minus[2][1] * (v.1 - g.1)
+                    + minus[2][2] * (v.2 - g.2));
+        }
+    }
+}
+
+#[derive(Clone, Debug)]
+pub struct WorkBuffers {
+    k: [Field; 4],
+    tmp: (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
+}
+
+impl WorkBuffers {
+    pub fn new(ny: usize, nx: usize) -> Self {
+        let arr2 = Array2::zeros((ny, nx));
+        let arr3 = Field::new(ny, nx);
+        Self {
+            k: [arr3.clone(), arr3.clone(), arr3.clone(), arr3],
+            tmp: (arr2.clone(), arr2.clone(), arr2.clone(), arr2),
+        }
+    }
+}

sbp/src/operators.rs

@@ -0,0 +1,78 @@
+#![allow(clippy::excessive_precision)]
+#![allow(clippy::unreadable_literal)]
+
+use ndarray::{ArrayView2, ArrayViewMut2};
+
+pub trait SbpOperator {
+    fn diffxi(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>);
+    fn diffeta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>);
+    fn h() -> &'static [f32];
+}
+
+pub trait UpwindOperator: SbpOperator {
+    fn dissxi(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>);
+    fn disseta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>);
+}
+
+#[macro_export]
+macro_rules! diff_op_1d {
+    ($self: ty, $name: ident, $BLOCK: expr, $DIAG: expr, $symmetric: expr) => {
+        impl $self {
+            fn $name(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
+                assert_eq!(prev.shape(), fut.shape());
+                let nx = prev.shape()[0];
+                assert!(nx >= 2 * $BLOCK.len());
+
+                let dx = 1.0 / (nx - 1) as f32;
+                let idx = 1.0 / dx;
+
+                let block = ::ndarray::arr2($BLOCK);
+                let diag = ::ndarray::arr1($DIAG);
+
+
+                let first_elems = prev.slice(::ndarray::s!(..block.len_of(::ndarray::Axis(1))));
+                for (bl, f) in block.outer_iter().zip(&mut fut) {
+                    let diff = first_elems.dot(&bl);
+                    *f = diff * idx;
+                }
+
+                // The window needs to be aligned to the diagonal elements,
+                // based on the block size
+                let window_elems_to_skip =
+                    block.len_of(::ndarray::Axis(0)) - ((diag.len() - 1) / 2);
+
+                for (window, f) in prev
+                    .windows(diag.len())
+                    .into_iter()
+                    .skip(window_elems_to_skip)
+                    .zip(fut.iter_mut().skip(block.len_of(::ndarray::Axis(0))))
+                    .take(nx - 2 * block.len_of(::ndarray::Axis(0)))
+                {
+                    let diff = diag.dot(&window);
+                    *f = diff * idx;
+                }
+
+                let last_elems = prev.slice(::ndarray::s!(nx - block.len_of(::ndarray::Axis(1))..;-1));
+                for (bl, f) in block.outer_iter()
+                    .zip(&mut fut.slice_mut(s![nx - block.len_of(::ndarray::Axis(0))..;-1]))
+                {
+                    let diff = if $symmetric {
+                        bl.dot(&last_elems)
+                    } else {
+                        -bl.dot(&last_elems)
+                    };
+                    *f = diff * idx;
+                }
+            }
+        }
+    };
+}
+
+mod upwind4;
+pub use upwind4::Upwind4;
+mod upwind9;
+pub use upwind9::Upwind9;
+mod traditional4;
+pub use traditional4::SBP4;
+mod traditional8;
+pub use traditional8::SBP8;

sbp/src/operators/traditional4.rs

@@ -0,0 +1,45 @@
+use super::SbpOperator;
+use crate::diff_op_1d;
+use ndarray::{s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
+
+pub struct SBP4 {}
+
+diff_op_1d!(SBP4, diff_1d, SBP4::BLOCK, SBP4::DIAG, false);
+
+impl SBP4 {
+    #[rustfmt::skip]
+    const HBLOCK: &'static [f32] = &[
+        17.0 / 48.0, 59.0 / 48.0, 43.0 / 48.0, 49.0 / 48.0,
+    ];
+    #[rustfmt::skip]
+    const DIAG: &'static [f32] = &[
+        1.0 / 12.0, -2.0 / 3.0, 0.0, 2.0 / 3.0, -1.0 / 12.0,
