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SummationByParts
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use 3d fields

This commit is contained in:
Magnus Ulimoen 2019-12-11 20:36:12 +01:00
parent 07e08c6236
commit 868e2ba648
3 changed files with 150 additions and 111 deletions
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9
src/benches/bench.rs
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@ -13,7 +13,14 @@ fn performance_benchmark(c: &mut Criterion) {
let w = 40; let w = 40;
let h = 26; let h = 26;
let mut universe = Universe::new(w, h); 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 = Universe::new(
w as u32,
h as u32,
x.as_slice().unwrap(),
y.as_slice().unwrap(),
);
group.bench_function("advance", |b| { group.bench_function("advance", |b| {
b.iter(|| { b.iter(|| {

23
src/lib.rs
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@ -3,7 +3,7 @@ use wasm_bindgen::prelude::*;
mod grid; mod grid;
mod maxwell; mod maxwell;
mod operators; mod operators;
pub use crate::maxwell::{System, WorkBuffers}; pub use crate::maxwell::{Field, WorkBuffers};
pub(crate) use grid::Grid; pub(crate) use grid::Grid;
#[cfg(feature = "wee_alloc")] #[cfg(feature = "wee_alloc")]
@ -18,7 +18,7 @@ pub fn set_panic_hook() {
#[wasm_bindgen] #[wasm_bindgen]
pub struct Universe { pub struct Universe {
sys: (System, System), sys: (Field, Field),
wb: WorkBuffers, wb: WorkBuffers,
grid: Grid<operators::Upwind4>, grid: Grid<operators::Upwind4>,
} }
@ -34,7 +34,10 @@ impl Universe {
"Could not create grid. Different number of elements compared to width*height?", "Could not create grid. Different number of elements compared to width*height?",
); );
Self { Self {
sys: (System::new(width, height), System::new(width, height)), sys: (
Field::new(width as usize, height as usize),
Field::new(width as usize, height as usize),
),
grid, grid,
wb: WorkBuffers::new(width as usize, height as usize), wb: WorkBuffers::new(width as usize, height as usize),
} }
@ -45,7 +48,7 @@ impl Universe {
} }
pub fn advance(&mut self, dt: f32) { pub fn advance(&mut self, dt: f32) {
System::advance::<operators::Upwind4>( Field::advance::<operators::Upwind4>(
&self.sys.0, &self.sys.0,
&mut self.sys.1, &mut self.sys.1,
dt, dt,
@ -55,15 +58,15 @@ impl Universe {
std::mem::swap(&mut self.sys.0, &mut self.sys.1); std::mem::swap(&mut self.sys.0, &mut self.sys.1);
} }
pub fn get_ex_ptr(&mut self) -> *mut u8 { pub fn get_ex_ptr(&self) -> *const u8 {
self.sys.0.ex.as_mut_ptr() as *mut u8 self.sys.0.ex().as_ptr() as *const u8
} }
pub fn get_ey_ptr(&mut self) -> *mut u8 { pub fn get_ey_ptr(&self) -> *const u8 {
self.sys.0.ey.as_mut_ptr() as *mut u8 self.sys.0.ey().as_ptr() as *const u8
} }
pub fn get_hz_ptr(&mut self) -> *mut u8 { pub fn get_hz_ptr(&self) -> *const u8 {
self.sys.0.hz.as_mut_ptr() as *mut u8 self.sys.0.hz().as_ptr() as *const u8
} }
} }

229
src/maxwell.rs
View File

@ -1,10 +1,21 @@
use super::operators::SbpOperator; use super::operators::SbpOperator;
use ndarray::{Array2, Zip}; use ndarray::prelude::*;
use ndarray::{azip, Zip};
