On the discretization of Laplace's equation with Neumann boundary conditions on polygonal domains

DOI10.1016/j.jcpx.2020.100072arXiv2001.05434OpenAlexW3080290339MaRDI QIDQ6145422

Jeremy G. Hoskins, Manas Rachh

Publication date: 9 January 2024

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

Full work available at URL: https://arxiv.org/abs/2001.05434

zbMATH Keywords

potential theoryboundary value problemsintegral equationssingular solutionscorners

Mathematics Subject Classification ID

Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx) Two-dimensional potential theory (31Axx)

Cites Work

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• A fast direct solver for the integral equations of scattering theory on planar curves with corners
• High-order accurate methods for Nyström discretization of integral equations on smooth curves in the plane
• Universal quadratures for boundary integral equations on two-dimensional domains with corners
• On the Nyström discretization of integral equations on planar curves with corners
• Integral equation methods for elliptic problems with boundary conditions of mixed type
• On the polarizability and capacitance of the cube
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• On the solution of the Helmholtz equation on regions with corners
• A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
• A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves
• Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques
• A Robust and Accurate Solver of Laplace's Equation with General Boundary Conditions on General Domains in the Plane
• On the Numerical Solution of Elliptic Partial Differential Equations on Polygonal Domains
• Solving Laplace Problems with Corner Singularities via Rational Functions
• Linear integral equations

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