+    ];
+    #[rustfmt::skip]
+    const BLOCK: &'static [[f32; 6]] = &[
+        [-1.41176470588235e+00, 1.73529411764706e+00, -2.35294117647059e-01, -8.82352941176471e-02, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-5.00000000000000e-01, 0.00000000000000e+00, 5.00000000000000e-01, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [9.30232558139535e-02, -6.86046511627907e-01, 0.00000000000000e+00, 6.86046511627907e-01, -9.30232558139535e-02, 0.00000000000000e+00],
+        [3.06122448979592e-02, 0.00000000000000e+00, -6.02040816326531e-01, 0.00000000000000e+00, 6.53061224489796e-01, -8.16326530612245e-02],
+    ];
+}
+
+impl SbpOperator for SBP4 {
+    fn diffxi(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Self::BLOCK.len());
+
+        for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+            Self::diff_1d(r0, r1);
+        }
+    }
+
+    fn diffeta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>) {
+        // transpose then use diffxi
+        Self::diffxi(prev.reversed_axes(), fut.reversed_axes());
+    }
+
+    fn h() -> &'static [f32] {
+        Self::HBLOCK
+    }
+}

sbp/src/operators/traditional8.rs

@@ -0,0 +1,49 @@
+use super::SbpOperator;
+use crate::diff_op_1d;
+use ndarray::{s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
+
+pub struct SBP8 {}
+
+diff_op_1d!(SBP8, diff_1d, SBP8::BLOCK, SBP8::DIAG, false);
+
+impl SBP8 {
+    #[rustfmt::skip]
+    const HBLOCK: &'static [f32] = &[
+        2.94890676177879e-01, 1.52572062389771e+00, 2.57452876984127e-01, 1.79811370149912e+00, 4.12708057760141e-01, 1.27848462301587e+00, 9.23295579805997e-01, 1.00933386085916e+00
+    ];
+    #[rustfmt::skip]
+    const DIAG: &'static [f32] = &[
+        3.57142857142857e-03, -3.80952380952381e-02, 2.00000000000000e-01, -8.00000000000000e-01, -0.00000000000000e+00, 8.00000000000000e-01, -2.00000000000000e-01, 3.80952380952381e-02, -3.57142857142857e-03
+    ];
+    #[rustfmt::skip]
+    const BLOCK: &'static [[f32; 12]] = &[
+        [-1.69554360443190e+00, 2.24741246341404e+00, -3.38931922601500e-02, -7.81028168126749e-01, 2.54881486107905e-02, 3.43865227388873e-01, -8.62858162633335e-02, -2.00150583315761e-02, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-4.34378988266985e-01, 0.00000000000000e+00, 9.18511925072956e-02, 4.94008626807984e-01, -2.46151762937235e-02, -1.86759403432935e-01, 5.27267838475813e-02, 7.16696483080115e-03, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [3.88218088704253e-02, -5.44329744454984e-01, 0.00000000000000e+00, 3.89516189693211e-01, 1.36433486528546e-01, 1.03290582800845e-01, -1.79720579323281e-01, 5.59882558852296e-02, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [1.28088632226564e-01, -4.19172130036008e-01, -5.57707021445779e-02, 0.00000000000000e+00, 1.24714160903055e-01, 2.81285212519100e-01, -3.94470423942641e-02, -1.96981310738430e-02, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-1.82119472519009e-02, 9.09986646154550e-02, -8.51090570277506e-02, -5.43362886365301e-01, 0.00000000000000e+00, 6.37392455438558e-01, -1.02950081118829e-01, 2.98964956216039e-02, -8.65364391190110e-03, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-7.93147196245203e-02, 2.22875323171502e-01, -2.07999824391436e-02, -3.95611167748401e-01, -2.05756876210586e-01, 0.00000000000000e+00, 5.45876519966127e-01, -9.42727926638298e-02, 2.97971812952850e-02, -2.79348574643297e-03, 0.00000000000000e+00, 0.00000000000000e+00],
+        [2.75587615266177e-02, -8.71295642560637e-02, 5.01135077563584e-02, 7.68229253600969e-02, 4.60181213406519e-02, -7.55873581663580e-01, 0.00000000000000e+00, 8.21713248844682e-01, -2.16615355227872e-01, 4.12600676624518e-02, -3.86813134335486e-03, 0.00000000000000e+00],
+        [5.84767272160451e-03, -1.08336661209337e-02, -1.42810403117803e-02, 3.50919361287023e-02, -1.22244235731112e-02, 1.19411743193552e-01, -7.51668243727123e-01, 0.00000000000000e+00, 7.92601963555477e-01, -1.98150490888869e-01, 3.77429506454989e-02, -3.53840162301552e-03],
