A proxy-method direct solver for Helmholtz transmission problems with many inclusions compresses the linear system to O(ωD) size and runs in O(N^{1.5}) time using the PMCHWT formulation, outperforming Burton-Miller.
Numerische Mathematik86(4), 565–589 (2000)
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Review chapter summarizing advances in parallel sparse direct solvers along communication reduction and data-sparse compression axes.
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An accelerated direct solver for scalar wave scattering by multiple transmissive inclusions in two dimensions
A proxy-method direct solver for Helmholtz transmission problems with many inclusions compresses the linear system to O(ωD) size and runs in O(N^{1.5}) time using the PMCHWT formulation, outperforming Burton-Miller.
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Parallel Sparse and Data-Sparse Factorization-based Linear Solvers
Review chapter summarizing advances in parallel sparse direct solvers along communication reduction and data-sparse compression axes.