2019-09-03 17:41:49 +00:00
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use super::operators::SbpOperator;
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2019-08-13 18:43:31 +00:00
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use ndarray::{Array2, Zip};
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pub struct System {
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pub(crate) ex: Array2<f32>,
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pub(crate) ey: Array2<f32>,
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pub(crate) hz: Array2<f32>,
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}
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fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 {
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use std::f32;
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let x = x - x0;
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let y = y - y0;
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let sigma = 0.05;
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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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impl System {
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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 ex = field.clone();
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let ey = field.clone();
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let hz = field;
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Self { ex, ey, hz }
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}
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pub fn set_gaussian(&mut self, x0: f32, y0: f32) {
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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.ex[(j, i)] = 0.0;
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self.ey[(j, i)] = 0.0;
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self.hz[(j, i)] = gaussian(x, x0, y, y0) / 32.0;
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}
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}
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}
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2019-11-07 19:41:49 +00:00
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pub fn advance<SBP>(&self, fut: &mut Self, dt: f32, work_buffers: Option<&mut WorkBuffers>)
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2019-09-03 17:41:49 +00:00
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where
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SBP: SbpOperator,
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{
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2019-08-13 18:43:31 +00:00
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assert_eq!(self.ex.shape(), fut.ex.shape());
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let mut wb: WorkBuffers;
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2019-11-07 19:41:49 +00:00
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let (y, k) = if let Some(x) = work_buffers {
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(&mut x.y, &mut x.buf)
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} else {
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wb = WorkBuffers::new(self.ex.shape()[1], self.ex.shape()[0]);
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(&mut wb.y, &mut wb.buf)
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2019-08-13 18:43:31 +00:00
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};
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for i in 0..4 {
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// y = y0 + c*kn
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y.0.assign(&self.ex);
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y.1.assign(&self.hz);
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y.2.assign(&self.ey);
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match i {
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0 => {}
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2019-11-07 19:41:49 +00:00
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1 | 2 => {
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2019-08-13 18:43:31 +00:00
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y.0.scaled_add(1.0 / 2.0 * dt, &k[i - 1].0);
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y.1.scaled_add(1.0 / 2.0 * dt, &k[i - 1].1);
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y.2.scaled_add(1.0 / 2.0 * dt, &k[i - 1].2);
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}
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3 => {
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y.0.scaled_add(dt, &k[i - 1].0);
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y.1.scaled_add(dt, &k[i - 1].1);
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y.2.scaled_add(dt, &k[i - 1].2);
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}
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_ => {
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unreachable!();
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}
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};
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2019-11-14 07:04:32 +00:00
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// hz = -ey_x + ex_y
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let tmp = &mut k[i].0;
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2019-12-08 20:00:47 +00:00
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SBP::diffxi(y.2.view(), tmp.view_mut());
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SBP::diffeta(y.0.view(), k[i].1.view_mut());
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2019-11-14 07:04:32 +00:00
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k[i].1.scaled_add(-1.0, tmp);
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2019-08-13 18:43:31 +00:00
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// ex = hz_y
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2019-12-08 20:00:47 +00:00
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SBP::diffeta(y.1.view(), k[i].0.view_mut());
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2019-08-13 18:43:31 +00:00
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// ey = -hz_x
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2019-12-08 20:00:47 +00:00
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SBP::diffxi(y.1.view(), k[i].2.view_mut());
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2019-08-13 18:43:31 +00:00
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k[i].2.mapv_inplace(|v| -v);
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2019-09-03 14:16:07 +00:00
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// Boundary conditions (SAT)
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2019-09-03 15:53:59 +00:00
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let ny = y.0.shape()[0];
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let nx = y.0.shape()[1];
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2019-09-03 16:17:00 +00:00
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2019-09-03 17:57:41 +00:00
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let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
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2019-09-03 14:16:07 +00:00
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for j in 0..ny {
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2019-09-03 18:26:07 +00:00
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// East boundary
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2019-09-03 15:53:59 +00:00
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let tau = -1.0;
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2019-09-03 14:16:07 +00:00
