3 research outputs found
Sparse Approximate Multifrontal Factorization with Butterfly Compression for High Frequency Wave Equations
We present a fast and approximate multifrontal solver for large-scale sparse
linear systems arising from finite-difference, finite-volume or finite-element
discretization of high-frequency wave equations. The proposed solver leverages
the butterfly algorithm and its hierarchical matrix extension for compressing
and factorizing large frontal matrices via graph-distance guided entry
evaluation or randomized matrix-vector multiplication-based schemes. Complexity
analysis and numerical experiments demonstrate
computation and memory complexity when applied to an sparse system arising from 3D high-frequency Helmholtz and Maxwell problems
A hierarchical butterfly LU preconditioner for two-dimensional electromagnetic scattering problems involving open surfaces
This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations (EFIEs) in electromagnetic scattering problems of perfect electrically conducting objects with open surfaces. H-IDBF-LU leverages the interpolative decomposition butterfly factorization (IDBF) to compress dense blocks of the discretized EFIE operator to expedite its application; this compressed operator also serves as an approximate LU factorization of the EFIE operator leading to an efficient preconditioner in iterative solvers. Both the memory requirement and computational cost of the H-IDBF-LU solver scale as O(Nlog2N) in one iteration; the total number of iterations required for a reasonably good accuracy scales as O(1) to O(log2N) in all of our numerical tests. The efficacy and accuracy of the proposed preconditioned iterative solver are demonstrated via its application to a broad range of scatterers involving up to 100 million unknowns