mulimoen/SummationByParts
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

solve 1D maxwell (periodic)

Browse Source
This commit is contained in:
Magnus Ulimoen
2019-08-09 17:46:59 +02:00
parent 8d51e69607
commit 3ab7e532c6
1 changed files with 121 additions and 73 deletions
Download Patch File Download Diff File Expand all files Collapse all files

194
src/lib.rs
View File

@@ -10,9 +10,9 @@ static ALLOC: wee_alloc::WeeAlloc = wee_alloc::WeeAlloc::INIT;
#[wasm_bindgen]
pub struct Universe {
e_x: Array2<f32>,
ex: Array2<f32>,
// e_y: Array2<f32>,
// h_z: Array2<f32>,
hz: Array2<f32>,
}
#[wasm_bindgen]
@@ -36,18 +36,29 @@ fn exponential(x: f32, y: f32, _t: f32) -> f32 {
1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp()
}
fn gaussian(x: f32, y: f32, t: f32) -> f32 {
use std::f32;
let x = x - 0.5;
let y = y - 0.5;
let sigma = 0.05;
1.0 / (2.0 * f32::consts::PI * sigma * sigma)
* (-(x + y - t) * (x + y - t) / (2.0 * sigma * sigma)).exp()
}
#[wasm_bindgen]
impl Universe {
pub fn new(width: u32, height: u32) -> Self {
let field = Array2::zeros((height as usize, width as usize));
let e_x = field.clone();
let ex = field.clone();
// let e_y = field.clone();
// let h_z = field.clone();
let hz = field.clone();
Universe {
e_x,
ex,
// e_y,
// h_z,
hz,
}
}
@@ -55,133 +66,162 @@ impl Universe {
let func = match selected_function {
"sin+cos" => sin_plus_cos,
"exp" => exponential,
"gauss" => gaussian,
_ => |_x: f32, _y: f32, _t: f32| 0.0,
};
let nx = self.e_x.shape()[1];
let ny = self.e_x.shape()[0];
let nx = self.ex.shape()[1];
let ny = self.ex.shape()[0];
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.e_x[(j, i)] = func(x, y, t);
self.ex[(j, i)] = func(x, y, t);
self.hz[(j, i)] = -func(x, y, t);
// self.e_y[(j as usize, i as usize)] = func(x, y, t);
// self.h_z[(j as usize, i as usize)] = func(x, y, t);
}
}
}
pub fn advance(&self, fut: &mut Universe, dt: f32, work_buffers: Option<WorkBuffers>) {
assert_eq!(self.e_x.shape(), fut.e_x.shape());
assert_eq!(self.ex.shape(), fut.ex.shape());
let mut y = self.e_x.clone();
let mut y_ex = self.ex.clone();
let mut y_hz = self.hz.clone();
let mut buffers = work_buffers
.unwrap_or_else(|| WorkBuffers::new(self.e_x.shape()[1], self.e_x.shape()[0]));
.unwrap_or_else(|| WorkBuffers::new(self.ex.shape()[1], self.ex.shape()[0]));
// y.assign(&self.e_x)
let mut k0 = &mut buffers.k1; // Only need k0 for first step in RK
k0.fill(0.0);
diffx_periodic(y.view(), k0.view_mut());
diffy_periodic(y.view(), k0.view_mut());
let mut k0_ex = &mut buffers.k1_ex;
let mut k0_hz = &mut buffers.k1_hz;
k0_ex.fill(0.0);
k0_hz.fill(0.0);
// u_x
diffx_periodic(y_ex.view(), k0_ex.view_mut());