+    ];
+}
+
+impl SbpOperator for SBP8 {
+    fn diffxi(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Self::BLOCK.len());
+
+        for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+            Self::diff_1d(r0, r1);
+        }
+    }
+
+    fn diffeta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>) {
+        // transpose then use diffxi
+        Self::diffxi(prev.reversed_axes(), fut.reversed_axes());
+    }
+
+    fn h() -> &'static [f32] {
+        Self::HBLOCK
+    }
+}

sbp/src/operators/upwind4.rs

@@ -0,0 +1,455 @@
+use super::{SbpOperator, UpwindOperator};
+use crate::diff_op_1d;
+use ndarray::{s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2, Axis};
+
+pub struct Upwind4 {}
+
+/// Simdtype used in diff_simd_col
+type SimdT = packed_simd::f32x8;
+
+diff_op_1d!(Upwind4, diff_1d, Upwind4::BLOCK, Upwind4::DIAG, false);
+diff_op_1d!(
+    Upwind4,
+    diss_1d,
+    Upwind4::DISS_BLOCK,
+    Upwind4::DISS_DIAG,
+    true
+);
+
+macro_rules! diff_simd_row_7_47 {
+    ($self: ident, $name: ident, $BLOCK: expr, $DIAG: expr, $symmetric: expr) => {
+        impl $self {
+            #[inline(never)]
+            fn $name(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
+                use packed_simd::{f32x8, u32x8};
+                assert_eq!(prev.shape(), fut.shape());
+                assert!(prev.len_of(Axis(1)) >= 2 * $BLOCK.len());
+                assert!(prev.len() >= f32x8::lanes());
+                // The prev and fut array must have contigous last dimension
+                assert_eq!(prev.strides()[1], 1);
+                assert_eq!(fut.strides()[1], 1);
+
+                let nx = prev.len_of(Axis(1));
+                let dx = 1.0 / (nx - 1) as f32;
+                let idx = 1.0 / dx;
+
+                for j in 0..prev.len_of(Axis(0)) {
+                    use std::slice;
+                    let prev =
+                        unsafe { slice::from_raw_parts(prev.uget((j, 0)) as *const f32, nx) };
+                    let fut =
+                        unsafe { slice::from_raw_parts_mut(fut.uget_mut((j, 0)) as *mut f32, nx) };
+                    //let mut fut = fut.slice_mut(s![j, ..]);
+
+                    let first_elems = unsafe { f32x8::from_slice_unaligned_unchecked(prev) };
+                    let block = {
+                        let bl = $BLOCK;
+                        [
+                            f32x8::new(
+                                bl[0][0], bl[0][1], bl[0][2], bl[0][3], bl[0][4], bl[0][5],
+                                bl[0][6], 0.0,
+                            ),
+                            f32x8::new(
+                                bl[1][0], bl[1][1], bl[1][2], bl[1][3], bl[1][4], bl[1][5],
+                                bl[1][6], 0.0,
+                            ),
+                            f32x8::new(
+                                bl[2][0], bl[2][1], bl[2][2], bl[2][3], bl[2][4], bl[2][5],
+                                bl[2][6], 0.0,
+                            ),
+                            f32x8::new(
+                                bl[3][0], bl[3][1], bl[3][2], bl[3][3], bl[3][4], bl[3][5],
+                                bl[3][6], 0.0,
+                            ),
+                        ]
+                    };
+                    fut[0] = idx * (block[0] * first_elems).sum();
+                    fut[1] = idx * (block[1] * first_elems).sum();
+                    fut[2] = idx * (block[2] * first_elems).sum();
+                    fut[3] = idx * (block[3] * first_elems).sum();
+
+                    let diag = {
+                        let diag = $DIAG;
+                        f32x8::new(
+                            diag[0], diag[1], diag[2], diag[3], diag[4], diag[5], diag[6], 0.0,
+                        )