pub struct System { #[derive(Clone, Debug)]
pub(crate) ex: Array2<f32>, pub struct Field(pub(crate) Array3<f32>);
pub(crate) ey: Array2<f32>,
pub(crate) hz: Array2<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
}
} }
fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 { fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 {
@ -17,28 +28,70 @@ fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 {
1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp() 1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp()
} }
impl System { impl Field {
pub fn new(width: u32, height: u32) -> Self { pub fn new(width: usize, height: usize) -> Self {
let field = Array2::zeros((height as usize, width as usize)); let field = Array3::zeros((3, height, width));
let ex = field.clone();
let ey = field.clone();
let hz = field;
Self { ex, ey, hz } 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 nx = self.nx();
let ny = self.ny();
let (ex, f) = self.0.view_mut().split_at(Axis(0), 1);
let (hz, ey) = f.split_at(Axis(0), 1);
(
ex.into_shape((ny, nx)).unwrap(),
hz.into_shape((ny, nx)).unwrap(),
ey.into_shape((ny, nx)).unwrap(),
)
} }
pub fn set_gaussian(&mut self, x0: f32, y0: f32) { pub fn set_gaussian(&mut self, x0: f32, y0: f32) {
let nx = self.ex.shape()[1]; let nx = self.nx();
let ny = self.ex.shape()[0]; let ny = self.ny();
let (mut ex, mut hz, mut ey) = self.components_mut();
for j in 0..ny { for j in 0..ny {
for i in 0..nx { for i in 0..nx {
// Must divice interval on nx/ny instead of nx - 1/ny-1 // Must divice interval on nx/ny instead of nx - 1/ny-1
// due to periodic conditions [0, 1) // due to periodic conditions [0, 1)
let x = i as f32 / nx as f32; let x = i as f32 / nx as f32;
let y = j as f32 / ny as f32; let y = j as f32 / ny as f32;
self.ex[(j, i)] = 0.0; ex[(j, i)] = 0.0;
self.ey[(j, i)] = 0.0; ey[(j, i)] = 0.0;
self.hz[(j, i)] = gaussian(x, x0, y, y0) / 32.0; hz[(j, i)] = gaussian(x, x0, y, y0) / 32.0;
} }
} }
} }
@ -52,32 +105,26 @@ impl System {
) where ) where
SBP: SbpOperator, SBP: SbpOperator,
{ {
assert_eq!(self.ex.shape(), fut.ex.shape()); assert_eq!(self.0.shape(), fut.0.shape());
let mut wb: WorkBuffers; let mut wb: WorkBuffers;
let (y, k, tmp) = if let Some(x) = work_buffers { let (y, k, tmp) = if let Some(x) = work_buffers {
(&mut x.y, &mut x.buf, &mut x.tmp) (&mut x.y, &mut x.buf, &mut x.tmp)
} else { } else {
wb = WorkBuffers::new(self.ex.shape()[1], self.ex.shape()[0]); wb = WorkBuffers::new(self.nx(), self.ny());
(&mut wb.y, &mut wb.buf, &mut wb.tmp) (&mut wb.y, &mut wb.buf, &mut wb.tmp)
}; };
for i in 0..4 { for i in 0..4 {
// y = y0 + c*kn // y = y0 + c*kn
y.0.assign(&self.ex); y.assign(&self);
y.1.assign(&self.hz);
y.2.assign(&self.ey);
match i { match i {
0 => {} 0 => {}
1 | 2 => { 1 | 2 => {
y.0.scaled_add(1.0 / 2.0 * dt, &k[i - 1].0); y.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
y.1.scaled_add(1.0 / 2.0 * dt, &k[i - 1].1);
y.2.scaled_add(1.0 / 2.0 * dt, &k[i - 1].2);
} }
3 => { 3 => {
y.0.scaled_add(dt, &k[i - 1].0); y.scaled_add(dt, &k[i - 1]);
y.1.scaled_add(dt, &k[i - 1].1);
y.2.scaled_add(dt, &k[i - 1].2);
