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Add matrix form to maxwell

This commit is contained in:
Magnus Ulimoen 2020-09-15 17:42:12 +02:00
parent d2c6d6af6c
commit 52ca29a51c
3 changed files with 169 additions and 107 deletions
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4
maxwell/src/lib.rs
View File

@ -104,7 +104,7 @@ impl<SBP: SbpOperator2d> System<SBP> {
let metrics = grid.metrics(&op).unwrap();
#[cfg(feature = "sparse")]
let rhs = sparse::rhs_matrix(&op, ny, nx);
let rhs = sparse::rhs_matrix(&op, &grid).rhs;
#[cfg(feature = "sparse")]
let lhs = sparse::implicit_matrix(rhs.view(), 0.2 / std::cmp::max(ny, nx) as Float);
@ -160,6 +160,7 @@ impl<SBP: SbpOperator2d> System<SBP> {
#[cfg(feature = "sparse")]
pub fn advance_sparse(&mut self, dt: Float) {
let rhs = self.rhs.view();
//let lhs = self.explicit.view();
let rhs_f = |next: &mut Field, now: &Field, _t: Float| {
next.fill(0.0);
sprs::prod::mul_acc_mat_vec_csr(
@ -167,6 +168,7 @@ impl<SBP: SbpOperator2d> System<SBP> {
now.as_slice().unwrap(),
next.as_slice_mut().unwrap(),
);
// sprs::lingalg::dsolve(..)
};
sbp::integrate::integrate::<sbp::integrate::Rk4, _, _>(
rhs_f,