diffx_periodic(y_hz.view(), k0_hz.view_mut());
// y.assign(&self.e_x);
y.scaled_add(-1.0 / 2.0 * dt, &k0);
let mut k1 = buffers.k1;
k1.fill(0.0);
diffx_periodic(y.view(), k1.view_mut());
diffy_periodic(y.view(), k1.view_mut());
// y = y + 1/2*dt Au_x
y_ex.scaled_add(1.0 / 2.0 * dt, &k0_hz);
y_hz.scaled_add(1.0 / 2.0 * dt, &k0_ex);
let mut k1_ex = buffers.k1_ex;
let mut k1_hz = buffers.k1_hz;
k1_ex.fill(0.0);
k1_hz.fill(0.0);
diffx_periodic(y_ex.view(), k1_ex.view_mut());
diffx_periodic(y_hz.view(), k1_hz.view_mut());
y.assign(&self.e_x);
y.scaled_add(-1.0 / 2.0 * dt, &k1);
let mut k2 = buffers.k2;
k2.fill(0.0);
diffx_periodic(y.view(), k2.view_mut());
diffy_periodic(y.view(), k2.view_mut());
y_ex.assign(&self.ex);
y_hz.assign(&self.hz);
y_ex.scaled_add(1.0 / 2.0 * dt, &k1_hz);
y_hz.scaled_add(1.0 / 2.0 * dt, &k1_ex);
let mut k2_ex = buffers.k2_ex;
let mut k2_hz = buffers.k2_hz;
k2_ex.fill(0.0);
k2_hz.fill(0.0);
diffx_periodic(y_ex.view(), k2_ex.view_mut());
diffx_periodic(y_hz.view(), k2_hz.view_mut());
y.assign(&self.e_x);
y.scaled_add(-1.0 / 2.0 * dt, &k2);
let mut k3 = buffers.k3;
k3.fill(0.0);
diffx_periodic(y.view(), k3.view_mut());
diffy_periodic(y.view(), k3.view_mut());
// y = y0
y_ex.assign(&self.ex);
y_hz.assign(&self.hz);
y_ex.scaled_add(1.0 / 2.0 * dt, &k2_hz);
y_hz.scaled_add(1.0 / 2.0 * dt, &k2_ex);
let mut k3_ex = buffers.k3_ex;
let mut k3_hz = buffers.k3_hz;
k3_ex.fill(0.0);
k3_hz.fill(0.0);
diffx_periodic(y_ex.view(), k3_ex.view_mut());
diffx_periodic(y_hz.view(), k3_hz.view_mut());
y.assign(&self.e_x);
y.scaled_add(-dt, &k2);
let mut k4 = buffers.k4;
k4.fill(0.0);
diffx_periodic(y.view(), k4.view_mut());
diffy_periodic(y.view(), k4.view_mut());
y_ex.assign(&self.ex);
y_hz.assign(&self.hz);
y_ex.scaled_add(dt, &k2_hz);
y_hz.scaled_add(dt, &k2_ex);
let mut k4_ex = buffers.k4_ex;
let mut k4_hz = buffers.k4_hz;
k4_ex.fill(0.0);
k4_hz.fill(0.0);
diffx_periodic(y_ex.view(), k4_ex.view_mut());
diffx_periodic(y_hz.view(), k4_hz.view_mut());
Zip::from(&mut fut.e_x)
.and(&self.e_x)
.and(&k1)
.and(&k2)
.and(&k3)
.and(&k4)
Zip::from(&mut fut.ex)
.and(&self.ex)
.and(&k1_hz)
.and(&k2_hz)
.and(&k3_hz)
.and(&k4_hz)
.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)
});
Zip::from(&mut fut.hz)
.and(&self.hz)
.and(&k1_ex)
.and(&k2_ex)
.and(&k3_ex)
.and(&k4_ex)
.apply(|y1, &y0, &k1, &k2, &k3, &k4| {
*y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
});
}
pub fn advance_upwind(&self, fut: &mut Universe, dt: f32) {
assert_eq!(self.e_x.dim(), fut.e_x.dim());
assert_eq!(self.ex.dim(), fut.ex.dim());
let mut ad = Array2::zeros(fut.e_x.dim());
let mut y = self.e_x.clone();
let mut ad = Array2::zeros(fut.ex.dim());