+                    };
+                    for (f, p) in fut
+                        .iter_mut()
+                        .skip(block.len())
+                        .zip(
+                            prev.windows(f32x8::lanes())
+                                .map(f32x8::from_slice_unaligned)
+                                .skip(1),
+                        )
+                        .take(nx - 2 * block.len())
+                    {
+                        *f = idx * (p * diag).sum();
+                    }
+
+                    let last_elems =
+                        unsafe { f32x8::from_slice_unaligned_unchecked(&prev[nx - 8..]) }
+                            .shuffle1_dyn(u32x8::new(7, 6, 5, 4, 3, 2, 1, 0));
+                    if $symmetric {
+                        fut[nx - 4] = idx * (block[3] * last_elems).sum();
+                        fut[nx - 3] = idx * (block[2] * last_elems).sum();
+                        fut[nx - 2] = idx * (block[1] * last_elems).sum();
+                        fut[nx - 1] = idx * (block[0] * last_elems).sum();
+                    } else {
+                        fut[nx - 4] = -idx * (block[3] * last_elems).sum();
+                        fut[nx - 3] = -idx * (block[2] * last_elems).sum();
+                        fut[nx - 2] = -idx * (block[1] * last_elems).sum();
+                        fut[nx - 1] = -idx * (block[0] * last_elems).sum();
+                    }
+                }
+            }
+        }
+    };
+}
+
+diff_simd_row_7_47!(Upwind4, diff_simd_row, Upwind4::BLOCK, Upwind4::DIAG, false);
+diff_simd_row_7_47!(
+    Upwind4,
+    diss_simd_row,
+    Upwind4::DISS_BLOCK,
+    Upwind4::DISS_DIAG,
+    true
+);
+
+macro_rules! diff_simd_col_7_47 {
+    ($self: ident, $name: ident, $BLOCK: expr, $DIAG: expr, $symmetric: expr) => {
+        impl $self {
+            #[inline(never)]
+            fn $name(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
+                use std::slice;
+                assert_eq!(prev.shape(), fut.shape());
+                assert_eq!(prev.stride_of(Axis(0)), 1);
+                assert_eq!(prev.stride_of(Axis(0)), 1);
+                let ny = prev.len_of(Axis(0));
+                let nx = prev.len_of(Axis(1));
+                assert!(nx >= 2 * $BLOCK.len());
+                assert!(ny >= SimdT::lanes());
+                assert!(ny % SimdT::lanes() == 0);
+
+                let dx = 1.0 / (nx - 1) as f32;
+                let idx = 1.0 / dx;
+
+                for j in (0..ny).step_by(SimdT::lanes()) {
+                    let a = unsafe {
+                        [
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, 0)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, 1)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, 2)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, 3)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, 4)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, 5)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, 6)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                        ]
+                    };
+
+                    for (i, bl) in $BLOCK.iter().enumerate() {
+                        let b = idx
+                            * (a[0] * bl[0]
+                                + a[1] * bl[1]
+                                + a[2] * bl[2]
+                                + a[3] * bl[3]
+                                + a[4] * bl[4]
+                                + a[5] * bl[5]
+                                + a[6] * bl[6]);
+                        unsafe {
+                            b.write_to_slice_unaligned(slice::from_raw_parts_mut(
+                                fut.uget_mut((j, i)) as *mut f32,
+                                SimdT::lanes(),
+                            ));
+                        }
+                    }
+
+                    let mut a = a;
