A hierarchical butterfly LU preconditioner for two-dimensional electromagnetic scattering problems involving open surfaces

Liu, Yang; Yang, Haizhao

doi:10.1016/j.jcp.2019.109014

Title: A hierarchical butterfly LU preconditioner for two-dimensional electromagnetic scattering problems involving open surfaces

Journal Article · Thu Oct 10 00:00:00 EDT 2019 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2019.109014· OSTI ID:1564075

Liu, Yang ^[1];

^[2]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
National Univ. of Singapore (Singapore). Dept. of Mathematics

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 $$O$$($$N$$ log² $$N$$) in one iteration; the total number of iterations required for a reasonably good accuracy scales as $$O$$(1) to O(log²$$N$$) 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.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1564075

Alternate ID(s):: OSTI ID: 1576807

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 5 works

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