266
maxwell/src/sparse.rs
View File

@ -14,14 +14,31 @@ pub fn implicit_matrix(rhs: sprs::CsMatView<Float>, dt: Float) -> sprs::CsMat<Fl
&eye(n) - &f
}
/// Assumes self boundaries
pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<Float> {
let fluxes = {
let d1_x = op.op_eta().diff_matrix(nx);
let d1_y = op.op_xi().diff_matrix(ny);
fn diagonal(values: &[Float]) -> sprs::CsMat<Float> {
let values = values.to_vec();
let indptr = (0..values.len() + 1).collect();
let indices = (0..values.len()).collect();
let dx = kronecker_product(eye(ny).view(), d1_x.view());
let dy = kronecker_product(d1_y.view(), eye(nx).view());
sprs::CsMat::new((values.len(), values.len()), indptr, indices, values)
}
pub struct Implicit {
pub(crate) rhs: sprs::CsMat<Float>,
/// Diagonal matrix
pub(crate) lhs: sprs::CsMat<Float>,
}
/// Assumes self boundaries
pub fn rhs_matrix(op: &dyn SbpOperator2d, grid: &super::Grid) -> Implicit {
let metrics = grid.metrics(op).unwrap();
let nx = grid.nx();
let ny = grid.ny();
let fluxes = {
let d1_xi = op.op_eta().diff_matrix(nx);
let d1_eta = op.op_xi().diff_matrix(ny);
let d1_xi = kronecker_product(eye(ny).view(), d1_xi.view());
let d1_eta = kronecker_product(d1_eta.view(), eye(nx).view());
let mut a_flux = sprs::CsMat::zero((3, 3));
a_flux.insert(1, 2, -1.0);
@ -31,29 +48,82 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
b_flux.insert(0, 1, 1.0);
b_flux.insert(1, 0, 1.0);
&kronecker_product(a_flux.view(), dx.view()) + &kronecker_product(b_flux.view(), dy.view())
let detj_dxi_dx = diagonal(metrics.detj_dxi_dx().as_slice().unwrap());
let detj_dxi_dx = &d1_xi * &detj_dxi_dx;
// Can multiply with the constant matrix after differentiation
let f_flux_dxi = kronecker_product(a_flux.view(), detj_dxi_dx.view());
let detj_dxi_dy = diagonal(metrics.detj_dxi_dy().as_slice().unwrap());
let detj_dxi_dy = &d1_xi * &detj_dxi_dy;
let f_flux_deta = kronecker_product(b_flux.view(), detj_dxi_dy.view());
let detj_deta_dx = diagonal(metrics.detj_deta_dx().as_slice().unwrap());
let detj_deta_dx = &d1_eta * &detj_deta_dx;
let g_flux_dxi = kronecker_product(a_flux.view(), detj_deta_dx.view());
let detj_deta_dy = diagonal(metrics.detj_deta_dy().as_slice().unwrap());
let detj_deta_dy = &d1_eta * &detj_deta_dy;
let g_flux_deta = kronecker_product(b_flux.view(), detj_deta_dy.view());
let f_flux = &f_flux_dxi + &f_flux_deta;
let g_flux = &g_flux_dxi + &g_flux_deta;
&f_flux + &g_flux
};
fn flux_matrix(
kx: ndarray::ArrayView2<Float>,
ky: ndarray::ArrayView2<Float>,
positive: bool,
) -> sprs::CsMat<Float> {
let mut r = &(&kx * &kx) + &(&ky * &ky);
r.map_inplace(|v| *v = v.sqrt());
let a00 = if positive {
&ky * &ky / (2.0 * &r)
} else {
-&ky * &ky / (2.0 * &r)
};
let a00 = diagonal(a00.as_slice().unwrap());
let a01 = &ky / 2.0;
let a01 = diagonal(a01.as_slice().unwrap());
let a02 = &kx * &ky / (2.0 * &r);
let a02 = diagonal(a02.as_slice().unwrap());
let a10 = &a01;
let a11 = if positive { &r / 2.0 } else { -&r / 2.0 };
let a11 = diagonal(a11.as_slice().unwrap());
let a12 = -&kx / 2.0;
let a12 = diagonal(a12.as_slice().unwrap());
let a20 = &a02;
let a21 = &a12;
let a22 = if positive {
&kx * &kx / (2.0 * &r)
} else {
-&kx * &kx / (2.0 * &r)
};
let a22 = diagonal(a22.as_slice().unwrap());
sprs::bmat(&[
[Some(a00.view()), Some(a01.view()), Some(a02.view())],
[Some(a10.view()), Some(a11.view()), Some(a12.view())],
[Some(a20.view()), Some(a21.view()), Some(a22.view())],
])
}
let e0 = |n| {
let mut e0 = sprs::CsMat::zero((n, 1));
e0.insert(0, 0, 1.0);
e0
};
let en = |n| {
let mut en = sprs::CsMat::zero((n, 1));
en.insert(n - 1, 0, 1.0);
en
};
let sat_west = {
// West boundary
let aminus = {
let mut aminus = sprs::CsMat::zero((3, 3));
aminus.insert(1, 1, -0.5);
aminus.insert(1, 2, -0.5);
aminus.insert(2, 1, -0.5);
aminus.insert(2, 2, -0.5);
aminus
};
let e0 = {
let mut e0 = sprs::CsMat::zero((nx, 1));
e0.insert(0, 0, 1.0);
e0
};
let en = {
let mut en = sprs::CsMat::zero((nx, 1));
en.insert(nx - 1, 0, 1.0);
en
};
let e0 = e0(nx);
let en = en(nx);
// Periodic => (e_0 - e_n)q => 0
let p = &e0 - &en;
@ -66,7 +136,8 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
// Upscaling to (nx * ny, nx * ny)
let mat = kronecker_product(eye(ny).view(), mat.view());
let mut sat = kronecker_product(aminus.view(), mat.view());
let aminus = flux_matrix(metrics.detj_dxi_dx(), metrics.detj_dxi_dy(), false);
let mut sat = &aminus * &kronecker_product(eye(3).view(), mat.view());
let tau = 1.0;
// Scaling by tau
@ -76,24 +147,8 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
let sat_east = {
// East boundary
let aminus = {
let mut aplus = sprs::CsMat::zero((3, 3));
aplus.insert(1, 1, 0.5);
aplus.insert(1, 2, -0.5);
aplus.insert(2, 1, -0.5);
aplus.insert(2, 2, 0.5);
aplus
};
let e0 = {
let mut e0 = sprs::CsMat::zero((nx, 1));
e0.insert(0, 0, 1.0);
e0
};
let en = {
let mut en = sprs::CsMat::zero((nx, 1));
en.insert(nx - 1, 0, 1.0);
en
};
let e0 = e0(nx);
let en = en(nx);
// Periodic => (e_0 - e_n) => 0
let p = &en - &e0;
@ -106,7 +161,9 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
// Upscaling to (nx * ny, nx * ny)
