add SBP trait
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@ -3,6 +3,7 @@ use wasm_bindgen::prelude::*;
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mod maxwell;
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mod operators;
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use maxwell::{System, WorkBuffers};
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use operators::Upwind4;
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#[cfg(feature = "wee_alloc")]
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#[global_allocator]
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@ -34,7 +35,7 @@ impl Universe {
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}
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pub fn advance(&mut self, dt: f32) {
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self.sys.0.advance(&mut self.sys.1, dt, Some(&mut self.wb));
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System::advance::<Upwind4>(&self.sys.0, &mut self.sys.1, dt, Some(&mut self.wb));
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std::mem::swap(&mut self.sys.0, &mut self.sys.1);
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}
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@ -1,4 +1,4 @@
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use super::operators::{diffx, diffy};
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use super::operators::SbpOperator;
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use ndarray::{Array2, Zip};
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pub struct System {
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@ -43,7 +43,10 @@ impl System {
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}
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}
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pub fn advance(&self, fut: &mut System, dt: f32, work_buffers: Option<&mut WorkBuffers>) {
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pub fn advance<SBP>(&self, fut: &mut System, dt: f32, work_buffers: Option<&mut WorkBuffers>)
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where
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SBP: SbpOperator,
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{
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assert_eq!(self.ex.shape(), fut.ex.shape());
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let mut wb: WorkBuffers;
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@ -84,18 +87,18 @@ impl System {
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// ex = hz_y
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k[i].0.fill(0.0);
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diffy(y.1.view(), k[i].0.view_mut());
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SBP::diffy(y.1.view(), k[i].0.view_mut());
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// ey = -hz_x
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k[i].2.fill(0.0);
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diffx(y.1.view(), k[i].2.view_mut());
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SBP::diffx(y.1.view(), k[i].2.view_mut());
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k[i].2.mapv_inplace(|v| -v);
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// hz = -ey_x + ex_y
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k[i].1.fill(0.0);
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diffx(y.2.view(), k[i].1.view_mut());
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SBP::diffx(y.2.view(), k[i].1.view_mut());
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k[i].1.mapv_inplace(|v| -v);
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diffy(y.0.view(), k[i].1.view_mut());
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SBP::diffy(y.0.view(), k[i].1.view_mut());
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// Boundary conditions (SAT)
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let ny = y.0.shape()[0];
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348
src/operators.rs
348
src/operators.rs
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@ -1,344 +1,10 @@
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#![allow(dead_code)]
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use ndarray::{arr1, arr2, s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
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use ndarray::{ArrayView2, ArrayViewMut2};
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pub(crate) fn diffx(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
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for j in 0..prev.shape()[0] {
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upwind4(prev.slice(s!(j, ..)), fut.slice_mut(s!(j, ..)));
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}
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pub trait SbpOperator {
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fn diffx(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>);
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fn diffy(prev: ArrayView2<f32>, fut: ArrayViewMut2<f32>);
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fn h() -> &'static [f32];
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}
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pub(crate) fn diffx_periodic(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
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for j in 0..prev.shape()[0] {
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upwind4_periodic(prev.slice(s!(j, ..)), fut.slice_mut(s!(j, ..)));
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}
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}
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pub(crate) fn diffy(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
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for i in 0..prev.shape()[1] {
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upwind4(prev.slice(s!(.., i)), fut.slice_mut(s!(.., i)));
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}
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}
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pub(crate) fn diffy_periodic(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
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for i in 0..prev.shape()[1] {
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upwind4_periodic(prev.slice(s!(.., i)), fut.slice_mut(s!(.., i)));
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}
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}
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pub(crate) fn dissx(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
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for j in 0..prev.shape()[0] {
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upwind4_diss(prev.slice(s!(j, ..)), fut.slice_mut(s!(j, ..)));
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}
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}
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pub(crate) fn dissy(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
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for i in 0..prev.shape()[1] {
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upwind4_diss(prev.slice(s!(.., i)), fut.slice_mut(s!(.., i)));
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}
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}
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fn trad4_periodic(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
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assert_eq!(prev.shape(), fut.shape());
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let nx = prev.shape()[0];
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let dx = 1.0 / (nx - 1) as f32;
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let diag = [1.0 / 12.0, -2.0 / 3.0, 0.0, 2.0 / 3.0, -1.0 / 12.0];
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let diff = diag[0] * prev[(nx - 2)]
