Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain.

DOI10.1016/j.cam.2005.04.025zbMath1096.65106OpenAlexW2095628847MaRDI QIDQ2490721

Xiao-Biao Lin, Ming-Chih Lai, Zhilin Li

Publication date: 18 May 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.04.025

zbMATH Keywords

numerical examplesfast Fourier transformfinite differencePoisson equationsspherical coordinatesartificial boundary conditioninfinite domainlevel set functionarbitrary interfaceblock tridiagonal systemcyclic reduction methodextension of jumpsfast 3D Poisson solvermmersed interface method

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

A coupling interface method for elliptic interface problems ⋮ Immersed interface interpolation schemes for particle-mesh methods ⋮ Discontinuous bubble scheme for elliptic problems with jumps in the solution ⋮ A fast parallel 3D Poisson solver with longitudinal periodic and transverse open boundary conditions for space-charge simulations ⋮ Fast Finite Element Method for the Three-Dimensional Poisson Equation in Infinite Domains ⋮ Spectral method for matching exterior and interior elliptic problems

Cites Work

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• Numerical solution of problems on unbounded domains. A review
• A note on immersed interface method for three-dimensional elliptic equations
• Nonlinear potential theory and weighted Sobolev spaces
• Accurate numerical methods for micromagnetics simulations with general geometries.
• Level-set function approach to an inverse interface problem
• Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions
• A direct Method for the Discrete Solution of Separable Elliptic Equations
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
• A Fast Iterative Algorithm for Elliptic Interface Problems
• New Formulations for Interface Problems in Polar Coordinates
• An immersed interface method for anisotropic elliptic problems on irregular domains in 2D
• A fast spectral/difference method without pole conditions for Poisson-type equations in cylindrical and spherical geometries
• A fast algorithm for particle simulations
• Function theory