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arbitrary grids

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This commit is contained in:
Magnus Ulimoen
2019-12-10 22:03:42 +01:00
parent 18969babb5
commit 7430e8793e
4 changed files with 295 additions and 36 deletions
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68
src/grid.rs Normal file
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@@ -0,0 +1,68 @@
use ndarray::Array2;
pub struct Grid<SBP>
where
SBP: super::operators::SbpOperator,
{
pub(crate) x: Array2<f32>,
pub(crate) y: Array2<f32>,
pub(crate) detj: Array2<f32>,
pub(crate) detj_dxi_dx: Array2<f32>,
pub(crate) detj_dxi_dy: Array2<f32>,
pub(crate) detj_deta_dx: Array2<f32>,
pub(crate) detj_deta_dy: Array2<f32>,
operator: std::marker::PhantomData<SBP>,
}
impl<SBP: super::operators::SbpOperator> Grid<SBP> {
pub fn new(width: u32, height: u32, x: &[f32], y: &[f32]) -> Result<Self, ndarray::ShapeError> {
let nx = width as usize;
let ny = height as usize;
let x = Array2::from_shape_vec((ny, nx), x.to_vec())?;
let y = Array2::from_shape_vec((ny, nx), y.to_vec())?;
let mut dx_dxi = Array2::zeros((ny, nx));
SBP::diffxi(x.view(), dx_dxi.view_mut());
let mut dx_deta = Array2::zeros((ny, nx));
SBP::diffeta(x.view(), dx_deta.view_mut());
let mut dy_dxi = Array2::zeros((ny, nx));
SBP::diffxi(y.view(), dy_dxi.view_mut());
let mut dy_deta = Array2::zeros((ny, nx));
SBP::diffeta(y.view(), dy_deta.view_mut());
let mut detj = Array2::zeros((ny, nx));
ndarray::azip!((detj in &mut detj,
&dx_dxi in &dx_dxi,
&dx_deta in &dx_deta,
&dy_dxi in &dy_dxi,
&dy_deta in &dy_deta) {
*detj = dx_dxi * dy_deta - dx_deta * dy_dxi;
assert!(*detj > 0.0);
});
let detj_dxi_dx = dy_deta;
let detj_dxi_dy = {
let mut dx_deta = dx_deta;
dx_deta.mapv_inplace(|v| -v);
dx_deta
};
let detj_deta_dx = {
let mut dy_dxi = dy_dxi;
dy_dxi.mapv_inplace(|v| -v);
dy_dxi
};
let detj_deta_dy = dx_dxi;
Ok(Self {
x,
y,
detj,
detj_dxi_dx,
detj_dxi_dy,
detj_deta_dx,
detj_deta_dy,
operator: std::marker::PhantomData,
})
}
}

20
src/lib.rs
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@@ -1,8 +1,10 @@
use wasm_bindgen::prelude::*;
mod grid;
mod maxwell;
mod operators;
pub use crate::maxwell::{System, WorkBuffers};
pub(crate) use grid::Grid;
#[cfg(feature = "wee_alloc")]
#[global_allocator]
@@ -18,14 +20,22 @@ pub fn set_panic_hook() {
pub struct Universe {
sys: (System, System),
wb: WorkBuffers,
grid: Grid<operators::Upwind4>,
}
#[wasm_bindgen]
impl Universe {
#[wasm_bindgen(constructor)]
pub fn new(width: u32, height: u32) -> Self {
pub fn new(width: u32, height: u32, x: &[f32], y: &[f32]) -> Self {
assert_eq!((width * height) as usize, x.len());
assert_eq!((width * height) as usize, y.len());
let grid = Grid::new(width, height, x, y).expect(
"Could not create grid. Different number of elements compared to width*height?",
);
Self {
sys: (System::new(width, height), System::new(width, height)),
grid,
wb: WorkBuffers::new(width as usize, height as usize),
}
}
@@ -35,7 +45,13 @@ impl Universe {
}
pub fn advance(&mut self, dt: f32) {