} }
_ => { _ => {
unreachable!(); unreachable!();
@ -102,19 +149,19 @@ impl System {
{ {
ndarray::azip!((a in &mut tmp.0, ndarray::azip!((a in &mut tmp.0,
&dxi_dy in &grid.detj_dxi_dy, &dxi_dy in &grid.detj_dxi_dy,
&hz in &y.1) &hz in &y.hz())
*a = dxi_dy * hz *a = dxi_dy * hz
); );
SBP::diffxi(tmp.0.view(), tmp.1.view_mut()); SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
ndarray::azip!((b in &mut tmp.2, ndarray::azip!((b in &mut tmp.2,
&deta_dy in &grid.detj_deta_dy, &deta_dy in &grid.detj_deta_dy,
&hz in &y.1) &hz in &y.hz())
*b = deta_dy * hz *b = deta_dy * hz
); );
SBP::diffeta(tmp.2.view(), tmp.3.view_mut()); SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
ndarray::azip!((flux in &mut k[i].0, &ax in &tmp.1, &by in &tmp.3) ndarray::azip!((flux in &mut k[i].ex_mut(), &ax in &tmp.1, &by in &tmp.3)
*flux = ax + by *flux = ax + by
); );
} }
@ -124,8 +171,8 @@ impl System {
ndarray::azip!((a in &mut tmp.0, ndarray::azip!((a in &mut tmp.0,
&dxi_dx in &grid.detj_dxi_dx, &dxi_dx in &grid.detj_dxi_dx,
&dxi_dy in &grid.detj_dxi_dy, &dxi_dy in &grid.detj_dxi_dy,
&ex in &y.0, &ex in &y.ex(),
&ey in &y.2) &ey in &y.ey())
*a = dxi_dx * -ey + dxi_dy * ex *a = dxi_dx * -ey + dxi_dy * ex
); );
SBP::diffxi(tmp.0.view(), tmp.1.view_mut()); SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
@ -133,13 +180,13 @@ impl System {
ndarray::azip!((b in &mut tmp.2, ndarray::azip!((b in &mut tmp.2,
&deta_dx in &grid.detj_deta_dx, &deta_dx in &grid.detj_deta_dx,
&deta_dy in &grid.detj_deta_dy, &deta_dy in &grid.detj_deta_dy,
&ex in &y.0, &ex in &y.ex(),
&ey in &y.2) &ey in &y.ey())
*b = deta_dx * -ey + deta_dy * ex *b = deta_dx * -ey + deta_dy * ex
); );
SBP::diffeta(tmp.2.view(), tmp.3.view_mut()); SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
ndarray::azip!((flux in &mut k[i].1, &ax in &tmp.1, &by in &tmp.3) ndarray::azip!((flux in &mut k[i].hz_mut(), &ax in &tmp.1, &by in &tmp.3)
*flux = ax + by *flux = ax + by
); );
} }
@ -148,26 +195,26 @@ impl System {
{ {
ndarray::azip!((a in &mut tmp.0, ndarray::azip!((a in &mut tmp.0,
&dxi_dx in &grid.detj_dxi_dx, &dxi_dx in &grid.detj_dxi_dx,
&hz in &y.1) &hz in &y.hz())
*a = dxi_dx * -hz *a = dxi_dx * -hz
); );
SBP::diffxi(tmp.0.view(), tmp.1.view_mut()); SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
ndarray::azip!((b in &mut tmp.2, azip!((b in &mut tmp.2,
&deta_dx in &grid.detj_deta_dx, &deta_dx in &grid.detj_deta_dx,
&hz in &y.1) &hz in &y.hz())
*b = deta_dx * -hz *b = deta_dx * -hz
); );
SBP::diffeta(tmp.2.view(), tmp.3.view_mut()); SBP::diffeta(tmp.2.view(), tmp.3.view_mut());
ndarray::azip!((flux in &mut k[i].2, &ax in &tmp.1, &by in &tmp.3) azip!((flux in &mut k[i].ey_mut(), &ax in &tmp.1, &by in &tmp.3)
*flux = ax + by *flux = ax + by
); );
} }
// Boundary conditions (SAT) // Boundary conditions (SAT)
let ny = y.0.shape()[0]; let ny = self.ny();
let nx = y.0.shape()[1]; let nx = self.nx();
let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32); let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
@ -191,25 +238,29 @@ impl System {
