Solver¶
Electromagnetic modeller in the diffusive limit (low frequencies) for 3D media
with tri-axial electrical anisotropy. The matrix-free multigrid solver can be
used as main solver or as preconditioner for one of the Krylov subspace methods
implemented in scipy.sparse.linalg, and the governing equations are
discretized on a staggered Yee grid. The code is written completely in Python
using the numpy/scipy-stack, where the most time-consuming parts are
sped-up through jitted numba-functions.
emg3d.solver Module¶
The actual multigrid solver routines. The most computationally intensive parts,
however, are in the emg3d.core as numba-jitted functions.
Functions¶
solve(grid, model, sfield[, efield, cycle, …]) |
Solver for 3D CSEM data with tri-axial electrical anisotropy. |
multigrid(grid, model, sfield, efield, var, …) |
Multigrid solver for 3D controlled-source electromagnetic (CSEM) data. |
smoothing(grid, model, sfield, efield, nu, …) |
Reducing high-frequency error by smoothing. |
restriction(grid, model, sfield, residual, …) |
Downsampling of grid, model, and fields to a coarser grid. |
prolongation(grid, efield, cgrid, cefield, …) |
Interpolating the electric field from coarse grid to fine grid. |
residual(grid, model, sfield, efield[, norm]) |
Computing the residual. |
krylov(grid, model, sfield, efield, var) |
Krylov Subspace iterative solver for 3D CSEM data. |
Classes¶
MGParameters(verb, cycle, sslsolver, …) |
Collect multigrid solver settings. |
RegularGridProlongator(x, y, cxy) |
Prolongate field from coarse to fine grid. |
emg3d.core Module¶
The core functionalities, the most computationally demanding parts, of the
emg3d.solver as just-in-time (jit) compiled functions using numba.
Functions¶
amat_x(rx, ry, rz, ex, ey, ez, eta_x, eta_y, …) |
Residual without or with source term. |
blocks_to_amat(amat, bvec, middle, left, …) |
Insert middle, left, and rhs into main arrays amat and bvec. |
gauss_seidel(ex, ey, ez, sx, sy, sz, eta_x, …) |
Gauss-Seidel method. |
gauss_seidel_x(ex, ey, ez, sx, sy, sz, …) |
Gauss-Seidel method with line relaxation in x-direction. |
gauss_seidel_y(ex, ey, ez, sx, sy, sz, …) |
Gauss-Seidel method with line relaxation in y-direction. |
gauss_seidel_z(ex, ey, ez, sx, sy, sz, …) |
Gauss-Seidel method with line relaxation in z-direction. |
restrict(crx, cry, crz, rx, ry, rz, wx, wy, …) |
Restriction of residual from fine to coarse grid. |
restrict_weights(vectorN, vectorCC, h, …) |
Restriction weights for the coarse-grid correction operator. |
solve(amat, bvec) |
Solve A x = b using a non-standard Cholesky factorisation. |