A fast, higher-order solver for scattering by penetrable bodies in three dimensions

DOI10.1016/j.jcp.2004.07.006zbMath1063.65132OpenAlexW2020978980MaRDI QIDQ703751

E. McKay Hyde, Oscar P. Bruno

Publication date: 11 January 2005

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2004.07.006

zbMATH Keywords

AlgorithmscatteringConvergenceHelmholtz equationFourier seriesParallel computationLippmann-Schwinger equationNumerical examplesFast Fourier transformHigh-order quadratureIntegral equation method

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for discrete and fast Fourier transforms (65T50) Boundary element methods applied to problems in optics and electromagnetic theory (78M15) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (7)

A fast rapidly convergent method for approximation of convolutions with applications to wave scattering and some other problems ⋮ Preconditioning Methods for Thin Scattering Structures Based on Asymptotic Results ⋮ A volume integral equation method for periodic scattering problems for anisotropic Maxwell's equations ⋮ FEM-BEM mortar coupling for the Helmholtz problem in three dimensions ⋮ Finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains ⋮ A Fourier Extension Based Numerical Integration Scheme for Fast and High-Order Approximation of Convolutions with Weakly Singular Kernels ⋮ Convergence bounds of GMRES with Schwarz' preconditioner for the scattering problem

Uses Software

• PETSc
• FFTW

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast adaptive 2D vortex methods
• Spectral simulations of electromagnetic wave scattering
• Inverse acoustic and electromagnetic scattering theory.
• An \(hp\)-adaptive finite element method for electromagnetics. I: Data structure and constrained approximation
• Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations
• 2D vortex methods and singular quadrature rules
• Convergence Analysis of a Coupled Finite Element and Spectral Method in Acoustic Scattering
• The k-space formulation of the scattering problem in the time domain
• Applications of analysis on nilpotent groups to partial differential equations
• An analysis of the coupling of finite-element and Nyström methods in acoustic scattering
• Locally Corrected Multidimensional Quadrature Rules for Singular Functions
• A fast high-order solver for EM scattering from complex penetrable bodies: TE case
• A fast high-order solver for problems of scattering by heterogeneous bodies
• Higher-Order Fourier Approximation in Scattering by Two-Dimensional, Inhomogeneous Media
• A fast, high-order algorithm for the solution of surface scattering problems: Basic implementation, tests, and applications
• Convergent Cartesian grid methods for Maxwell's equations in complex geometries.

This page was built for publication: A fast, higher-order solver for scattering by penetrable bodies in three dimensions