for j in 0..ny { for j in 0..ny {
// East boundary, positive flux // East boundary, positive flux
let tau = -1.0; let tau = -1.0;
let g = (y.0[(j, 0)], y.1[(j, 0)], y.2[(j, 0)]); let g = (y.ex()[(j, 0)], y.hz()[(j, 0)], y.ey()[(j, 0)]);
let v = (y.0[(j, nx - 1)], y.1[(j, nx - 1)], y.2[(j, nx - 1)]); let v = (
y.ex()[(j, nx - 1)],
y.hz()[(j, nx - 1)],
y.ey()[(j, nx - 1)],
);
let kx = grid.detj_dxi_dx[(j, nx - 1)]; let kx = grid.detj_dxi_dx[(j, nx - 1)];
let ky = grid.detj_dxi_dy[(j, nx - 1)]; let ky = grid.detj_dxi_dy[(j, nx - 1)];
let plus = positive_flux(kx, ky); let plus = positive_flux(kx, ky);
k[i].0[(j, nx - 1)] += tau k[i].ex_mut()[(j, nx - 1)] += tau
* hinv * hinv
* (plus[0][0] * (v.0 - g.0) * (plus[0][0] * (v.0 - g.0)
+ plus[0][1] * (v.1 - g.1) + plus[0][1] * (v.1 - g.1)
+ plus[0][2] * (v.2 - g.2)); + plus[0][2] * (v.2 - g.2));
k[i].1[(j, nx - 1)] += tau k[i].hz_mut()[(j, nx - 1)] += tau
* hinv * hinv
* (plus[1][0] * (v.0 - g.0) * (plus[1][0] * (v.0 - g.0)
+ plus[1][1] * (v.1 - g.1) + plus[1][1] * (v.1 - g.1)
+ plus[1][2] * (v.2 - g.2)); + plus[1][2] * (v.2 - g.2));
k[i].2[(j, nx - 1)] += tau k[i].ey_mut()[(j, nx - 1)] += tau
* hinv * hinv
* (plus[2][0] * (v.0 - g.0) * (plus[2][0] * (v.0 - g.0)
+ plus[2][1] * (v.1 - g.1) + plus[2][1] * (v.1 - g.1)
@ -224,17 +275,17 @@ impl System {
let minus = negative_flux(kx, ky); let minus = negative_flux(kx, ky);
k[i].0[(j, 0)] += tau k[i].ex_mut()[(j, 0)] += tau
* hinv * hinv
* (minus[0][0] * (v.0 - g.0) * (minus[0][0] * (v.0 - g.0)
+ minus[0][1] * (v.1 - g.1) + minus[0][1] * (v.1 - g.1)
+ minus[0][2] * (v.2 - g.2)); + minus[0][2] * (v.2 - g.2));
k[i].1[(j, 0)] += tau k[i].hz_mut()[(j, 0)] += tau
* hinv * hinv
* (minus[1][0] * (v.0 - g.0) * (minus[1][0] * (v.0 - g.0)
+ minus[1][1] * (v.1 - g.1) + minus[1][1] * (v.1 - g.1)
+ minus[1][2] * (v.2 - g.2)); + minus[1][2] * (v.2 - g.2));
k[i].2[(j, 0)] += tau k[i].ey_mut()[(j, 0)] += tau
* hinv * hinv
* (minus[2][0] * (v.0 - g.0) * (minus[2][0] * (v.0 - g.0)
+ minus[2][1] * (v.1 - g.1) + minus[2][1] * (v.1 - g.1)
@ -246,25 +297,29 @@ impl System {
for j in 0..nx { for j in 0..nx {
// North boundary, positive flux // North boundary, positive flux
let tau = -1.0; let tau = -1.0;
let g = (y.0[(0, j)], y.1[(0, j)], y.2[(0, j)]); let g = (y.ex()[(0, j)], y.hz()[(0, j)], y.ey()[(0, j)]);
let v = (y.0[(ny - 1, j)], y.1[(ny - 1, j)], y.2[(ny - 1, j)]); let v = (
y.ex()[(ny - 1, j)],
y.hz()[(ny - 1, j)],
y.ey()[(ny - 1, j)],
);
let kx = grid.detj_deta_dx[(ny - 1, j)]; let kx = grid.detj_deta_dx[(ny - 1, j)];
let ky = grid.detj_deta_dy[(ny - 1, j)]; let ky = grid.detj_deta_dy[(ny - 1, j)];
let plus = positive_flux(kx, ky); let plus = positive_flux(kx, ky);
k[i].0[(ny - 1, j)] += tau k[i].ex_mut()[(ny - 1, j)] += tau
* hinv * hinv
* (plus[0][0] * (v.0 - g.0) * (plus[0][0] * (v.0 - g.0)
+ plus[0][1] * (v.1 - g.1) + plus[0][1] * (v.1 - g.1)
+ plus[0][2] * (v.2 - g.2)); + plus[0][2] * (v.2 - g.2));
k[i].1[(ny - 1, j)] += tau k[i].hz_mut()[(ny - 1, j)] += tau
* hinv * hinv
* (plus[1][0] * (v.0 - g.0) * (plus[1][0] * (v.0 - g.0)
+ plus[1][1] * (v.1 - g.1) + plus[1][1] * (v.1 - g.1)