let mat = kronecker_product(eye(ny).view(), mat.view());
let mut sat = kronecker_product(aminus.view(), mat.view());
let aplus = flux_matrix(metrics.detj_dxi_dx(), metrics.detj_dxi_dy(), true);
let mut sat = &aplus * &kronecker_product(eye(3).view(), mat.view());
let tau = -1.0;
// Scaling by tau
@ -116,24 +173,8 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
let sat_south = {
// South boundary
let bminus = {
let mut bminus = sprs::CsMat::zero((3, 3));
bminus.insert(0, 0, -0.5);
bminus.insert(0, 1, 0.5);
bminus.insert(1, 0, 0.5);
bminus.insert(1, 1, -0.5);
bminus
};
let e0 = {
let mut e0 = sprs::CsMat::zero((ny, 1));
e0.insert(0, 0, 1.0);
e0
};
let en = {
let mut en = sprs::CsMat::zero((ny, 1));
en.insert(ny - 1, 0, 1.0);
en
};
let e0 = e0(ny);
let en = en(ny);
// Periodic => (e_0 - e_n) => 0
let p = &e0 - &en;
@ -146,7 +187,9 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
// Upscaling to (nx * ny, nx * ny)
let mat = kronecker_product(mat.view(), eye(nx).view());
let mut sat = kronecker_product(bminus.view(), mat.view());
let bminus = flux_matrix(metrics.detj_deta_dx(), metrics.detj_deta_dy(), false);
let mut sat = &bminus * &kronecker_product(eye(3).view(), mat.view());
let tau = 1.0;
// Scaling by tau
@ -156,24 +199,8 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
let sat_north = {
// North boundary
let bplus = {
let mut bplus = sprs::CsMat::zero((3, 3));
bplus.insert(0, 0, 0.5);
bplus.insert(0, 1, 0.5);
bplus.insert(1, 0, 0.5);
bplus.insert(1, 1, 0.5);
bplus
};
let e0 = {
let mut e0 = sprs::CsMat::zero((ny, 1));
e0.insert(0, 0, 1.0);
e0
};
let en = {
let mut en = sprs::CsMat::zero((ny, 1));
en.insert(ny - 1, 0, 1.0);
en
};
let e0 = e0(ny);
let en = en(ny);
// Periodic => (e_0 - e_n) => 0
let p = &en - &e0;
@ -186,7 +213,9 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
// Upscaling to (nx * ny, nx * ny)
let mat = kronecker_product(mat.view(), eye(nx).view());
let mut sat = kronecker_product(bplus.view(), mat.view());
let bminus = flux_matrix(metrics.detj_deta_dx(), metrics.detj_deta_dy(), true);
let mut sat = &bminus * &kronecker_product(eye(3).view(), mat.view());
let tau = -1.0;
// Scaling by tau
@ -194,49 +223,74 @@ pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<F
sat
};
&fluxes + &(&(&sat_west + &sat_east) + &(&sat_north + &sat_south))
let rhs = &fluxes + &(&(&sat_west + &sat_east) + &(&sat_north + &sat_south));
Implicit {
rhs,
lhs: kronecker_product(
sprs::CsMat::eye(3).view(),
diagonal(metrics.detj().as_slice().unwrap()).view(),
),
}
}
/// RHS with some additional dissipation from the upwind operator
pub fn rhs_matrix_with_upwind_dissipation(
op: &dyn UpwindOperator2d,
ny: usize,
nx: usize,
grid: &super::Grid,
) -> sprs::CsMat<Float> {
let rhs = rhs_matrix(op.as_sbp(), ny, nx);
let rhs = rhs_matrix(op.as_sbp(), grid).rhs;
let metrics = grid.metrics(op.as_sbp()).unwrap();
let nx = grid.nx();
let ny = grid.ny();
let diss = |kx: ndarray::ArrayView2<Float>, ky: ndarray::ArrayView2<Float>| {
let r = &kx * &kx + &ky * &ky;
let s00 = &ky * &ky / &r;
let s00 = diagonal(s00.as_slice().unwrap());
let s02 = -&kx * &ky / &r;
let s02 = diagonal(s02.as_slice().unwrap());
let s11 = diagonal(r.as_slice().unwrap());
let s20 = &s02;
let s22 = &kx * &kx / &r;
let s22 = diagonal(s22.as_slice().unwrap());
sprs::bmat(&[
[Some(s00.view()), None, Some(s02.view())],
[None, Some(s11.view()), None],
[Some(s20.view()), None, Some(s22.view())],
])
};
let diss_x = {
let diss_x = UpwindOperator2d::op_xi(op).diss_matrix(nx);
let diss_x = kronecker_product(eye(ny).view(), diss_x.view());
let sa = {
let mut sa = sprs::CsMat::zero((3, 3));
sa.insert(1, 1, 1.0);
sa.insert(2, 2, 1.0);
sa
};
kronecker_product(sa.view(), diss_x.view())
let met = diss(metrics.detj_dxi_dx(), metrics.detj_dxi_dy());
&met * &kronecker_product(eye(3).view(), diss_x.view())
};
let diss_y = {
let diss_y = UpwindOperator2d::op_eta(op).diss_matrix(ny);
let diss_y = kronecker_product(diss_y.view(), eye(nx).view());
let sa = {
let mut sa = sprs::CsMat::zero((3, 3));
sa.insert(0, 0, 1.0);
sa.insert(1, 1, 1.0);
sa
};
kronecker_product(sa.view(), diss_y.view())
let met = diss(metrics.detj_deta_dx(), metrics.detj_deta_dy());
&met * &kronecker_product(eye(3).view(), diss_y.view())
};
&rhs + &(&diss_x + &diss_y)
}
#[test]
fn dummy() {
fn creation() {
let ny = 16;
let nx = 17;
let nx = 170;
let rhs = rhs_matrix(&sbp::operators::Upwind4, ny, nx);
let _lhs = implicit_matrix(rhs.view(), 1e-2);
let x = ndarray::Array::from_shape_fn((ny, nx), |(_j, i)| i as Float / (nx - 1) as Float);
let y = ndarray::Array::from_shape_fn((ny, nx), |(j, _i)| j as Float / (ny - 1) as Float);
let op = &sbp::operators::Upwind4;
let grid = sbp::grid::Grid::new(x, y).unwrap();
let _rhs = rhs_matrix(op, &grid);
// let _lhs = implicit_matrix(rhs.view(), 1e-2);
let _rhs_upwind = rhs_matrix_with_upwind_dissipation(op, &grid);
}

6
sbp/src/grid.rs
View File

@ -114,6 +114,12 @@ impl Metrics {
detj_deta_dy,
})
}
pub fn nx(&self) -> usize {
self.detj.shape()[1]
}
pub fn ny(&self) -> usize {
self.detj.shape()[0]
}
}
impl Metrics {