+                    for i in $BLOCK.len()..nx - $BLOCK.len() {
+                        // Push a onto circular buffer
+                        a = [a[1], a[2], a[3], a[4], a[5], a[6], unsafe {
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, i + 3)) as *const f32,
+                                SimdT::lanes(),
+                            ))
+                        }];
+                        let b = idx
+                            * (a[0] * $DIAG[0]
+                                + a[1] * $DIAG[1]
+                                + a[2] * $DIAG[2]
+                                + a[3] * $DIAG[3]
+                                + a[4] * $DIAG[4]
+                                + a[5] * $DIAG[5]
+                                + a[6] * $DIAG[6]);
+                        unsafe {
+                            b.write_to_slice_unaligned(slice::from_raw_parts_mut(
+                                fut.uget_mut((j, i)) as *mut f32,
+                                SimdT::lanes(),
+                            ));
+                        }
+                    }
+
+                    let a = unsafe {
+                        [
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, nx - 1)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, nx - 2)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, nx - 3)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, nx - 4)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, nx - 5)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, nx - 6)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                            SimdT::from_slice_unaligned(slice::from_raw_parts(
+                                prev.uget((j, nx - 7)) as *const f32,
+                                SimdT::lanes(),
+                            )),
+                        ]
+                    };
+
+                    for (i, bl) in $BLOCK.iter().enumerate() {
+                        let idx = if $symmetric { idx } else { -idx };
+                        let b = idx
+                            * (a[0] * bl[0]
+                                + a[1] * bl[1]
+                                + a[2] * bl[2]
+                                + a[3] * bl[3]
+                                + a[4] * bl[4]
+                                + a[5] * bl[5]
+                                + a[6] * bl[6]);
+                        unsafe {
+                            b.write_to_slice_unaligned(slice::from_raw_parts_mut(
+                                fut.uget_mut((j, nx - 1 - i)) as *mut f32,
+                                SimdT::lanes(),
+                            ));
+                        }
+                    }
+                }
+            }
+        }
+    };
+}
+
+diff_simd_col_7_47!(Upwind4, diff_simd_col, Upwind4::BLOCK, Upwind4::DIAG, false);
+diff_simd_col_7_47!(
+    Upwind4,
+    diss_simd_col,
+    Upwind4::DISS_BLOCK,
+    Upwind4::DISS_DIAG,
+    true
+);
+
+impl Upwind4 {
+    #[rustfmt::skip]
+    const HBLOCK: &'static [f32] = &[
+        49.0 / 144.0, 61.0 / 48.0, 41.0 / 48.0, 149.0 / 144.0
+    ];
+    #[rustfmt::skip]
+    const DIAG: &'static [f32] = &[
+        -1.0 / 24.0, 1.0 / 4.0, -7.0 / 8.0, 0.0, 7.0 / 8.0, -1.0 / 4.0, 1.0 / 24.0
+    ];
+    #[rustfmt::skip]
+    const BLOCK: &'static [[f32; 7]] = &[
+        [  -72.0 / 49.0, 187.0 / 98.0,   -20.0 / 49.0,   -3.0 / 98.0,           0.0,           0.0,         0.0],
+        [-187.0 / 366.0,          0.0,   69.0 / 122.0, -16.0 / 183.0,    2.0 / 61.0,           0.0,         0.0],
+        [  20.0 / 123.0, -69.0 / 82.0,            0.0, 227.0 / 246.0,  -12.0 / 41.0,    2.0 / 41.0,         0.0],
+        [   3.0 / 298.0, 16.0 / 149.0, -227.0 / 298.0,           0.0, 126.0 / 149.0, -36.0 / 149.0, 6.0 / 149.0],
+    ];
+
+    #[rustfmt::skip]
+    const DISS_BLOCK: &'static [[f32; 7]; 4] = &[