System::advance::<operators::Upwind4>(&self.sys.0, &mut self.sys.1, dt, Some(&mut self.wb));
System::advance::<operators::Upwind4>(
&self.sys.0,
&mut self.sys.1,
dt,
&self.grid,
Some(&mut self.wb),
);
std::mem::swap(&mut self.sys.0, &mut self.sys.1);
}

234
src/maxwell.rs
View File

@@ -43,18 +43,23 @@ impl System {
}
}
pub fn advance<SBP>(&self, fut: &mut Self, dt: f32, work_buffers: Option<&mut WorkBuffers>)
where
pub(crate) fn advance<SBP>(
&self,
fut: &mut Self,
dt: f32,
grid: &super::Grid<SBP>,
work_buffers: Option<&mut WorkBuffers>,
) where
SBP: SbpOperator,
{
assert_eq!(self.ex.shape(), fut.ex.shape());
let mut wb: WorkBuffers;
let (y, k) = if let Some(x) = work_buffers {
(&mut x.y, &mut x.buf)
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]);
(&mut wb.y, &mut wb.buf)
(&mut wb.y, &mut wb.buf, &mut wb.tmp)
};
for i in 0..4 {
@@ -79,18 +84,86 @@ impl System {
}
};
// hz = -ey_x + ex_y
let tmp = &mut k[i].0;
SBP::diffxi(y.2.view(), tmp.view_mut());
SBP::diffeta(y.0.view(), k[i].1.view_mut());
k[i].1.scaled_add(-1.0, tmp);
// Solving (Au)_x + (Bu)_y
// with:
// A B
// [ 0, 0, 0] [ 0, 1, 0]
// [ 0, 0, -1] [ 1, 0, 0]
// [ 0, -1, 0] [ 0, 0, 0]
// This flux is rotated by the grid metrics
// (Au)_x + (Bu)_y = 1/J [
// (J xi_x Au)_xi + (J eta_x Au)_eta
// (J xi_y Bu)_xi + (J eta_y Bu)_eta
// ]
// where J is the grid determinant
// ex = hz_y
SBP::diffeta(y.1.view(), k[i].0.view_mut());
{
ndarray::azip!((a in &mut tmp.0,
&dxi_dy in &grid.detj_dxi_dy,
&hz in &y.1)
*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)
*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)
*flux = ax + by
);
}
{
// hz = -ey_x + ex_y
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)
*a = dxi_dx * -ey + dxi_dy * ex
);
SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
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)
*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)
*flux = ax + by
);
}
// ey = -hz_x
SBP::diffxi(y.1.view(), k[i].2.view_mut());
k[i].2.mapv_inplace(|v| -v);
{
ndarray::azip!((a in &mut tmp.0,
&dxi_dx in &grid.detj_dxi_dx,
&hz in &y.1)
*a = dxi_dx * -hz
);
SBP::diffxi(tmp.0.view(), tmp.1.view_mut());
ndarray::azip!((b in &mut tmp.2,
&deta_dx in &grid.detj_deta_dx,
&hz in &y.1)
*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)
*flux = ax + by
);
}
// Boundary conditions (SAT)
let ny = y.0.shape()[0];
@@ -98,48 +171,139 @@ impl System {
let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as f32);
fn positive_flux(kx: f32, ky: f32) -> [[f32; 3]; 3] {
let r = (kx * kx + ky * ky).sqrt();
[
[ky * ky / r / 2.0, ky / 2.0, -kx * ky / r / 2.0],
[ky / 2.0, r / 2.0, -kx / 2.0],
[-kx * ky / r / 2.0, -kx / 2.0, kx * kx / r / 2.0],
]
}
fn negative_flux(kx: f32, ky: f32) -> [[f32; 3]; 3] {
let r = (kx * kx + ky * ky).sqrt();
[
[-ky * ky / r / 2.0, ky / 2.0, kx * ky / r / 2.0],
[ky / 2.0, -r / 2.0, -kx / 2.0],
[kx * ky / r / 2.0, -kx / 2.0, -kx * kx / r / 2.0],
]
}
for j in 0..ny {
// East boundary
// 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)]);
