A New Directional Algebraic Fast Multipole Method Based Iterative Solver for the Lippmann-Schwinger Equation Accelerated with HODLR Preconditioner

DOI10.4208/cicp.OA-2022-0103MaRDI QIDQ5045675

Vaishnavi Gujjula, Sivaram Ambikasaran

Publication date: 7 November 2022

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.00326

zbMATH Keywords

preconditionerLippmann-Schwinger equationlow-rank matrixnested cross approximationHelmholtz kerneldirectional algebraic fast multipole methodHODLR direct solver

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for integral transforms (65R10) Green's functions for elliptic equations (35J08) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80) Numerical methods for low-rank matrix approximation; matrix compression (65F55)

Related Items

Lippmann_Schwinger, HODLR2D: A New Class of Hierarchical Matrices, An explicitly-sparse representation for oscillatory kernels with wave atom-like functions, Algebraic inverse fast multipole method: a fast direct solver that is better than HODLR based fast direct solver

Uses Software

• Boost C++ Libraries
• DLMF
• Boost
• HODLRlib

Cites Work

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