fixup maxwell rhs matrix
This commit is contained in:
Magnus Ulimoen
parent
459581a3c9
commit
9e22f239c2
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@ -13,242 +13,195 @@ pub fn implicit_matrix(rhs: sprs::CsMatView<Float>, dt: Float) -> sprs::CsMat<Fl
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/// Assumes self boundaries
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pub fn rhs_matrix(op: &dyn SbpOperator2d, ny: usize, nx: usize) -> sprs::CsMat<Float> {
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let d1_x = op.op_eta().diff_matrix(nx);
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let d1_y = op.op_xi().diff_matrix(ny);
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let eye = |n: usize| sprs::CsMat::eye(n);
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let ix = sprs::CsMat::<Float>::eye(nx);
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let iy = sprs::CsMat::eye(ny);
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let fluxes = {
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let d1_x = op.op_eta().diff_matrix(nx);
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let d1_y = op.op_xi().diff_matrix(ny);
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let dx = sparse_sparse_outer_product(iy.view(), d1_x.view());
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let dy = sparse_sparse_outer_product(d1_y.view(), ix.view());
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let dx = sparse_sparse_outer_product(eye(ny).view(), d1_x.view());
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let dy = sparse_sparse_outer_product(d1_y.view(), eye(nx).view());
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let mut a_flux = sprs::TriMat::new((3, 3));
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a_flux.add_triplet(1, 2, -1.0);
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a_flux.add_triplet(2, 1, -1.0);
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let a_flux = a_flux.to_csr();
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let mut a_flux = sprs::CsMat::zero((3, 3));
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a_flux.insert(1, 2, -1.0);
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a_flux.insert(2, 1, -1.0);
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let mut b_flux = sprs::TriMat::new((3, 3));
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b_flux.add_triplet(0, 1, 1.0);
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b_flux.add_triplet(1, 0, 1.0);
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let b_flux = b_flux.to_csr();
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let mut b_flux = sprs::CsMat::zero((3, 3));
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b_flux.insert(0, 1, 1.0);
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b_flux.insert(1, 0, 1.0);
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let f = &sparse_sparse_outer_product(a_flux.view(), dx.view())
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+ &sparse_sparse_outer_product(b_flux.view(), dy.view());
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&sparse_sparse_outer_product(a_flux.view(), dx.view())
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+ &sparse_sparse_outer_product(b_flux.view(), dy.view())
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};
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let mut hx = sparse_sparse_outer_product(iy.view(), op.op_xi().h_matrix(nx).view());
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hx.map_inplace(|h| 1.0 / h);
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let ihx = hx;
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let mut hy = sparse_sparse_outer_product(op.op_eta().h_matrix(ny).view(), ix.view());
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hy.map_inplace(|h| 1.0 / h);
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let ihy = hy;
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let _f = {
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let sat_west = {
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// West boundary
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let mut aminus = sprs::TriMat::new((3, 3));
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aminus.add_triplet(1, 1, -0.5);
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aminus.add_triplet(1, 2, -0.5);
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aminus.add_triplet(2, 1, -0.5);
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aminus.add_triplet(2, 2, -0.5);
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let aminus = aminus.to_csr();
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let aminus = {
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let mut aminus = sprs::CsMat::zero((3, 3));
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aminus.insert(1, 1, -0.5);
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aminus.insert(1, 2, -0.5);
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aminus.insert(2, 1, -0.5);
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aminus.insert(2, 2, -0.5);
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aminus
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};
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let e0 = {
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let mut e0 = sprs::CsMat::zero((nx, 1));
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e0.insert(0, 0, 1.0);
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e0
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};
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let en = {
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let mut en = sprs::CsMat::zero((nx, 1));
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en.insert(nx - 1, 0, 1.0);
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en
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};
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let mut e0x = sprs::TriMat::new((nx, 1));
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e0x.add_triplet(0, 0, 1.0);
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let e0x = e0x.to_csr();
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let e0x_nt = &e0x * &e0x.transpose_view();
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let e0x_nt = sparse_sparse_outer_product(iy.view(), e0x_nt.view());
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// Periodic => (e_0 - e_n)q => 0
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let p = &e0 - &en;
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let sat0 = &ihx * &e0x_nt;
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let mut sat0 = sparse_sparse_outer_product(aminus.view(), sat0.view());
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// Forming the matrix of size (nx,nx)
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let mat = &e0 * &p.transpose_view();
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// Must be scaled by the h norm
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let hi = op.op_xi().h_matrix(nx).map(|h| 1.0 / h);
