solve 1D maxwell (periodic)
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Magnus Ulimoen
parent
8d51e69607
commit
3ab7e532c6
194
src/lib.rs
194
src/lib.rs
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@ -10,9 +10,9 @@ static ALLOC: wee_alloc::WeeAlloc = wee_alloc::WeeAlloc::INIT;
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#[wasm_bindgen]
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pub struct Universe {
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e_x: Array2<f32>,
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ex: Array2<f32>,
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// e_y: Array2<f32>,
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// h_z: Array2<f32>,
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hz: Array2<f32>,
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}
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#[wasm_bindgen]
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@ -36,18 +36,29 @@ fn exponential(x: f32, y: f32, _t: f32) -> f32 {
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1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp()
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}
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fn gaussian(x: f32, y: f32, t: f32) -> f32 {
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use std::f32;
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let x = x - 0.5;
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let y = y - 0.5;
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let sigma = 0.05;
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1.0 / (2.0 * f32::consts::PI * sigma * sigma)
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* (-(x + y - t) * (x + y - t) / (2.0 * sigma * sigma)).exp()
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}
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#[wasm_bindgen]
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impl Universe {
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pub fn new(width: u32, height: u32) -> Self {
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let field = Array2::zeros((height as usize, width as usize));
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let e_x = field.clone();
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let ex = field.clone();
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// let e_y = field.clone();
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// let h_z = field.clone();
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let hz = field.clone();
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Universe {
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e_x,
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ex,
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// e_y,
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// h_z,
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hz,
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}
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}
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@ -55,133 +66,162 @@ impl Universe {
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let func = match selected_function {
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"sin+cos" => sin_plus_cos,
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"exp" => exponential,
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"gauss" => gaussian,
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_ => |_x: f32, _y: f32, _t: f32| 0.0,
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};
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let nx = self.e_x.shape()[1];
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let ny = self.e_x.shape()[0];
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let nx = self.ex.shape()[1];
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let ny = self.ex.shape()[0];
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for j in 0..ny {
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for i in 0..nx {
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// Must divice interval on nx/ny instead of nx - 1/ny-1
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// due to periodic conditions [0, 1)
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let x = i as f32 / nx as f32;
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let y = j as f32 / ny as f32;
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self.e_x[(j, i)] = func(x, y, t);
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self.ex[(j, i)] = func(x, y, t);
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self.hz[(j, i)] = -func(x, y, t);
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// self.e_y[(j as usize, i as usize)] = func(x, y, t);
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// self.h_z[(j as usize, i as usize)] = func(x, y, t);
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}
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}
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}
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pub fn advance(&self, fut: &mut Universe, dt: f32, work_buffers: Option<WorkBuffers>) {
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assert_eq!(self.e_x.shape(), fut.e_x.shape());
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assert_eq!(self.ex.shape(), fut.ex.shape());
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let mut y = self.e_x.clone();
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let mut y_ex = self.ex.clone();
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let mut y_hz = self.hz.clone();
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let mut buffers = work_buffers
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.unwrap_or_else(|| WorkBuffers::new(self.e_x.shape()[1], self.e_x.shape()[0]));
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.unwrap_or_else(|| WorkBuffers::new(self.ex.shape()[1], self.ex.shape()[0]));
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// y.assign(&self.e_x)
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let mut k0 = &mut buffers.k1; // Only need k0 for first step in RK
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k0.fill(0.0);
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diffx_periodic(y.view(), k0.view_mut());
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diffy_periodic(y.view(), k0.view_mut());
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let mut k0_ex = &mut buffers.k1_ex;
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let mut k0_hz = &mut buffers.k1_hz;
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k0_ex.fill(0.0);
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k0_hz.fill(0.0);
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// u_x
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diffx_periodic(y_ex.view(), k0_ex.view_mut());
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diffx_periodic(y_hz.view(), k0_hz.view_mut());
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// y.assign(&self.e_x);
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y.scaled_add(-1.0 / 2.0 * dt, &k0);
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let mut k1 = buffers.k1;
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k1.fill(0.0);
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diffx_periodic(y.view(), k1.view_mut());
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diffy_periodic(y.view(), k1.view_mut());
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// y = y + 1/2*dt Au_x
