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Local solver for DOLFINx
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| # Local solver using Scipy | |
| # To be used with DOLFINx and a local-assembler | |
| # | |
| # Author: Jørgen S. Dokken | |
| # | |
| # License: MIT | |
| import scipy | |
| import scipy.linalg | |
| import numpy | |
| import numpy.typing | |
| from typing import List | |
| import numba | |
| def plu_solve(P: numpy.typing.NDArray[numpy.float64], | |
| L: numpy.typing.NDArray[numpy.float64], | |
| U: numpy.typing.NDArray[numpy.float64], | |
| b_local: numpy.typing.NDArray[numpy.float64], | |
| x: numpy.typing.NDArray[numpy.float64]): | |
| """Solve a partial LU pivoted sustem using a forward and backward solve""" | |
| numpy.dot(P.T, b_local, out=x) | |
| scipy.linalg.solve_triangular(L, x, lower=True, overwrite_b=True) | |
| scipy.linalg.solve_triangular(U, x, lower=False, overwrite_b=True) | |
| class LocalSolver(): | |
| # Lookup for LU factorization | |
| lookup_index = numpy.typing.NDArray[numpy.int32] | |
| # Caches for matrix factorization | |
| Ps: List[numpy.typing.NDArray[numpy.float64]] | |
| Ls: List[numpy.typing.NDArray[numpy.float64]] | |
| Us: List[numpy.typing.NDArray[numpy.float64]] | |
| # Arrays for store solutions while solving | |
| sol: numpy.typing.NDArray[numpy.float64] | |
| def __init__(self, num_cells_local: int): | |
| self.lookup_index = numpy.full(num_cells_local, -1, dtype=numpy.int32) | |
| self.Ps = [] | |
| self.Ls = [] | |
| self.Us = [] | |
| self.sol = None | |
| def factorize(self, A_local:numpy.typing.NDArray, cell: int): | |
| """ | |
| Factorize Local matrix A and store lookup for cell index `i` | |
| """ | |
| assert cell < len(self.lookup_index), f"Illegal {cell=} > {len(self.lookup_index)}" | |
| # Insert new matrices if LU-decomposition has not been computed | |
| P, L, U = scipy.linalg.lu(A_local) | |
| if (input_index:=self.lookup_index[cell]) >= 0: | |
| print(f"Cache exists, overwriting {input_index} for {cell}") | |
| self.Ps[input_index] = P | |
| self.Ls[input_index] = L | |
| self.Us[input_index] = U | |
| else: | |
| print(f"New {cell} inserting at {len(self.Ps)}") | |
| self.lookup_index[cell] = len(self.Ps) | |
| self.Ps.append(P) | |
| self.Ls.append(L) | |
| self.Us.append(U) | |
| def solve(self, b_local:numpy.typing.NDArray[numpy.float64], cell:int): | |
| index = self.lookup_index[cell] | |
| assert index >= 0, f"Missing factorization for {cell=}. Have you called `factorize(A_local, {cell})`" | |
| if self.sol is None: | |
| self.sol = numpy.empty_like(b_local) | |
| else: | |
| assert len(self.sol) == len(b_local), f"Inconsistent size of solution vector and input vector" | |
| plu_solve(self.Ps[index], self.Ls[index], self.Us[index], b_local, self.sol) | |
| return self.sol | |
| h = 0.2 | |
| A = numpy.array([[1, 0, 0, 0, 0, 0], | |
| [-1/h, 2/h, -1/h, 0, 0, 0], | |
| [0, -1/h, 2/h, -1/h, 0, 0], | |
| [0, 0, -1/h, 2/h, -1/h, 0], | |
| [0, 0, 0, -1/h, 2/h, -1/h], | |
| [0, 0, 0, 0, 0, 1]], dtype=numpy.float64) | |
| P, L, U = scipy.linalg.lu(A) | |
| b = numpy.array([-3, 0, 0, 0, 0, 2], dtype=numpy.float64) | |
| x = numpy.empty_like(b) | |
| plu_solve(P, L, U, b, x) | |
| print("Hardcoded sol", x) | |
| solver = LocalSolver(10) | |
| solver.factorize(A, 0) | |
| solver.factorize(A, 0) | |
| solver.factorize(A, 1) | |
| solver.factorize(A, 1) | |
| print(solver.solve(b, 0)) | |
| print(solver.solve(b, 1)) | |
| #solver.solve(b, 2) |
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