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let mat = &hi * &mat;
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// Upscaling to (nx * ny, nx * ny)
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let mat = sparse_sparse_outer_product(eye(ny).view(), mat.view());
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let mut sat = sparse_sparse_outer_product(aminus.view(), mat.view());
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let tau = 1.0;
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sat0.map_inplace(|x| tau * x);
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&f + &sat0
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// Scaling by tau
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sat.map_inplace(|x| tau * x);
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sat
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};
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let _f = {
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let sat_east = {
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// East boundary
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let mut aplus = sprs::TriMat::new((3, 3));
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aplus.add_triplet(1, 1, 0.5);
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aplus.add_triplet(1, 2, -0.5);
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aplus.add_triplet(2, 1, -0.5);
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aplus.add_triplet(2, 2, 0.5);
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let aplus = aplus.to_csr();
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let aminus = {
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let mut aplus = sprs::CsMat::zero((3, 3));
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aplus.insert(1, 1, 0.5);
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aplus.insert(1, 2, -0.5);
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aplus.insert(2, 1, -0.5);
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aplus.insert(2, 2, 0.5);
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aplus
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};
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let e0 = {
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let mut e0 = sprs::CsMat::zero((nx, 1));
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e0.insert(0, 0, 1.0);
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e0
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};
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let en = {
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let mut en = sprs::CsMat::zero((nx, 1));
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en.insert(nx - 1, 0, 1.0);
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en
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};
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let mut enx = sprs::TriMat::new((nx, 1));
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enx.add_triplet(nx - 1, 0, 1.0);
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let enx = enx.to_csr();
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let enx_nt = &enx * &enx.transpose_view();
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let enx_nt = sparse_sparse_outer_product(iy.view(), enx_nt.view());
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// Periodic => (e_0 - e_n) => 0
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let p = &en - &e0;
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let satn = &ihx * &enx_nt;
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let mut satn = sparse_sparse_outer_product(aplus.view(), satn.view());
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// Forming the matrix of size (nx,nx)
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let mat = &en * &p.transpose_view();
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// Must be scaled by the h norm
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let hi = op.op_xi().h_matrix(nx).map(|h| 1.0 / h);
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let mat = &hi * &mat;
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// Upscaling to (nx * ny, nx * ny)
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let mat = sparse_sparse_outer_product(eye(ny).view(), mat.view());
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let mut sat = sparse_sparse_outer_product(aminus.view(), mat.view());
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let tau = -1.0;
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satn.map_inplace(|x| tau * x);
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&f + &satn
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// Scaling by tau
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sat.map_inplace(|x| tau * x);
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sat
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};
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let _f = {
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let sat_south = {
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// South boundary
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let mut bminus = sprs::TriMat::new((3, 3));
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bminus.add_triplet(0, 0, -0.5);
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bminus.add_triplet(0, 1, 0.5);
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bminus.add_triplet(1, 0, 0.5);
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bminus.add_triplet(1, 1, -0.5);
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let bminus = bminus.to_csr();
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let bminus = {
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let mut bminus = sprs::CsMat::zero((3, 3));
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bminus.insert(0, 0, -0.5);
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bminus.insert(0, 1, 0.5);
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bminus.insert(1, 0, 0.5);
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bminus.insert(1, 1, -0.5);
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bminus
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};
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let e0 = {
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let mut e0 = sprs::CsMat::zero((ny, 1));
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e0.insert(0, 0, 1.0);
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e0
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};
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let en = {
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let mut en = sprs::CsMat::zero((ny, 1));
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en.insert(ny - 1, 0, 1.0);
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en
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};
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let mut e0y = sprs::TriMat::new((ny, 1));
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e0y.add_triplet(0, 0, 1.0);