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let g = (y.0[(j, 0)], y.1[(j, 0)], y.2[(j, 0)]);
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let v = (y.0[(j, nx - 1)], y.1[(j, nx - 1)], y.2[(j, nx - 1)]);
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// A+ = (0, 0, 0; 0, 1/2, -1/2; 0, -1/2, 1/2);
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2019-09-03 18:26:07 +00:00
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// k[i].0[(j, nx - 1)] += 0.0;
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2019-09-03 15:53:59 +00:00
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k[i].1[(j, nx - 1)] += tau * hinv * (0.5 * (v.1 - g.1) - 0.5 * (v.2 - g.2));
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k[i].2[(j, nx - 1)] += tau * hinv * (-0.5 * (v.1 - g.1) + 0.5 * (v.2 - g.2));
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2019-09-03 14:16:07 +00:00
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2019-09-03 18:26:07 +00:00
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// West boundary
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let tau = 1.0;
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let (v, g) = (g, v);
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2019-09-03 14:16:07 +00:00
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// A- = (0, 0, 0; 0, -1/2, -1/2; 0, -1/2, -1/2);
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2019-09-03 18:26:07 +00:00
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// k[i].0[(j, 0)] += 0.0;
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2019-09-03 15:53:59 +00:00
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k[i].1[(j, 0)] += tau * hinv * (-0.5 * (v.1 - g.1) - 0.5 * (v.2 - g.2));
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k[i].2[(j, 0)] += tau * hinv * (-0.5 * (v.1 - g.1) - 0.5 * (v.2 - g.2));
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2019-09-03 14:16:07 +00:00
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}
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2019-09-03 16:17:00 +00:00
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2019-09-03 17:57:41 +00:00
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let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as f32);
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2019-09-03 16:17:00 +00:00
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for j in 0..nx {
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2019-09-03 18:26:07 +00:00
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// North boundary
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2019-09-03 16:17:00 +00:00
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let tau = -1.0;
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let g = (y.0[(0, j)], y.1[(0, j)], y.2[(0, j)]);
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let v = (y.0[(ny - 1, j)], y.1[(ny - 1, j)], y.2[(ny - 1, j)]);
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// B+ = (1/2, 1/2, 0; 1/2, 1/2, 0; 0, 0, 0)
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k[i].0[(ny - 1, j)] += tau * hinv * (0.5 * (v.0 - g.0) + 0.5 * (v.1 - g.1));
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k[i].1[(ny - 1, j)] += tau * hinv * (0.5 * (v.0 - g.0) + 0.5 * (v.1 - g.1));
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2019-09-03 18:26:07 +00:00
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// k[i].2[(ny - 1, j)] += 0.0;
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2019-09-03 16:17:00 +00:00
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2019-09-03 18:26:07 +00:00
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// South boundary
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2019-09-03 16:17:00 +00:00
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let tau = 1.0;
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2019-09-03 18:26:07 +00:00
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let (g, v) = (v, g);
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2019-09-03 16:17:00 +00:00
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// B- = (-1/2, 1/2, 0; 1/2, -1/2, 0; 0, 0, 0);
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k[i].0[(0, j)] += tau * hinv * (-0.5 * (v.0 - g.0) + 0.5 * (v.1 - g.1));
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k[i].1[(0, j)] += tau * hinv * (0.5 * (v.0 - g.0) - 0.5 * (v.1 - g.1));
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2019-09-03 18:26:07 +00:00
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// k[i].2[(0, j)] += 0.0;
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2019-09-03 16:17:00 +00:00
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}
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2019-08-13 18:43:31 +00:00
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}
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Zip::from(&mut fut.ex)
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.and(&self.ex)
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.and(&k[0].0)
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.and(&k[1].0)
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.and(&k[2].0)
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.and(&k[3].0)
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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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Zip::from(&mut fut.hz)
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.and(&self.hz)
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.and(&k[0].1)
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.and(&k[1].1)
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.and(&k[2].1)
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.and(&k[3].1)
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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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Zip::from(&mut fut.ey)
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.and(&self.ey)
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.and(&k[0].2)
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.and(&k[1].2)
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.and(&k[2].2)
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.and(&k[3].2)
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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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}
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pub struct WorkBuffers {
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y: (Array2<f32>, Array2<f32>, Array2<f32>),
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buf: [(Array2<f32>, Array2<f32>, Array2<f32>); 4],
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}
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impl WorkBuffers {
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pub fn new(nx: usize, ny: usize) -> Self {
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let arr = Array2::zeros((ny, nx));
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Self {
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y: (arr.clone(), arr.clone(), arr.clone()),
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buf: [
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(arr.clone(), arr.clone(), arr.clone()),
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(arr.clone(), arr.clone(), arr.clone()),
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(arr.clone(), arr.clone(), arr.clone()),
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(arr.clone(), arr.clone(), arr),
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],
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}
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}
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}
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