+ plus[1][2] * (v.2 - g.2)); + plus[1][2] * (v.2 - g.2));
k[i].2[(ny - 1, j)] += tau k[i].ey_mut()[(ny - 1, j)] += tau
* hinv * hinv
* (plus[2][0] * (v.0 - g.0) * (plus[2][0] * (v.0 - g.0)
+ plus[2][1] * (v.1 - g.1) + plus[2][1] * (v.1 - g.1)
@ -279,57 +334,35 @@ impl System {
let minus = negative_flux(kx, ky); let minus = negative_flux(kx, ky);
k[i].0[(0, j)] += tau k[i].ex_mut()[(0, j)] += tau
* hinv * hinv
* (minus[0][0] * (v.0 - g.0) * (minus[0][0] * (v.0 - g.0)
+ minus[0][1] * (v.1 - g.1) + minus[0][1] * (v.1 - g.1)
+ minus[0][2] * (v.2 - g.2)); + minus[0][2] * (v.2 - g.2));
k[i].1[(0, j)] += tau k[i].hz_mut()[(0, j)] += tau
* hinv * hinv
* (minus[1][0] * (v.0 - g.0) * (minus[1][0] * (v.0 - g.0)
+ minus[1][1] * (v.1 - g.1) + minus[1][1] * (v.1 - g.1)
+ minus[1][2] * (v.2 - g.2)); + minus[1][2] * (v.2 - g.2));
k[i].2[(0, j)] += tau k[i].ey_mut()[(0, j)] += tau
* hinv * hinv
* (minus[2][0] * (v.0 - g.0) * (minus[2][0] * (v.0 - g.0)
+ minus[2][1] * (v.1 - g.1) + minus[2][1] * (v.1 - g.1)
+ minus[2][2] * (v.2 - g.2)); + minus[2][2] * (v.2 - g.2));
} }
ndarray::azip!((k0 in &mut k[i].0, azip!((k in &mut k[i].0,
k1 in &mut k[i].1, &detj in &grid.detj.broadcast((3, ny, nx)).unwrap()) {
k2 in &mut k[i].2, *k /= detj;
&detj in &grid.detj) {
*k0 /= detj;
*k1 /= detj;
*k2 /= detj;
}); });
} }
Zip::from(&mut fut.ex) Zip::from(&mut fut.0)
.and(&self.ex) .and(&self.0)
.and(&k[0].0) .and(&*k[0])
.and(&k[1].0) .and(&*k[1])
.and(&k[2].0) .and(&*k[2])
.and(&k[3].0) .and(&*k[3])
.apply(|y1, &y0, &k1, &k2, &k3, &k4| {
*y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
});
Zip::from(&mut fut.hz)
.and(&self.hz)
.and(&k[0].1)
.and(&k[1].1)
.and(&k[2].1)
.and(&k[3].1)
.apply(|y1, &y0, &k1, &k2, &k3, &k4| {
*y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
});
Zip::from(&mut fut.ey)
.and(&self.ey)
.and(&k[0].2)
.and(&k[1].2)
.and(&k[2].2)
.and(&k[3].2)
.apply(|y1, &y0, &k1, &k2, &k3, &k4| { .apply(|y1, &y0, &k1, &k2, &k3, &k4| {
*y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4) *y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
}); });
@ -337,23 +370,19 @@ impl System {
} }
pub struct WorkBuffers { pub struct WorkBuffers {
y: (Array2<f32>, Array2<f32>, Array2<f32>), y: Field,
buf: [(Array2<f32>, Array2<f32>, Array2<f32>); 4], buf: [Field; 4],
tmp: (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>), tmp: (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
} }
impl WorkBuffers { impl WorkBuffers {
pub fn new(nx: usize, ny: usize) -> Self { pub fn new(nx: usize, ny: usize) -> Self {
let arr = Array2::zeros((ny, nx)); let arr2 = Array2::zeros((ny, nx));
let arr3 = Field::new(nx, ny);
Self { Self {
y: (arr.clone(), arr.clone(), arr.clone()), y: arr3.clone(),
buf: [ buf: [arr3.clone(), arr3.clone(), arr3.clone(), arr3],
(arr.clone(), arr.clone(), arr.clone()), tmp: (arr2.clone(), arr2.clone(), arr2.clone(), arr2),
(arr.clone(), arr.clone(), arr.clone()),
(arr.clone(), arr.clone(), arr.clone()),
(arr.clone(), arr.clone(), arr.clone()),
],
tmp: (arr.clone(), arr.clone(), arr.clone(), arr),
} }
} }
} }