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let e0y = e0y.to_csr();
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let e0y_nt = &e0y * &e0y.transpose_view();
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let e0y_nt = sparse_sparse_outer_product(e0y_nt.view(), ix.view());
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// Periodic => (e_0 - e_n) => 0
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let p = &e0 - &en;
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let sat0 = &ihx * &e0y_nt;
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let mut sat0 = sparse_sparse_outer_product(bminus.view(), sat0.view());
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// Forming the matrix of size (ny,ny)
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let mat = &e0 * &p.transpose_view();
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// Must be scaled by the h norm
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let hi = op.op_eta().h_matrix(ny).map(|h| 1.0 / h);
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let mat = &hi * &mat;
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// Upscaling to (nx * ny, nx * ny)
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let mat = sparse_sparse_outer_product(mat.view(), eye(nx).view());
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let mut sat = sparse_sparse_outer_product(bminus.view(), mat.view());
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let tau = 1.0;
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sat0.map_inplace(|x| tau * x);
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&f + &sat0
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// Scaling by tau
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sat.map_inplace(|x| tau * x);
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sat
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};
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let _f = {
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let sat_north = {
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// North boundary
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let mut bplus = sprs::TriMat::new((3, 3));
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bplus.add_triplet(0, 0, 0.5);
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bplus.add_triplet(0, 1, 0.5);
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bplus.add_triplet(1, 0, 0.5);
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bplus.add_triplet(1, 1, 0.5);
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let bplus = bplus.to_csr();
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let bplus = {
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let mut bplus = sprs::CsMat::zero((3, 3));
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bplus.insert(0, 0, 0.5);
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bplus.insert(0, 1, 0.5);
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bplus.insert(1, 0, 0.5);
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bplus.insert(1, 1, 0.5);
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bplus
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};
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let e0 = {
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let mut e0 = sprs::CsMat::zero((ny, 1));
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e0.insert(0, 0, 1.0);
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e0
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};
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let en = {
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let mut en = sprs::CsMat::zero((ny, 1));
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en.insert(ny - 1, 0, 1.0);
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en
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};
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let mut eny = sprs::TriMat::new((ny, 1));
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eny.add_triplet(ny - 1, 0, 1.0);
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let eny = eny.to_csr();
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let eny_nt = &eny * &eny.transpose_view();
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let eny_nt = sparse_sparse_outer_product(eny_nt.view(), ix.view());
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// Periodic => (e_0 - e_n) => 0
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let p = &en - &e0;
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let satn = &ihy * &eny_nt;
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let mut satn = sparse_sparse_outer_product(bplus.view(), satn.view());
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// Forming the matrix of size (ny,ny)
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let mat = &en * &p.transpose_view();
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// Must be scaled by the h norm
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let hi = op.op_eta().h_matrix(ny).map(|h| 1.0 / h);
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let mat = &hi * &mat;
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// Upscaling to (nx * ny, nx * ny)
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let mat = sparse_sparse_outer_product(mat.view(), eye(nx).view());
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let mut sat = sparse_sparse_outer_product(bplus.view(), mat.view());
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let tau = -1.0;
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satn.map_inplace(|x| tau * x);
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&f + &satn
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};
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// Setting up the periodic boundaries
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let _f = {
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// West
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let mut aminus = sprs::TriMat::new((3, 3));
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aminus.add_triplet(1, 1, -0.5);
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aminus.add_triplet(1, 2, -0.5);
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aminus.add_triplet(2, 1, -0.5);
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aminus.add_triplet(2, 2, -0.5);
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let aminus = aminus.to_csr();
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let mut e0x = sprs::TriMat::new((nx, 1));
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e0x.add_triplet(0, 0, 1.0);
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let e0x = e0x.to_csr();
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let mut enx = sprs::TriMat::new((nx, 1));
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enx.add_triplet(nx - 1, 0, 1.0);
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let enx = enx.to_csr();
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let e0nx_nt = &e0x * &enx.transpose_view();
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let e0nx_nt = sparse_sparse_outer_product(iy.view(), e0nx_nt.view());