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+ diag[1] * prev[(nx - 1)]
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+ diag[2] * prev[(0)]
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+ diag[3] * prev[(1)]
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+ diag[4] * prev[(2)];
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fut[(0)] += diff / dx;
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let diff = diag[0] * prev[(nx - 1)]
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+ diag[1] * prev[(0)]
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+ diag[2] * prev[(1)]
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+ diag[3] * prev[(2)]
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+ diag[4] * prev[(3)];
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fut[(1)] += diff / dx;
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for i in 2..nx - 2 {
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let diff = diag[0] * prev[(i - 2)]
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+ diag[1] * prev[(i - 1)]
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+ diag[2] * prev[(i)]
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+ diag[3] * prev[(i + 1)]
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+ diag[4] * prev[(i + 2)];
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fut[(i)] += diff / dx;
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}
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let diff = diag[0] * prev[(nx - 4)]
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+ diag[1] * prev[(nx - 3)]
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+ diag[2] * prev[(nx - 2)]
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+ diag[3] * prev[(nx - 1)]
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+ diag[4] * prev[(0)];
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fut[(nx - 2)] += diff / dx;
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let diff = diag[0] * prev[(nx - 3)]
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+ diag[1] * prev[(nx - 2)]
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+ diag[2] * prev[(nx - 1)]
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+ diag[3] * prev[(0)]
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+ diag[4] * prev[(1)];
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fut[(nx - 1)] += diff / dx;
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}
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fn upwind4(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
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assert_eq!(prev.shape(), fut.shape());
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let nx = prev.shape()[0];
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let dx = 1.0 / (nx - 1) as f32;
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let diag = arr1(&[
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-1.0 / 24.0,
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1.0 / 4.0,
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-7.0 / 8.0,
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0.0,
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7.0 / 8.0,
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-1.0 / 4.0,
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1.0 / 24.0,
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]);
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let block = arr2(&[
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[
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-72.0 / 49.0f32,
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187.0 / 98.0,
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-20.0 / 49.0,
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-3.0 / 98.0,
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0.0,
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0.0,
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0.0,
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],
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[
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-187.0 / 366.0,
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0.0,
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69.0 / 122.0,
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-16.0 / 183.0,
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2.0 / 61.0,
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0.0,
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0.0,
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],
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[
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20.0 / 123.0,
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-69.0 / 82.0,
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0.0,
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227.0 / 246.0,
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-12.0 / 41.0,
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2.0 / 41.0,
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0.0,
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],
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[
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3.0 / 298.0,
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16.0 / 149.0,
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-227.0 / 298.0,
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0.0,
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126.0 / 149.0,
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-36.0 / 149.0,
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6.0 / 149.0,
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],
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]);
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// let h_block = [49.0 / 144.0, 61.0 / 48.0, 41.0 / 48.0, 149.0 / 144.0];
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let first_elems = prev.slice(s!(..7));
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for i in 0..4 {
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let diff = first_elems.dot(&block.slice(s!(i, ..)));
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fut[i] += diff / dx;
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}
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for i in 4..nx - 4 {
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let diff = diag.dot(&prev.slice(s!(i - 3..i + 3 + 1)));
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fut[(i)] += diff / dx;
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}
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let last_elems = prev.slice(s!(nx - 7..));
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for i in 0..4 {
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let ii = nx - 4 + i;
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let block = block.slice(s!(3 - i, ..;-1));
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let diff = last_elems.dot(&block);
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fut[ii] += -diff / dx;
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}
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}
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fn upwind4_periodic(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
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assert_eq!(prev.shape(), fut.shape());
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let nx = prev.shape()[0];
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let dx = 1.0 / (nx - 1) as f32;
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let diag = [
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-1.0 / 24.0,
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1.0 / 4.0,
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-7.0 / 8.0,
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0.0,
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7.0 / 8.0,
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-1.0 / 4.0,
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1.0 / 24.0,
