Laplace's equation and the Dirichlet-Neumann map: a new mode for Mikhlin's method

DOI10.1016/j.jcp.2004.06.024zbMath1063.65130OpenAlexW2086261919MaRDI QIDQ703768

Johan Helsing, Eddie Wadbro

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.2004.06.024

zbMATH Keywords

computational complexityLaplace's equationDirichlet-Neumann mapNumerical examplesIntegral equationsFast solversExterior problemMikhlin's methodMultiply connected domains

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Complexity and performance of numerical algorithms (65Y20) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (13)

Simulating local fields in carbon nanotube-reinforced composites for infinite strip with voids ⋮ A local target specific quadrature by expansion method for evaluation of layer potentials in 3D ⋮ Boundary integral equations with the generalized Neumann kernel for Laplace's equation in multiply connected regions ⋮ An adaptive fast multipole accelerated Poisson solver for complex geometries ⋮ Computing the logarithmic capacity of compact sets having (infinitely) many components with the charge simulation method ⋮ Structure of the scalar field around unidirectional circular cylinders ⋮ A boundary integral equation with the generalized Neumann kernel for a certain class of mixed boundary value problem ⋮ A boundary integral equation with the generalized Neumann kernel for a mixed boundary value problem in unbounded multiply connected regions ⋮ On the evaluation of layer potentials close to their sources ⋮ Approximate inverse preconditioners for some large dense random electrostatic interaction matrices ⋮ Faster convergence and higher accuracy for the Dirichlet-Neumann map ⋮ Integral Equation Methods for Elastance and Mobility Problems in Two Dimensions ⋮ Boundary integral equations for potential flow past multiple aerofoils

Uses Software

• FMM Toolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Microstructural evolution in inhomogeneous elastic media
• Stress calculations on multiply connected domains
• Rapid solution of integral equations of classical potential theory
• A boundary integral method for the simulation for two-dimensional particle coarsening
• Second-kind integral formulations of the capacitance problem
• Second kind integral equations for the classical potential theory on open surfaces I: Analytical apparatus.
• A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow.
• A fast solver for the Stokes equations with distributed forces in complex geometries.
• Second kind integral equations for the classical potential theory on open surfaces. II.
• Integral equation methods for Stokes flow in doubly-periodic domains
• Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
• Integral equation methods for Stokes flow and isotropic elasticity in the plane
• Thin bridges in isotropic electrostatics
• On the Interior Stress Problem for Elastic Bodies
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A Fast Adaptive Multipole Algorithm for Particle Simulations
• On Deriving the Inverse of a Sum of Matrices
• The completed double layer boundary integral equation method for two-dimensional Stokes flow
• Preconditioned, Adaptive, Multipole-Accelerated Iterative Methods for Three-Dimensional First-Kind Integral Equations of Potential Theory
• A fast algorithm for particle simulations
• Boundary integral methods for multicomponent fluids and multiphase materials.
• Large-scale simulations of microstructural evolution in elastically stressed solids.

This page was built for publication: Laplace's equation and the Dirichlet-Neumann map: a new mode for Mikhlin's method