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y_ex.scaled_add(1.0 / 2.0 * dt, &k0_hz);
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y_hz.scaled_add(1.0 / 2.0 * dt, &k0_ex);
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let mut k1_ex = buffers.k1_ex;
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let mut k1_hz = buffers.k1_hz;
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k1_ex.fill(0.0);
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k1_hz.fill(0.0);
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diffx_periodic(y_ex.view(), k1_ex.view_mut());
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diffx_periodic(y_hz.view(), k1_hz.view_mut());
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y.assign(&self.e_x);
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y.scaled_add(-1.0 / 2.0 * dt, &k1);
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let mut k2 = buffers.k2;
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k2.fill(0.0);
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diffx_periodic(y.view(), k2.view_mut());
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diffy_periodic(y.view(), k2.view_mut());
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y_ex.assign(&self.ex);
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y_hz.assign(&self.hz);
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y_ex.scaled_add(1.0 / 2.0 * dt, &k1_hz);
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y_hz.scaled_add(1.0 / 2.0 * dt, &k1_ex);
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let mut k2_ex = buffers.k2_ex;
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let mut k2_hz = buffers.k2_hz;
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k2_ex.fill(0.0);
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k2_hz.fill(0.0);
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diffx_periodic(y_ex.view(), k2_ex.view_mut());
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diffx_periodic(y_hz.view(), k2_hz.view_mut());
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y.assign(&self.e_x);
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y.scaled_add(-1.0 / 2.0 * dt, &k2);
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let mut k3 = buffers.k3;
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k3.fill(0.0);
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diffx_periodic(y.view(), k3.view_mut());
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diffy_periodic(y.view(), k3.view_mut());
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// y = y0
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y_ex.assign(&self.ex);
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y_hz.assign(&self.hz);
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y_ex.scaled_add(1.0 / 2.0 * dt, &k2_hz);
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y_hz.scaled_add(1.0 / 2.0 * dt, &k2_ex);
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let mut k3_ex = buffers.k3_ex;
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let mut k3_hz = buffers.k3_hz;
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k3_ex.fill(0.0);
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k3_hz.fill(0.0);
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diffx_periodic(y_ex.view(), k3_ex.view_mut());
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diffx_periodic(y_hz.view(), k3_hz.view_mut());
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y.assign(&self.e_x);
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y.scaled_add(-dt, &k2);
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let mut k4 = buffers.k4;
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k4.fill(0.0);
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diffx_periodic(y.view(), k4.view_mut());
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diffy_periodic(y.view(), k4.view_mut());
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y_ex.assign(&self.ex);
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y_hz.assign(&self.hz);
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y_ex.scaled_add(dt, &k2_hz);
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y_hz.scaled_add(dt, &k2_ex);
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let mut k4_ex = buffers.k4_ex;
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let mut k4_hz = buffers.k4_hz;
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k4_ex.fill(0.0);
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k4_hz.fill(0.0);
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diffx_periodic(y_ex.view(), k4_ex.view_mut());
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diffx_periodic(y_hz.view(), k4_hz.view_mut());
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Zip::from(&mut fut.e_x)
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.and(&self.e_x)
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.and(&k1)
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.and(&k2)
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.and(&k3)
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.and(&k4)
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Zip::from(&mut fut.ex)
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.and(&self.ex)
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.and(&k1_hz)
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.and(&k2_hz)
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.and(&k3_hz)
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.and(&k4_hz)
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.apply(|y1, &y0, &k1, &k2, &k3, &k4| {
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*y1 = y0 + -dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
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*y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
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});
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Zip::from(&mut fut.hz)
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.and(&self.hz)
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.and(&k1_ex)
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.and(&k2_ex)
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.and(&k3_ex)
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.and(&k4_ex)
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.apply(|y1, &y0, &k1, &k2, &k3, &k4| {
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*y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
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});
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}
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pub fn advance_upwind(&self, fut: &mut Universe, dt: f32) {
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assert_eq!(self.e_x.dim(), fut.e_x.dim());
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assert_eq!(self.ex.dim(), fut.ex.dim());
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let mut ad = Array2::zeros(fut.e_x.dim());
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let mut y = self.e_x.clone();
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let mut ad = Array2::zeros(fut.ex.dim());
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let mut y = self.ex.clone();
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// y.assign(&self.e_x)
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// y.assign(&self.ex)
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// ad.fill(0.0);
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let mut k0 = Array2::zeros(self.e_x.dim());
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let mut k0 = Array2::zeros(self.ex.dim());