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let sat0 = &ihx * &e0nx_nt;
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let mut sat0 = sparse_sparse_outer_product(aminus.view(), sat0.view());
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let tau = 1.0;
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// Negative => subtracting this boundary
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sat0.map_inplace(|x| -tau * x);
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&f + &sat0
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// Scaling by tau
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sat.map_inplace(|x| tau * x);
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sat
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};
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let _f = {
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// East boundary
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let mut aplus = sprs::TriMat::new((3, 3));
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aplus.add_triplet(1, 1, 0.5);
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aplus.add_triplet(1, 2, -0.5);
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aplus.add_triplet(2, 1, -0.5);
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aplus.add_triplet(2, 2, 0.5);
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let aplus = aplus.to_csr();
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let mut enx = sprs::TriMat::new((nx, 1));
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enx.add_triplet(nx - 1, 0, 1.0);
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let enx = enx.to_csr();
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let mut e0x = sprs::TriMat::new((nx, 1));
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e0x.add_triplet(0, 0, 1.0);
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let e0x = e0x.to_csr();
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let en0x_nt = &enx * &e0x.transpose_view();
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let en0x_nt = sparse_sparse_outer_product(iy.view(), en0x_nt.view());
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let satn = &ihx * &en0x_nt;
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let mut satn = sparse_sparse_outer_product(aplus.view(), satn.view());
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let tau = -1.0;
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satn.map_inplace(|x| -tau * x);
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&f + &satn
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};
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let _f = {
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// South boundary
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let mut bminus = sprs::TriMat::new((3, 3));
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bminus.add_triplet(0, 0, -0.5);
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bminus.add_triplet(0, 1, 0.5);
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bminus.add_triplet(1, 0, 0.5);
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bminus.add_triplet(1, 1, -0.5);
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let bminus = bminus.to_csr();
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let mut e0y = sprs::TriMat::new((ny, 1));
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e0y.add_triplet(0, 0, 1.0);
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let e0y = e0y.to_csr();
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let mut eny = sprs::TriMat::new((ny, 1));
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eny.add_triplet(ny - 1, 0, 1.0);
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let eny = eny.to_csr();
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let e0ny_nt = &e0y * &eny.transpose_view();
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let e0ny_nt = sparse_sparse_outer_product(e0ny_nt.view(), ix.view());
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let sat0 = &ihx * &e0ny_nt;
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let mut sat0 = sparse_sparse_outer_product(bminus.view(), sat0.view());
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let tau = 1.0;
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sat0.map_inplace(|x| -tau * x);
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&f + &sat0
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};
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let _f = {
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// North boundary
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let mut bplus = sprs::TriMat::new((3, 3));
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bplus.add_triplet(0, 0, 0.5);
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bplus.add_triplet(0, 1, 0.5);
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bplus.add_triplet(1, 0, 0.5);
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bplus.add_triplet(1, 1, 0.5);
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let bplus = bplus.to_csr();
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let mut eny = sprs::TriMat::new((ny, 1));
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eny.add_triplet(ny - 1, 0, 1.0);
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let eny = eny.to_csr();
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let mut e0y = sprs::TriMat::new((ny, 1));
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e0y.add_triplet(0, 0, 1.0);
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let e0y = e0y.to_csr();
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let en0y_nt = &eny * &e0y.transpose_view();
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let en0y_nt = sparse_sparse_outer_product(en0y_nt.view(), ix.view());
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let satn = &ihy * &en0y_nt;
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let mut satn = sparse_sparse_outer_product(bplus.view(), satn.view());
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let tau = -1.0;
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satn.map_inplace(|x| -tau * x);
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&f + &satn
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};
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f
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&fluxes + &(&(&sat_west + &sat_east) + &(&sat_north + &sat_south))
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}
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#[test]
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fn dummy() {
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let ny = 16;
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let nx = 17;
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let rhs = rhs_matrix(&sbp::operators::Upwind4, ny, nx);
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let _lhs = implicit_matrix(rhs.view(), 1e-2);
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}
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