+        [-3.0 / 49.0,    9.0 / 49.0,  -9.0 / 49.0,     3.0 / 49.0,          0.0,           0.0,         0.0],
+        [ 3.0 / 61.0,  -11.0 / 61.0,  15.0 / 61.0,    -9.0 / 61.0,   2.0 / 61.0,           0.0,         0.0],
+        [-3.0 / 41.0,   15.0 / 41.0, -29.0 / 41.0,    27.0 / 41.0, -12.0 / 41.0,    2.0 / 41.0,         0.0],
+        [3.0 / 149.0, -27.0 / 149.0, 81.0 / 149.0, -117.0 / 149.0, 90.0 / 149.0, -36.0 / 149.0, 6.0 / 149.0],
+    ];
+
+    #[rustfmt::skip]
+    const DISS_DIAG: &'static [f32; 7] = &[
+        1.0 / 24.0, -1.0 / 4.0, 5.0 / 8.0, -5.0 / 6.0, 5.0 / 8.0, -1.0 / 4.0, 1.0 / 24.0
+    ];
+}
+
+impl SbpOperator for Upwind4 {
+    fn diffxi(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Self::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                Self::diff_simd_row(prev, fut);
+            }
+            ([1, _], [1, _]) if prev.len_of(Axis(0)) % SimdT::lanes() == 0 => {
+                Self::diff_simd_col(prev, fut);
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    Self::diff_1d(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+
+    fn diffeta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>) {
+        // transpose then use diffxi
+        Self::diffxi(prev.reversed_axes(), fut.reversed_axes());
+    }
+
+    fn h() -> &'static [f32] {
+        Self::HBLOCK
+    }
+}
+
+#[test]
+fn upwind4_test() {
+    use ndarray::prelude::*;
+    let nx = 20;
+    let dx = 1.0 / (nx - 1) as f32;
+    let mut source: ndarray::Array1<f32> = ndarray::Array1::zeros(nx);
+    let mut res = ndarray::Array1::zeros(nx);
+    let mut target = ndarray::Array1::zeros(nx);
+
+    for i in 0..nx {
+        source[i] = i as f32 * dx;
+        target[i] = 1.0;
+    }
+    res.fill(0.0);
+    Upwind4::diff_1d(source.view(), res.view_mut());
+    approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-4);
+    {
+        let source = source.to_owned().insert_axis(ndarray::Axis(0));
+        let mut res = res.to_owned().insert_axis(ndarray::Axis(0));
+        let target = target.to_owned().insert_axis(ndarray::Axis(0));
+        res.fill(0.0);
+        Upwind4::diffxi(source.view(), res.view_mut());
+        approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
+    }
+
+    {
+        let source = Array2::from_shape_fn((nx, 8), |(i, _)| source[i]);
+        let target = Array2::from_shape_fn((nx, 8), |(i, _)| target[i]);
+        let mut res = Array2::zeros((nx, 8));
+        res.fill(0.0);
+        Upwind4::diffeta(source.view(), res.view_mut());
+        approx::assert_abs_diff_eq!(&res.to_owned(), &target.to_owned(), epsilon = 1e-2);
+    }
+
+    for i in 0..nx {
+        let x = i as f32 * dx;
+        source[i] = x * x;
+        target[i] = 2.0 * x;
+    }
+    res.fill(0.0);
+    Upwind4::diff_1d(source.view(), res.view_mut());
+    approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-4);
+    {
+        let source = source.to_owned().insert_axis(ndarray::Axis(0));
+        let mut res = res.to_owned().insert_axis(ndarray::Axis(0));
+        let target = target.to_owned().insert_axis(ndarray::Axis(0));
+        res.fill(0.0);
+        Upwind4::diffxi(source.view(), res.view_mut());
+        approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
+    }
+
+    {
+        let source = Array2::from_shape_fn((nx, 8), |(i, _)| source[i]);
+        let target = Array2::from_shape_fn((nx, 8), |(i, _)| target[i]);
+        let mut res = Array2::zeros((nx, 8));
+        res.fill(0.0);
+        Upwind4::diffeta(source.view(), res.view_mut());
+        approx::assert_abs_diff_eq!(&res.to_owned(), &target.to_owned(), epsilon = 1e-2);
+    }
+
+    for i in 0..nx {
+        let x = i as f32 * dx;
+        source[i] = x * x * x;
+        target[i] = 3.0 * x * x;
+    }
+    res.fill(0.0);
+    Upwind4::diff_1d(source.view(), res.view_mut());
+    approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
+
+    {
