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use 3d fields

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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
View File

@@ -13,7 +13,14 @@ fn performance_benchmark(c: &mut Criterion) {
let w = 40;
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| {
b.iter(|| {

23
src/lib.rs
View File

@@ -3,7 +3,7 @@ use wasm_bindgen::prelude::*;
mod grid;
mod maxwell;
mod operators;
pub use crate::maxwell::{System, WorkBuffers};
pub use crate::maxwell::{Field, WorkBuffers};
pub(crate) use grid::Grid;
#[cfg(feature = "wee_alloc")]
@@ -18,7 +18,7 @@ pub fn set_panic_hook() {
#[wasm_bindgen]
pub struct Universe {
sys: (System, System),
sys: (Field, Field),
wb: WorkBuffers,
grid: Grid<operators::Upwind4>,
}
@@ -34,7 +34,10 @@ impl Universe {
"Could not create grid. Different number of elements compared to width*height?",
);
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,
wb: WorkBuffers::new(width as usize, height as usize),
}
@@ -45,7 +48,7 @@ impl Universe {
}
pub fn advance(&mut self, dt: f32) {
System::advance::<operators::Upwind4>(
Field::advance::<operators::Upwind4>(
&self.sys.0,
&mut self.sys.1,
dt,
@@ -55,15 +58,15 @@ impl Universe {
std::mem::swap(&mut self.sys.0, &mut self.sys.1);
}
pub fn get_ex_ptr(&mut self) -> *mut u8 {
self.sys.0.ex.as_mut_ptr() as *mut u8
pub fn get_ex_ptr(&self) -> *const u8 {
self.sys.0.ex().as_ptr() as *const u8
}
pub fn get_ey_ptr(&mut self) -> *mut u8 {
self.sys.0.ey.as_mut_ptr() as *mut u8
pub fn get_ey_ptr(&self) -> *const u8 {
self.sys.0.ey().as_ptr() as *const u8
}
pub fn get_hz_ptr(&mut self) -> *mut u8 {
self.sys.0.hz.as_mut_ptr() as *mut u8
pub fn get_hz_ptr(&self) -> *const 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 ndarray::{Array2, Zip};
use ndarray::prelude::*;
use ndarray::{azip, Zip};
pub struct System {
pub(crate) ex: Array2<f32>,
pub(crate) ey: Array2<f32>,
pub(crate) hz: Array2<f32>,
#[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
}
}
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()
}
impl System {
pub fn new(width: u32, height: u32) -> Self {
let field = Array2::zeros((height as usize, width as usize));
let ex = field.clone();
let ey = field.clone();
let hz = field;
impl Field {
pub fn new(width: usize, height: usize) -> Self {
let field = Array3::zeros((3, height, width));
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) {
let nx = self.ex.shape()[1];
let ny = self.ex.shape()[0];
let nx = self.nx();
let ny = self.ny();
let (mut ex, mut hz, mut ey) = self.components_mut();
for j in 0..ny {
for i in 0..nx {
// Must divice interval on nx/ny instead of nx - 1/ny-1
// due to periodic conditions [0, 1)
let x = i as f32 / nx as f32;
let y = j as f32 / ny as f32;
self.ex[(j, i)] = 0.0;
self.ey[(j, i)] = 0.0;
self.hz[(j, i)] = gaussian(x, x0, y, y0) / 32.0;
ex[(j, i)] = 0.0;
ey[(j, i)] = 0.0;
hz[(j, i)] = gaussian(x, x0, y, y0) / 32.0;
}
}
}
@@ -52,32 +105,26 @@ impl System {
) where
SBP: SbpOperator,
{
assert_eq!(self.ex.shape(), fut.ex.shape());
assert_eq!(self.0.shape(), fut.0.shape());
let mut wb: WorkBuffers;
let (y, k, tmp) = if let Some(x) = work_buffers {
(&mut x.y, &mut x.buf, &mut x.tmp)
} 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)
};
for i in 0..4 {
// y = y0 + c*kn
y.0.assign(&self.ex);
y.1.assign(&self.hz);
y.2.assign(&self.ey);
y.assign(&self);
match i {
0 => {}
1 | 2 => {
y.0.scaled_add(1.0 / 2.0 * dt, &k[i - 1].0);
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);
y.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
}
3 => {
y.0.scaled_add(dt, &k[i - 1].0);
y.1.scaled_add(dt, &k[i - 1].1);
y.2.scaled_add(dt, &k[i - 1].2);
y.scaled_add(dt, &k[i - 1]);
}
_ => {
unreachable!();
@@ -102,19 +149,19 @@ impl System {
{
ndarray::azip!((a in &mut tmp.0,
&dxi_dy in &grid.detj_dxi_dy,
&hz in &y.1)
&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.1)
&hz in &y.hz())
*b = deta_dy * hz
);
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
);
}
@@ -124,8 +171,8 @@ impl System {
ndarray::azip!((a in &mut tmp.0,
&dxi_dx in &grid.detj_dxi_dx,
&dxi_dy in &grid.detj_dxi_dy,
&ex in &y.0,
&ey in &y.2)
&ex in &y.ex(),
&ey in &y.ey())
*a = dxi_dx * -ey + dxi_dy * ex
);
SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
@@ -133,13 +180,13 @@ impl System {
ndarray::azip!((b in &mut tmp.2,