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diffx(y.view(), k0.view_mut());
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diffy(y.view(), k0.view_mut());
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dissx(y.view(), ad.view_mut());
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dissy(y.view(), ad.view_mut());
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k0.scaled_add(-0.5, &ad);
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// y.assign(&self.e_x);
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// y.assign(&self.ex);
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ad.fill(0.0);
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y.scaled_add(-1.0 / 2.0 * dt, &k0);
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let mut k1 = Array2::zeros(self.e_x.dim());
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let mut k1 = Array2::zeros(self.ex.dim());
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diffx(y.view(), k1.view_mut());
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diffy(y.view(), k1.view_mut());
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dissx(y.view(), ad.view_mut());
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dissy(y.view(), ad.view_mut());
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k1.scaled_add(-0.5, &ad);
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y.assign(&self.e_x);
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y.assign(&self.ex);
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ad.fill(0.0);
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y.scaled_add(-1.0 / 2.0 * dt, &k1);
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let mut k2 = Array2::zeros(self.e_x.dim());
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let mut k2 = Array2::zeros(self.ex.dim());
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diffx(y.view(), k2.view_mut());
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diffy(y.view(), k2.view_mut());
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dissx(y.view(), ad.view_mut());
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dissy(y.view(), ad.view_mut());
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k2.scaled_add(-0.5, &ad);
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y.assign(&self.e_x);
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y.assign(&self.ex);
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ad.fill(0.0);
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y.scaled_add(-1.0 / 2.0 * dt, &k2);
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let mut k3 = Array2::zeros(self.e_x.dim());
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let mut k3 = Array2::zeros(self.ex.dim());
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diffx(y.view(), k3.view_mut());
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diffy(y.view(), k3.view_mut());
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dissx(y.view(), ad.view_mut());
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dissy(y.view(), ad.view_mut());
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k3.scaled_add(-0.5, &ad);
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y.assign(&self.e_x);
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y.assign(&self.ex);
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ad.fill(0.0);
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y.scaled_add(-dt, &k2);
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let mut k4 = Array2::zeros(self.e_x.dim());
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let mut k4 = Array2::zeros(self.ex.dim());
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diffx(y.view(), k4.view_mut());
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diffy(y.view(), k4.view_mut());
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dissx(y.view(), ad.view_mut());
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dissy(y.view(), ad.view_mut());
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k4.scaled_add(-0.5, &ad);
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Zip::from(&mut fut.e_x)
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.and(&self.e_x)
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Zip::from(&mut fut.ex)
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.and(&self.ex)
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.and(&k1)
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.and(&k2)
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.and(&k3)
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@ -192,26 +232,34 @@ impl Universe {
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}
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pub fn get_ptr(&mut self) -> *mut u8 {
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self.e_x.as_mut_ptr() as *mut u8
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self.ex.as_mut_ptr() as *mut u8
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}
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}
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#[wasm_bindgen]
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pub struct WorkBuffers {
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k1: Array2<f32>,
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k2: Array2<f32>,
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k3: Array2<f32>,
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k4: Array2<f32>,
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k1_ex: Array2<f32>,
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k1_hz: Array2<f32>,
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k2_ex: Array2<f32>,
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k2_hz: Array2<f32>,
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k3_ex: Array2<f32>,
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k3_hz: Array2<f32>,
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k4_ex: Array2<f32>,
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k4_hz: Array2<f32>,
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}
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#[wasm_bindgen]
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impl WorkBuffers {
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pub fn new(nx: usize, ny: usize) -> Self {
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Self {
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k1: Array2::zeros((ny, nx)),
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k2: Array2::zeros((ny, nx)),
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k3: Array2::zeros((ny, nx)),
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k4: Array2::zeros((ny, nx)),
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k1_ex: Array2::zeros((ny, nx)),
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k1_hz: Array2::zeros((ny, nx)),
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k2_ex: Array2::zeros((ny, nx)),
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k2_hz: Array2::zeros((ny, nx)),
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k3_ex: Array2::zeros((ny, nx)),
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k3_hz: Array2::zeros((ny, nx)),
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k4_ex: Array2::zeros((ny, nx)),
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k4_hz: Array2::zeros((ny, nx)),
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}
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}
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}
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