Boundary integral equations with the generalized Neumann kernel for Laplace's equation in multiply connected regions

DOI10.1016/j.amc.2010.11.027zbMath1211.65159OpenAlexW2161697123MaRDI QIDQ621020

Sumit K. Garg

Publication date: 2 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.11.027

zbMATH Keywords

Dirichlet problemnumerical resultsboundary integral equationLaplace equationNeumann problemNyström methodtrapezoidal rulemultiply connected regions

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (23)

Solving Robin problems in multiply connected regions via an integral equation with the generalized Neumann kernel ⋮ Fast computing of conformal mapping and its inverse of bounded multiply connected regions onto second, third and fourth categories of Koebe's canonical slit regions ⋮ Radial slit maps of bounded multiply connected regions ⋮ Numerical computation of the capacity of generalized condensers ⋮ Circular slits map of bounded multiply connected regions ⋮ A boundary integral equation with the generalized Neumann kernel for a certain class of mixed boundary value problem ⋮ A Boundary Integral Method for the General Conjugation Problem in Multiply Connected Circle Domains ⋮ Vortex generated fluid flows in multiply connected domains ⋮ Numerical conformal mapping onto the parabolic, elliptic and hyperbolic slit domains ⋮ A boundary integral equation with the generalized Neumann kernel for a mixed boundary value problem in unbounded multiply connected regions ⋮ Linear integral equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits ⋮ A fast numerical method for ideal fluid flow in domains with multiple stirrers ⋮ Numerical computation of the conformal map onto lemniscatic domains ⋮ Fractal local fields in random composites ⋮ Spiral slits map and its inverse of bounded multiply connected regions ⋮ Conformal mapping of unbounded multiply connected regions onto canonical slit regions ⋮ SERIES SOLUTION OF LAPLACE PROBLEMS ⋮ Analysis of the dipole simulation method for two-dimensional Dirichlet problems in Jordan regions with analytic boundaries ⋮ Numerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions ⋮ Parallel slits map of bounded multiply connected regions ⋮ Boundary integral equations for potential flow past multiple aerofoils ⋮ Straight slits map and its inverse of bounded multiply connected regions ⋮ Fast computation of the circular map

Uses Software

• Algorithm 788

Cites Work

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• The Riemann--Hilbert problem and the generalized Neumann kernel
• Laplace's equation and the Dirichlet-Neumann map: a new mode for Mikhlin's method
• Rapid methods for the conformal mapping of multiply connected regions
• Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
• A boundary integral equation for conformal mapping of bounded multiply connected regions
• The Riemann-Hilbert problem and the generalized Neumann kernel on multiply connected regions
• On the evaluation of layer potentials close to their sources
• The solution of non-unique linear integral equations
• A boundary integral method for the Riemann–Hilbert problem in domains with corners
• Numerical Conformal Mapping via a Boundary Integral Equation with the Generalized Neumann Kernel
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Algorithm 788: automatic boundary integral equation programs for the planar Laplace equation
• The Schwarz problem in multiply connected domains and the Schottky–Klein prime function
• The Numerical Solution of Fredholm integral Equations of the Second Kind
• The Numerical Solution of the Eigenvalue Problem for Compact Integral Operators
• Linear integral equations

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