&deta_dx in &grid.detj_deta_dx,
&deta_dy in &grid.detj_deta_dy,
&ex in &y.0,
&ey in &y.2)
&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[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
);
}
@@ -148,26 +195,26 @@ impl System {
{
ndarray::azip!((a in &mut tmp.0,
&dxi_dx in &grid.detj_dxi_dx,
&hz in &y.1)
&hz in &y.hz())
*a = dxi_dx * -hz
);
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,
&hz in &y.1)
&hz in &y.hz())
*b = deta_dx * -hz
);
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
);
}
// Boundary conditions (SAT)
let ny = y.0.shape()[0];
let nx = y.0.shape()[1];
let ny = self.ny();
let nx = self.nx();
let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
@@ -191,25 +238,29 @@ impl System {
for j in 0..ny {
// East boundary, positive flux
let tau = -1.0;
let g = (y.0[(j, 0)], y.1[(j, 0)], y.2[(j, 0)]);
let v = (y.0[(j, nx - 1)], y.1[(j, nx - 1)], y.2[(j, nx - 1)]);
let g = (y.ex()[(j, 0)], y.hz()[(j, 0)], y.ey()[(j, 0)]);
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 ky = grid.detj_dxi_dy[(j, nx - 1)];
let plus = positive_flux(kx, ky);
k[i].0[(j, nx - 1)] += tau
k[i].ex_mut()[(j, nx - 1)] += tau
* hinv
* (plus[0][0] * (v.0 - g.0)
+ plus[0][1] * (v.1 - g.1)
+ plus[0][2] * (v.2 - g.2));
k[i].1[(j, nx - 1)] += tau
k[i].hz_mut()[(j, nx - 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[i].2[(j, nx - 1)] += tau
k[i].ey_mut()[(j, nx - 1)] += tau
* hinv
* (plus[2][0] * (v.0 - g.0)
+ plus[2][1] * (v.1 - g.1)
@@ -224,17 +275,17 @@ impl System {
let minus = negative_flux(kx, ky);
k[i].0[(j, 0)] += tau
k[i].ex_mut()[(j, 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[i].1[(j, 0)] += tau
k[i].hz_mut()[(j, 0)] += tau
* hinv
* (minus[1][0] * (v.0 - g.0)
+ minus[1][1] * (v.1 - g.1)
+ minus[1][2] * (v.2 - g.2));
k[i].2[(j, 0)] += tau
k[i].ey_mut()[(j, 0)] += tau
* hinv
* (minus[2][0] * (v.0 - g.0)
+ minus[2][1] * (v.1 - g.1)
@@ -246,25 +297,29 @@ impl System {
for j in 0..nx {
// North boundary, positive flux
let tau = -1.0;
let g = (y.0[(0, j)], y.1[(0, j)], y.2[(0, j)]);
let v = (y.0[(ny - 1, j)], y.1[(ny - 1, j)], y.2[(ny - 1, j)]);
let g = (y.ex()[(0, j)], y.hz()[(0, j)], y.ey()[(0, 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 ky = grid.detj_deta_dy[(ny - 1, j)];
let plus = positive_flux(kx, ky);
k[i].0[(ny - 1, j)] += tau
k[i].ex_mut()[(ny - 1, j)] += tau
* hinv
* (plus[0][0] * (v.0 - g.0)
+ plus[0][1] * (v.1 - g.1)
+ plus[0][2] * (v.2 - g.2));
k[i].1[(ny - 1, j)] += tau
k[i].hz_mut()[(ny - 1, j)] += tau
* hinv
* (plus[1][0] * (v.0 - g.0)
+ plus[1][1] * (v.1 - g.1)
+ plus[1][2] * (v.2 - g.2));
k[i].2[(ny - 1, j)] += tau
k[i].ey_mut()[(ny - 1, j)] += tau
* hinv
* (plus[2][0] * (v.0 - g.0)
+ plus[2][1] * (v.1 - g.1)
@@ -279,57 +334,35 @@ impl System {
let minus = negative_flux(kx, ky);
k[i].0[(0, j)] += tau
k[i].ex_mut()[(0, j)] += tau
* hinv
* (minus[0][0] * (v.0 - g.0)
+ minus[0][1] * (v.1 - g.1)
+ minus[0][2] * (v.2 - g.2));
k[i].1[(0, j)] += tau
k[i].hz_mut()[(0, j)] += tau
* hinv
* (minus[1][0] * (v.0 - g.0)
+ minus[1][1] * (v.1 - g.1)
+ minus[1][2] * (v.2 - g.2));
k[i].2[(0, j)] += tau
k[i].ey_mut()[(0, j)] += tau
* hinv
* (minus[2][0] * (v.0 - g.0)
+ minus[2][1] * (v.1 - g.1)
+ minus[2][2] * (v.2 - g.2));
}
ndarray::azip!((k0 in &mut k[i].0,
k1 in &mut k[i].1,
k2 in &mut k[i].2,
&detj in &grid.detj) {
*k0 /= detj;
*k1 /= detj;
*k2 /= detj;
azip!((k in &mut k[i].0,
&detj in &grid.detj.broadcast((3, ny, nx)).unwrap()) {
*k /= detj;
});
}
Zip::from(&mut fut.ex)
.and(&self.ex)
.and(&k[0].0)
.and(&k[1].0)
.and(&k[2].0)
.and(&k[3].0)
.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)
Zip::from(&mut fut.0)
.and(&self.0)
.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)
});
@@ -337,23 +370,19 @@ impl System {
}
pub struct WorkBuffers {
y: (Array2<f32>, Array2<f32>, Array2<f32>),
buf: [(Array2<f32>, Array2<f32>, Array2<f32>); 4],
y: Field,
buf: [Field; 4],
tmp: (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
}
impl WorkBuffers {
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 {
y: (arr.clone(), arr.clone(), arr.clone()),
buf: [
(arr.clone(), arr.clone(), arr.clone()),
(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),
y: arr3.clone(),
buf: [arr3.clone(), arr3.clone(), arr3.clone(), arr3],
tmp: (arr2.clone(), arr2.clone(), arr2.clone(), arr2),
}
}
}