An Efficient Cartesian Grid-Based Method for Scattering Problems with Inhomogeneous Media

DOI10.4208/nmtma.oa-2022-0159OpenAlexW4362636409MaRDI QIDQ6191779

Jiwei Zhang, Haixia Dong, Wenjun Ying

Publication date: 11 March 2024

Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/nmtma.oa-2022-0159

zbMATH Keywords

transmission probleminhomogeneous mediaCartesian grid-based methodfast Fourier transform preconditioned conjugate gradient solvermodified fourth-order compact difference scheme

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Cites Work

• Unnamed Item
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• High order numerical simulation of the transmission and scattering of waves using the method of difference potentials
• A kernel-free boundary integral method for implicitly defined surfaces
• A general approach for high order absorbing boundary conditions for the Helmholtz equation
• A robust and non-singular formulation of the boundary integral method for the potential problem
• A system of boundary integral equations for the transmission problem in acoustics
• A fast and well-conditioned spectral method for singular integral equations
• A hybridizable discontinuous Galerkin method for elliptic interface problems in the formulation of boundary integral equations
• Non-reflecting boundary conditions
• Symmetric boundary integral formulations for Helmholtz transmission problems
• High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces
• Boundary integral solutions of coupled Stokes and Darcy flows
• A direct boundary integral equation method for transmission problems
• Exact non-reflecting boundary conditions
• Numerical solution of problems on unbounded domains. A review
• A perfectly matched layer for the absorption of electromagnetic waves
• A high-order algorithm for obstacle scattering in three dimensions
• On nonreflecting boundary conditions
• The method of difference potentials for the Helmholtz equation using compact high order schemes
• High-order finite difference methods for the Helmholtz equation
• An efficient iterative method for solving multiple scattering in locally inhomogeneous media
• A fourth-order kernel-free boundary integral method for the modified Helmholtz equation
• A fourth-order kernel-free boundary integral method for implicitly defined surfaces in three space dimensions
• The boundary element-free method for 2D interior and exterior Helmholtz problems
• Error analysis of symmetric linear/bilinear partially penalized immersed finite element methods for Helmholtz interface problems
• Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
• Coupling of boundary integral equation and finite element methods for transmission problems in acoustics
• Solving interface problems of the Helmholtz equation by immersed finite element methods
• Direct implementation of high order BGT artificial boundary conditions
• A high-order kernel-free boundary integral method for the biharmonic equation on irregular domains
• A kernel-free boundary integral method for elliptic boundary value problems
• Mixed boundary integral methods for Helmholtz transmission problems
• GMRES and the minimal polynomial
• Analysis of Finite Element Methods and Domain Decomposition Algorithms for a Fluid-Solid Interaction Problem
• A Method for Computing Nearly Singular Integrals
• The Method of Regularized Stokeslets
• High Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients
• Corrected trapezoidal rules for a class of singular functions
• Convergence of the Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems in Two-Layered Media
• Non-singular boundary integral methods for fluid mechanics applications
• Numerical Methods for Exterior Problems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions
• The Perfectly Matched Layer in Curvilinear Coordinates
• Some notes on singular integral techniques in boundary element analysis
• A Grid-Based Boundary Integral Method for Elliptic Problems in Three Dimensions
• A high-order compact scheme for the one-dimensional Helmholtz equation with a discontinuous coefficient
• A High-Order Piecewise Quartic Spline Rule for Hadamard Integral and Its Application of the Cavity Scattering
• A Cartesian Grid-Based Boundary Integral Method for an Elliptic Interface Problem on Closely Packed Cells
• An Adaptive Finite Element PML Method for the Open Cavity Scattering Problems
• Acoustic Scattering Problems with Convolution Quadrature and the Method of Fundamental Solutions
• Fast High Order Accurate Solution of Laplace’s Equation on Irregular Regions
• Nitsche's method for Helmholtz problems with embedded interfaces
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Boundary Integral Equation Methods for the Two-Dimensional Fluid-Solid Interaction Problem
• Nearly Singular Integrals in 3D Stokes Flow
• A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs
• A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces
• The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions