The Invertibility of the Double Layer Potential Operator in the Space of Continuous Functions Defined on a Polyhedron: The Panel Method

DOI10.1080/00036819208840093zbMath0749.31003OpenAlexW2020155094WikidataQ58243398 ScholiaQ58243398MaRDI QIDQ4007147

Andreas Rathsfeld

Publication date: 27 September 1992

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036819208840093

zbMATH Keywords

collocation methodinvertibilitynumerical solutionboundary integralpanel methoddouble layer potential operator

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

Related Items (22)

On quadrature methods for the double layer potential equation over the boundary of a polyhedron ⋮ Solvability of a boundary integral equation on a polyhedron ⋮ Finite Section Method for the Double Layer Potential Operator over Polyhedral Boundaries ⋮ On the spectrum of the double-layer operator on locally-dilation-invariant Lipschitz domains ⋮ The invetibility of the double layer potential operator in the space of continuous functions defined over a polyhedron. the panel method. erratum ⋮ The quasi-static plasmonic problem for polyhedra ⋮ A spline collocation method for multidimensional strongly elliptic pseudodifferential operators of order zero ⋮ Solution of the Robin problem for the Laplace equation ⋮ Spline approximation methods for multidimensional periodic pseudodifferential equations ⋮ The harmonic dirichlet problem for a cracked domain with jump conditions on cracks ⋮ Solution of the Dirichlet problem for the Laplace equation. ⋮ Representations and estimates for inverse operators in the harmonic potential theory for polyhedra ⋮ On C. Neumann's method for second-order elliptic systems in domains with non-smooth boundaries ⋮ Continuous Extendibility of Solutions of the Neumann Problem for the Laplace Equation ⋮ Continuous Extendibility of Solutions of the Third Problem for the Laplace Equation ⋮ Boundedness of the solution of the third problem for the Laplace equation ⋮ Boundary Problems for Harmonic Functions and Norm Estimates for Inverses of Singular Integrals in Two Dimensions ⋮ The third boundary value problem in potential theory for domains with a piecewise smooth boundary ⋮ On the traction problem for the Lamé system on curvilinear polygons ⋮ On the essential norm of the double layer potential on polyhedral domains and the stability of the collocation method ⋮ Solution of the Neumann problem for the Laplace equation ⋮ Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains

Cites Work

• Eigenvalues for spherical domains with corners via boundary integral equations
• Corner singularity for transmission problems in three dimensions
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Integral operators in potential theory
• The Dirichlet problem in non-smooth domains
• The Neumann problem on Lipschitz domains

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