+        let source = source.to_owned().insert_axis(ndarray::Axis(0));
+        let mut res = res.to_owned().insert_axis(ndarray::Axis(0));
+        let target = target.to_owned().insert_axis(ndarray::Axis(0));
+        res.fill(0.0);
+        Upwind4::diffxi(source.view(), res.view_mut());
+        approx::assert_abs_diff_eq!(&res, &target, epsilon = 1e-2);
+    }
+
+    {
+        let source = Array2::from_shape_fn((nx, 8), |(i, _)| source[i]);
+        let target = Array2::from_shape_fn((nx, 8), |(i, _)| target[i]);
+        let mut res = Array2::zeros((nx, 8));
+        res.fill(0.0);
+        Upwind4::diffeta(source.view(), res.view_mut());
+        approx::assert_abs_diff_eq!(&res.to_owned(), &target.to_owned(), epsilon = 1e-2);
+    }
+}
+
+impl UpwindOperator for Upwind4 {
+    fn dissxi(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Self::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                Self::diss_simd_row(prev, fut);
+            }
+            ([1, _], [1, _]) if prev.len_of(Axis(0)) % SimdT::lanes() == 0 => {
+                Self::diss_simd_col(prev, fut);
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    Self::diss_1d(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+
+    fn disseta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>) {
+        // diffeta = transpose then use dissxi
+        Self::dissxi(prev.reversed_axes(), fut.reversed_axes());
+    }
+}

sbp/src/operators/upwind9.rs

@@ -0,0 +1,89 @@
+use super::{SbpOperator, UpwindOperator};
+use crate::diff_op_1d;
+use ndarray::{s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
+
+pub struct Upwind9 {}
+
+diff_op_1d!(Upwind9, diff_1d, Upwind9::BLOCK, Upwind9::DIAG, false);
+diff_op_1d!(
+    Upwind9,
+    diss_1d,
+    Upwind9::DISS_BLOCK,
+    Upwind9::DISS_DIAG,
+    true
+);
+
+impl Upwind9 {
+    #[rustfmt::skip]
+    const HBLOCK: &'static [f32] = &[
+        1070017.0/3628800.0, 5537111.0/3628800.0, 103613.0/403200.0, 261115.0/145152.0, 298951.0/725760.0, 515677.0/403200.0, 3349879.0/3628800.0, 3662753.0/3628800.0
+    ];
+    #[rustfmt::skip]
+    const DIAG: &'static [f32] = &[
+        -1.0/1260.0, 5.0/504.0, -5.0/84.0, 5.0/21.0, -5.0/6.0, 0.0, 5.0/6.0, -5.0/21.0, 5.0/84.0, -5.0/504.0, 1.0/1260.0,
+    ];
+    #[rustfmt::skip]
+    const BLOCK: &'static [[f32; 13]] = &[
+        [-1.69567399396458e+00, 2.29023358159400e+00, -2.16473500425698e-01, -5.05879766354449e-01, -1.01161106778154e-01, 2.59147072064383e-01, 1.93922119400659e-02, -4.95844980755642e-02, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-4.42575354959737e-01, 0.00000000000000e+00, 1.91582959381899e-01, 2.82222626681305e-01, 1.12083989713257e-01, -1.51334868892111e-01, -2.23600502721044e-02, 3.03806983474913e-02, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [2.48392603571843e-01, -1.13758367065272e+00, 0.00000000000000e+00, 1.95334726810969e+00, -1.58879011773212e+00, 3.93797129320378e-01, 2.52140821030291e-01, -1.21304033647356e-01, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [8.29213105268236e-02, -2.39388470313226e-01, -2.79038666398460e-01, 0.00000000000000e+00, 3.43018053395471e-01, 1.10370852514749e-01, 1.72029988649808e-03, -2.00445645303789e-02, 4.41184918522490e-04, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [7.24159504343116e-02, -4.15199475743626e-01, 9.91181694804303e-01, -1.49802407438608e+00, 0.00000000000000e+00, 1.30188867830442e+00, -6.03535071819214e-01, 1.73429775718218e-01, -2.40842144699299e-02, 1.92673715759439e-03, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-5.97470838462221e-02, 1.80551858630298e-01, -7.91241454636765e-02, -1.55240829877729e-01, -4.19298775383066e-01, 0.00000000000000e+00, 6.42287612546289e-01, -1.48833147569152e-01, 4.65407609802260e-02, -7.75679349670433e-03, 6.20543479736347e-04, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-6.19425252179959e-03, 3.69595678895333e-02, -7.01892820620398e-02, -3.35233082197107e-03, 2.69304373763091e-01, -8.89857974743355e-01, 0.00000000000000e+00, 8.66656645522330e-01, -2.57919763669076e-01, 6.44799409172690e-02, -1.07466568195448e-02, 8.59732545563586e-04, 0.00000000000000e+00],