let mut y = self.ex.clone();
// y.assign(&self.e_x)
// y.assign(&self.ex)
// ad.fill(0.0);
let mut k0 = Array2::zeros(self.e_x.dim());
let mut k0 = Array2::zeros(self.ex.dim());
diffx(y.view(), k0.view_mut());
diffy(y.view(), k0.view_mut());
dissx(y.view(), ad.view_mut());
dissy(y.view(), ad.view_mut());
k0.scaled_add(-0.5, &ad);
// y.assign(&self.e_x);
// y.assign(&self.ex);
ad.fill(0.0);
y.scaled_add(-1.0 / 2.0 * dt, &k0);
let mut k1 = Array2::zeros(self.e_x.dim());
let mut k1 = Array2::zeros(self.ex.dim());
diffx(y.view(), k1.view_mut());
diffy(y.view(), k1.view_mut());
dissx(y.view(), ad.view_mut());
dissy(y.view(), ad.view_mut());
k1.scaled_add(-0.5, &ad);
y.assign(&self.e_x);
y.assign(&self.ex);
ad.fill(0.0);
y.scaled_add(-1.0 / 2.0 * dt, &k1);
let mut k2 = Array2::zeros(self.e_x.dim());
let mut k2 = Array2::zeros(self.ex.dim());
diffx(y.view(), k2.view_mut());
diffy(y.view(), k2.view_mut());
dissx(y.view(), ad.view_mut());
dissy(y.view(), ad.view_mut());
k2.scaled_add(-0.5, &ad);
y.assign(&self.e_x);
y.assign(&self.ex);
ad.fill(0.0);
y.scaled_add(-1.0 / 2.0 * dt, &k2);
let mut k3 = Array2::zeros(self.e_x.dim());
let mut k3 = Array2::zeros(self.ex.dim());
diffx(y.view(), k3.view_mut());
diffy(y.view(), k3.view_mut());
dissx(y.view(), ad.view_mut());
dissy(y.view(), ad.view_mut());
k3.scaled_add(-0.5, &ad);
y.assign(&self.e_x);
y.assign(&self.ex);
ad.fill(0.0);
y.scaled_add(-dt, &k2);
let mut k4 = Array2::zeros(self.e_x.dim());
let mut k4 = Array2::zeros(self.ex.dim());
diffx(y.view(), k4.view_mut());
diffy(y.view(), k4.view_mut());
dissx(y.view(), ad.view_mut());
dissy(y.view(), ad.view_mut());
k4.scaled_add(-0.5, &ad);
Zip::from(&mut fut.e_x)
.and(&self.e_x)
Zip::from(&mut fut.ex)
.and(&self.ex)
.and(&k1)
.and(&k2)
.and(&k3)
@@ -192,26 +232,34 @@ impl Universe {
}
pub fn get_ptr(&mut self) -> *mut u8 {
self.e_x.as_mut_ptr() as *mut u8
self.ex.as_mut_ptr() as *mut u8
}
}
#[wasm_bindgen]
pub struct WorkBuffers {
k1: Array2<f32>,
k2: Array2<f32>,
k3: Array2<f32>,
k4: Array2<f32>,
k1_ex: Array2<f32>,
k1_hz: Array2<f32>,
k2_ex: Array2<f32>,
k2_hz: Array2<f32>,
k3_ex: Array2<f32>,
k3_hz: Array2<f32>,
k4_ex: Array2<f32>,
k4_hz: Array2<f32>,
}
#[wasm_bindgen]
impl WorkBuffers {
pub fn new(nx: usize, ny: usize) -> Self {
Self {
k1: Array2::zeros((ny, nx)),
k2: Array2::zeros((ny, nx)),
k3: Array2::zeros((ny, nx)),
k4: Array2::zeros((ny, nx)),
k1_ex: Array2::zeros((ny, nx)),
k1_hz: Array2::zeros((ny, nx)),
k2_ex: Array2::zeros((ny, nx)),
k2_hz: Array2::zeros((ny, nx)),
k3_ex: Array2::zeros((ny, nx)),
k3_hz: Array2::zeros((ny, nx)),
k4_ex: Array2::zeros((ny, nx)),
k4_hz: Array2::zeros((ny, nx)),
}
}
}