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127 lines
3.5 KiB
Python
127 lines
3.5 KiB
Python
"""
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Solvers and solver interface for FDFD problems.
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"""
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from typing import List, Callable, Dict, Any
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import logging
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import numpy
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from numpy.linalg import norm
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import scipy.sparse.linalg
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from ..fdmath import dx_lists_t, vfdfield_t
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from . import operators
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logger = logging.getLogger(__name__)
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def _scipy_qmr(A: scipy.sparse.csr_matrix,
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b: numpy.ndarray,
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**kwargs
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) -> numpy.ndarray:
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"""
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Wrapper for scipy.sparse.linalg.qmr
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Args:
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A: Sparse matrix
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b: Right-hand-side vector
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kwargs: Passed as **kwargs to the wrapped function
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Returns:
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Guess for solution (returned even if didn't converge)
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"""
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'''
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Report on our progress
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'''
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iter = 0
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def log_residual(xk):
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nonlocal iter
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iter += 1
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if iter % 100 == 0:
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logger.info('Solver residual at iteration {} : {}'.format(iter, norm(A @ xk - b)))
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if 'callback' in kwargs:
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def augmented_callback(xk):
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log_residual(xk)
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kwargs['callback'](xk)
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kwargs['callback'] = augmented_callback
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else:
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kwargs['callback'] = log_residual
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'''
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Run the actual solve
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'''
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x, _ = scipy.sparse.linalg.qmr(A, b, **kwargs)
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return x
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def generic(omega: complex,
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dxes: dx_lists_t,
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J: vfdfield_t,
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epsilon: vfdfield_t,
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mu: vfdfield_t = None,
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pec: vfdfield_t = None,
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pmc: vfdfield_t = None,
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adjoint: bool = False,
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matrix_solver: Callable[..., numpy.ndarray] = _scipy_qmr,
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matrix_solver_opts: Dict[str, Any] = None,
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) -> vfdfield_t:
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"""
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Conjugate gradient FDFD solver using CSR sparse matrices.
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All ndarray arguments should be 1D arrays, as returned by `meanas.vec()`.
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Args:
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omega: Complex frequency to solve at.
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dxes: `[[dx_e, dy_e, dz_e], [dx_h, dy_h, dz_h]]` (complex cell sizes) as
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discussed in `meanas.fdmath.types`
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J: Electric current distribution (at E-field locations)
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epsilon: Dielectric constant distribution (at E-field locations)
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mu: Magnetic permeability distribution (at H-field locations)
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pec: Perfect electric conductor distribution
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(at E-field locations; non-zero value indicates PEC is present)
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pmc: Perfect magnetic conductor distribution
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(at H-field locations; non-zero value indicates PMC is present)
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adjoint: If true, solves the adjoint problem.
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matrix_solver: Called as `matrix_solver(A, b, **matrix_solver_opts) -> x`,
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where `A`: `scipy.sparse.csr_matrix`;
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`b`: `numpy.ndarray`;
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`x`: `numpy.ndarray`;
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Default is a wrapped version of `scipy.sparse.linalg.qmr()`
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which doesn't return convergence info and logs the residual
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every 100 iterations.
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matrix_solver_opts: Passed as kwargs to `matrix_solver(...)`
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Returns:
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E-field which solves the system.
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"""
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if matrix_solver_opts is None:
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matrix_solver_opts = dict()
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b0 = -1j * omega * J
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A0 = operators.e_full(omega, dxes, epsilon=epsilon, mu=mu, pec=pec, pmc=pmc)
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Pl, Pr = operators.e_full_preconditioners(dxes)
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if adjoint:
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A = (Pl @ A0 @ Pr).H
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b = Pr.H @ b0
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else:
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A = Pl @ A0 @ Pr
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b = Pl @ b0
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x = matrix_solver(A.tocsr(), b, **matrix_solver_opts)
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if adjoint:
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x0 = Pl.H @ x
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else:
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x0 = Pr @ x
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return x0
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