+        [1.44853491014330e-02, -4.59275574977554e-02, 3.08833474560615e-02, 3.57240610228828e-02, -7.07760049349999e-02, 1.88587240076292e-01, -7.92626447113877e-01, 0.00000000000000e+00, 8.25608497215073e-01, -2.35888142061449e-01, 5.89720355153623e-02, -9.82867258589373e-03, 7.86293806871498e-04],
+    ];
+
+    #[rustfmt::skip]
+    const DISS_BLOCK: &'static [[f32; 13]] = &[
+        [-3.99020778658945e-04, 2.05394169917502e-03, -4.24493243399805e-03, 4.38126393542801e-03, -2.18883813216888e-03, 2.98565988131608e-04, 1.38484104084115e-04, -3.94643819928825e-05, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [3.96913216138553e-04, -2.28230530115522e-03, 5.43069719436758e-03, -6.81086901935894e-03, 4.69064759201504e-03, -1.61429862514855e-03, 1.62083873811316e-04, 2.71310693302277e-05, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-4.87084939816571e-03, 3.22464611075207e-02, -9.06094757860846e-02, 1.39830191253413e-01, -1.27675500367419e-01, 6.87310321912961e-02, -2.00917702215270e-02, 2.43991122096699e-03, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [7.18155125886276e-04, -5.77715378536685e-03, 1.99749582302141e-02, -3.87940986951101e-02, 4.62756436981388e-02, -3.46770570075288e-02, 1.59058082995305e-02, -4.06744078428648e-03, 4.41184918522490e-04, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [-1.56687484682703e-03, 1.73758484693946e-02, -7.96515646886111e-02, 2.02094401829054e-01, -3.16098733124618e-01, 3.17999240131250e-01, -2.06522928911140e-01, 8.37112455598470e-02, -1.92673715759439e-02, 1.92673715759439e-03, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
+        [6.88352254356072e-05, -1.92595810396278e-03, 1.38098624496279e-02, -4.87746083763075e-02, 1.02417890394006e-01, -1.38292226669620e-01, 1.23829022892659e-01, -7.34723830823462e-02, 2.79244565881356e-02, -6.20543479736347e-03, 6.20543479736347e-04, 0.00000000000000e+00, 0.00000000000000e+00],
+        [4.42345367100640e-05, 2.67913080025652e-04, -5.59301314813691e-03, 3.09954862110834e-02, -9.21529346596015e-02, 1.71559035817103e-01, -2.12738289547735e-01, 1.79835101537893e-01, -1.03167905467630e-01, 3.86879645503614e-02, -8.59732545563586e-03, 8.59732545563586e-04, 0.00000000000000e+00],
+        [-1.15289127131636e-05, 4.10149803795578e-05, 6.21188131452618e-04, -7.24912245235322e-03, 3.41622279353287e-02, -9.30972311856124e-02, 1.64473506705108e-01, -1.98013074867399e-01, 1.65121699443015e-01, -9.43552568245798e-02, 3.53832213092174e-02, -7.86293806871498e-03, 7.86293806871498e-04]
+    ];
+
+    #[rustfmt::skip]
+    const DISS_DIAG: &'static [f32] = &[
+        1.0/1260.0, -1.0/126.0, 1.0/28.0, -2.0/21.0, 1.0/6.0, -1.0/5.0, 1.0/6.0, -2.0/21.0, 1.0/28.0, -1.0/126.0, 1.0/1260.0,
+    ];
+}
+
+impl SbpOperator for Upwind9 {
+    fn diffxi(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Self::BLOCK.len());
+
+        for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+            Self::diff_1d(r0, r1);
+        }
+    }
+
+    fn diffeta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>) {
+        // transpose then use diffxi
+        Self::diffxi(prev.reversed_axes(), fut.reversed_axes());
+    }
+
+    fn h() -> &'static [f32] {
+        Self::HBLOCK
+    }
+}
+
+impl UpwindOperator for Upwind9 {
+    fn dissxi(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Self::BLOCK.len());
+
+        for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+            Self::diss_1d(r0, r1);
+        }
+    }
+
+    fn disseta(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>) {
+        // diffeta = transpose then use dissxi
+        Self::dissxi(prev.reversed_axes(), fut.reversed_axes());
+    }
+}