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];
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let diff = diag[0] * prev[(nx - 3)]
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+ diag[1] * prev[(nx - 2)]
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+ diag[2] * prev[(nx - 1)]
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+ diag[3] * prev[(0)]
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+ diag[4] * prev[(1)]
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+ diag[5] * prev[(2)]
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+ diag[6] * prev[(3)];
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fut[0] += diff / dx;
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let diff = diag[0] * prev[(nx - 2)]
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+ diag[1] * prev[(nx - 1)]
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+ diag[2] * prev[(0)]
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+ diag[3] * prev[(1)]
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+ diag[4] * prev[(2)]
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+ diag[5] * prev[(3)]
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+ diag[6] * prev[(4)];
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fut[1] += diff / dx;
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let diff = diag[0] * prev[(nx - 1)]
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+ diag[1] * prev[(0)]
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+ diag[2] * prev[(1)]
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+ diag[3] * prev[(2)]
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+ diag[4] * prev[(3)]
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+ diag[5] * prev[(4)]
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+ diag[6] * prev[(5)];
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fut[2] += diff / dx;
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for i in 3..nx - 3 {
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let diff = diag[0] * prev[(i - 3)]
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+ diag[1] * prev[(i - 2)]
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+ diag[2] * prev[(i - 1)]
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+ diag[3] * prev[(i)]
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+ diag[4] * prev[(i + 1)]
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+ diag[5] * prev[(i + 2)]
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+ diag[6] * prev[(i + 3)];
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fut[(i)] += diff / dx;
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}
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let diff = diag[0] * prev[(nx - 6)]
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+ diag[1] * prev[(nx - 5)]
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+ diag[2] * prev[(nx - 4)]
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+ diag[3] * prev[(nx - 3)]
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+ diag[4] * prev[(nx - 2)]
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+ diag[5] * prev[(nx - 1)]
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+ diag[6] * prev[(0)];
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fut[(nx - 3)] += diff / dx;
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let diff = diag[0] * prev[(nx - 5)]
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+ diag[1] * prev[(nx - 4)]
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+ diag[2] * prev[(nx - 3)]
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+ diag[3] * prev[(nx - 2)]
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+ diag[4] * prev[(nx - 1)]
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+ diag[5] * prev[(0)]
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+ diag[6] * prev[(1)];
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fut[(nx - 2)] += diff / dx;
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let diff = diag[0] * prev[(nx - 4)]
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+ diag[1] * prev[(nx - 3)]
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+ diag[2] * prev[(nx - 2)]
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+ diag[3] * prev[(nx - 1)]
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+ diag[4] * prev[(0)]
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+ diag[5] * prev[(1)]
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+ diag[6] * prev[(2)];
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fut[(nx - 1)] += diff / dx;
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}
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#[test]
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fn upwind4_test() {
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let nx = 20;
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let dx = 1.0 / (nx - 1) as f32;
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let mut source: ndarray::Array1<f32> = ndarray::Array1::zeros((nx));
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let mut res = ndarray::Array1::zeros((nx));
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let mut target = ndarray::Array1::zeros((nx));
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for i in 0..nx {
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source[i] = i as f32 * dx;
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target[i] = 1.0;
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}
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res.fill(0.0);
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upwind4(source.view(), res.view_mut());
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assert!(res.all_close(&target, 1e-4));
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for i in 0..nx {
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let x = i as f32 * dx;
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source[i] = x * x;
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target[i] = 2.0 * x;
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}
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res.fill(0.0);
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upwind4(source.view(), res.view_mut());
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assert!(res.all_close(&target, 1e-4));
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for i in 0..nx {
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let x = i as f32 * dx;
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source[i] = x * x * x;
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target[i] = 3.0 * x * x;
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}
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res.fill(0.0);
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upwind4(source.view(), res.view_mut());
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assert!(res.all_close(&target, 1e-2));
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}
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fn upwind4_diss(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
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assert_eq!(prev.shape(), fut.shape());
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let nx = prev.shape()[0];
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let dx = 1.0 / (nx - 1) as f32;
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let diag = [
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1.0 / 24.0,
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-1.0 / 4.0,
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5.0 / 8.0,
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-5.0 / 6.0,
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5.0 / 8.0,
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-1.0 / 4.0,
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1.0 / 24.0,
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];
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let diff = diag[0] * prev[(nx - 3)]