// A+ = (0, 0, 0; 0, 1/2, -1/2; 0, -1/2, 1/2);
// k[i].0[(j, nx - 1)] += 0.0;
k[i].1[(j, nx - 1)] += tau * hinv * (0.5 * (v.1 - g.1) - 0.5 * (v.2 - g.2));
k[i].2[(j, nx - 1)] += tau * hinv * (-0.5 * (v.1 - g.1) + 0.5 * (v.2 - g.2));
let kx = grid.detj_dxi_dx[(j, nx - 1)];
let ky = grid.detj_dxi_dy[(j, nx - 1)];
// West boundary
let plus = positive_flux(kx, ky);
k[i].0[(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
* 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
* hinv
* (plus[2][0] * (v.0 - g.0)
+ plus[2][1] * (v.1 - g.1)
+ plus[2][2] * (v.2 - g.2));
// West boundary, negative flux
let tau = 1.0;
let (v, g) = (g, v);
// A- = (0, 0, 0; 0, -1/2, -1/2; 0, -1/2, -1/2);
// k[i].0[(j, 0)] += 0.0;
k[i].1[(j, 0)] += tau * hinv * (-0.5 * (v.1 - g.1) - 0.5 * (v.2 - g.2));
k[i].2[(j, 0)] += tau * hinv * (-0.5 * (v.1 - g.1) - 0.5 * (v.2 - g.2));
let kx = grid.detj_dxi_dx[(j, 0)];
let ky = grid.detj_dxi_dy[(j, 0)];
let minus = negative_flux(kx, ky);
k[i].0[(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
* 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
* hinv
* (minus[2][0] * (v.0 - g.0)
+ minus[2][1] * (v.1 - g.1)
+ minus[2][2] * (v.2 - g.2));
}
let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as f32);
for j in 0..nx {
// North boundary
// 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)]);
// B+ = (1/2, 1/2, 0; 1/2, 1/2, 0; 0, 0, 0)
k[i].0[(ny - 1, j)] += tau * hinv * (0.5 * (v.0 - g.0) + 0.5 * (v.1 - g.1));
k[i].1[(ny - 1, j)] += tau * hinv * (0.5 * (v.0 - g.0) + 0.5 * (v.1 - g.1));
// k[i].2[(ny - 1, j)] += 0.0;
let kx = grid.detj_deta_dx[(ny - 1, j)];
let ky = grid.detj_deta_dy[(ny - 1, j)];
// South boundary
let plus = positive_flux(kx, ky);
k[i].0[(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
* 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
* hinv
* (plus[2][0] * (v.0 - g.0)
+ plus[2][1] * (v.1 - g.1)
+ plus[2][2] * (v.2 - g.2));
// South boundary, negative flux
let tau = 1.0;
let (g, v) = (v, g);
// B- = (-1/2, 1/2, 0; 1/2, -1/2, 0; 0, 0, 0);
k[i].0[(0, j)] += tau * hinv * (-0.5 * (v.0 - g.0) + 0.5 * (v.1 - g.1));
k[i].1[(0, j)] += tau * hinv * (0.5 * (v.0 - g.0) - 0.5 * (v.1 - g.1));
// k[i].2[(0, j)] += 0.0;
let kx = grid.detj_deta_dx[(0, j)];
let ky = grid.detj_deta_dy[(0, j)];
let minus = negative_flux(kx, ky);
k[i].0[(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
* 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
* 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;
});
}
Zip::from(&mut fut.ex)
@@ -175,6 +339,7 @@ impl System {
pub struct WorkBuffers {
y: (Array2<f32>, Array2<f32>, Array2<f32>),
buf: [(Array2<f32>, Array2<f32>, Array2<f32>); 4],
tmp: (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
}
impl WorkBuffers {
@@ -186,8 +351,9 @@ impl WorkBuffers {
(arr.clone(), arr.clone(), arr.clone()),
(arr.clone(), arr.clone(), arr.clone()),
(arr.clone(), arr.clone(), arr.clone()),
(arr.clone(), arr.clone(), arr),
(arr.clone(), arr.clone(), arr.clone()),
],
tmp: (arr.clone(), arr.clone(), arr.clone(), arr),
}
}
}