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+ diag[1] * prev[(nx - 2)]
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+ diag[2] * prev[(nx - 1)]
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+ diag[3] * prev[(0)]
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+ diag[4] * prev[(1)]
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+ diag[5] * prev[(2)]
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+ diag[6] * prev[(3)];
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fut[0] += diff / dx;
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let diff = diag[0] * prev[(nx - 2)]
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+ diag[1] * prev[(nx - 1)]
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+ diag[2] * prev[(0)]
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+ diag[3] * prev[(1)]
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+ diag[4] * prev[(2)]
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+ diag[5] * prev[(3)]
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+ diag[6] * prev[(4)];
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fut[1] += diff / dx;
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let diff = diag[0] * prev[(nx - 1)]
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+ diag[1] * prev[(0)]
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+ diag[2] * prev[(1)]
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+ diag[3] * prev[(2)]
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+ diag[4] * prev[(3)]
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+ diag[5] * prev[(4)]
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+ diag[6] * prev[(5)];
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fut[2] += diff / dx;
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for i in 3..nx - 3 {
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let diff = diag[0] * prev[(i - 3)]
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+ diag[1] * prev[(i - 2)]
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+ diag[2] * prev[(i - 1)]
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+ diag[3] * prev[(i)]
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+ diag[4] * prev[(i + 1)]
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+ diag[5] * prev[(i + 2)]
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+ diag[6] * prev[(i + 3)];
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fut[(i)] += diff / dx;
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}
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let diff = diag[0] * prev[(nx - 6)]
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+ diag[1] * prev[(nx - 5)]
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+ diag[2] * prev[(nx - 4)]
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+ diag[3] * prev[(nx - 3)]
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+ diag[4] * prev[(nx - 2)]
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+ diag[5] * prev[(nx - 1)]
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+ diag[6] * prev[(0)];
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fut[(nx - 3)] += diff / dx;
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let diff = diag[0] * prev[(nx - 5)]
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+ diag[1] * prev[(nx - 4)]
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+ diag[2] * prev[(nx - 3)]
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+ diag[3] * prev[(nx - 2)]
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+ diag[4] * prev[(nx - 1)]
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+ diag[5] * prev[(0)]
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+ diag[6] * prev[(1)];
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fut[(nx - 2)] += diff / dx;
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let diff = diag[0] * prev[(nx - 4)]
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+ diag[1] * prev[(nx - 3)]
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+ diag[2] * prev[(nx - 2)]
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+ diag[3] * prev[(nx - 1)]
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+ diag[4] * prev[(0)]
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+ diag[5] * prev[(1)]
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+ diag[6] * prev[(2)];
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fut[(nx - 1)] += diff / dx;
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}
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mod upwind4;
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pub use upwind4::Upwind4;
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@ -0,0 +1,136 @@
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use super::SbpOperator;
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use ndarray::{arr1, arr2, s, ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
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pub struct Upwind4 {}
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impl Upwind4 {
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const HBLOCK: &'static [f32] = &[49.0 / 144.0, 61.0 / 48.0, 41.0 / 48.0, 149.0 / 144.0];
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const DIAG: &'static [f32] = &[
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-1.0 / 24.0,
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1.0 / 4.0,
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-7.0 / 8.0,
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0.0,
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7.0 / 8.0,
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-1.0 / 4.0,
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1.0 / 24.0,
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];
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const BLOCK: &'static [[f32; 7]] = &[
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[
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-72.0 / 49.0f32,
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187.0 / 98.0,
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-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,
|
||||
],
|
||||
];
|
||||
|
||||
fn diff(prev: ArrayView1<f32>, mut fut: ArrayViewMut1<f32>) {
|
||||
assert_eq!(prev.shape(), fut.shape());
|
||||
let nx = prev.shape()[0];
|
||||
|
||||
let dx = 1.0 / (nx - 1) as f32;
|
||||
|
||||
let diag = arr1(Upwind4::DIAG);
|
||||
let block = arr2(Upwind4::BLOCK);
|
||||
|
||||
let first_elems = prev.slice(s!(..7));
|
||||
for i in 0..4 {
|
||||
let diff = first_elems.dot(&block.slice(s!(i, ..)));
|
||||
fut[i] += diff / dx;
|
||||
}
|
||||
|
||||
for i in 4..nx - 4 {
|
||||
let diff = diag.dot(&prev.slice(s!(i - 3..i + 3 + 1)));
|
||||
fut[(i)] += diff / dx;
|
||||
}
|
||||
let last_elems = prev.slice(s!(nx - 7..));
|
||||
for i in 0..4 {
|
||||
let ii = nx - 4 + i;
|
||||
let block = block.slice(s!(3 - i, ..;-1));
|
||||
let diff = last_elems.dot(&block);
|
||||
fut[ii] += -diff / dx;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn upwind4_test() {
|
||||
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(source.view(), res.view_mut());
|
||||
assert!(res.all_close(&target, 1e-4));
|
||||
|
||||
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(source.view(), res.view_mut());
|
||||
assert!(res.all_close(&target, 1e-4));
|
||||
|
||||
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(source.view(), res.view_mut());
|
||||
assert!(res.all_close(&target, 1e-2));
|
||||
}
|
||||
|
||||
impl SbpOperator for Upwind4 {
|
||||
fn diffx(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
|
||||
for j in 0..prev.shape()[0] {
|
||||
Upwind4::diff(prev.slice(s!(j, ..)), fut.slice_mut(s!(j, ..)));
|
||||
}
|
||||
}
|
||||
|
||||
fn diffy(prev: ArrayView2<f32>, mut fut: ArrayViewMut2<f32>) {
|
||||
for i in 0..prev.shape()[1] {
|
||||
Upwind4::diff(prev.slice(s!(.., i)), fut.slice_mut(s!(.., i)));
|
||||
}
|
||||
}
|
||||
|
||||
fn h() -> &'static [f32] {
|
||||
Upwind4::HBLOCK
|
||||
}
|
||||
}
|
Loading…
Reference in New Issue