Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D

DOI10.1016/j.jcp.2018.10.002zbMath1416.65491arXiv1711.04236OpenAlexW2798848328MaRDI QIDQ2311471

Luiz M. Faria, Catalin Turc, Carlos Pérez-Arancibia

Publication date: 10 July 2019

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

Full work available at URL: https://arxiv.org/abs/1711.04236

zbMATH Keywords

harmonic polynomialsLaplace equationNyström methodboundary integral operatorslayer potentialsTaylor interpolation

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral operators (45P05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (11)

A Chebyshev-based rectangular-polar integral solver for scattering by geometries described by non-overlapping patches ⋮ On the regularization of Cauchy-type integral operators via the density interpolation method and applications ⋮ Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping ⋮ Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow ⋮ A Non-Singular Boundary Element Method for Interactions between Acoustical Field Sources and Structures ⋮ General-purpose kernel regularization of boundary integral equations via density interpolation ⋮ Planewave Density Interpolation Methods for 3D Helmholtz Boundary Integral Equations ⋮ Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme ⋮ A scalable computational platform for particulate Stokes suspensions ⋮ A fast, high-order scheme for evaluating volume potentials on complex 2D geometries via area-to-line integral conversion and domain mappings ⋮ High-Order Close Evaluation of Laplace Layer Potentials: A Differential Geometric Approach

Uses Software

• BEM++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A high-order integral solver for scalar problems of diffraction by screens and apertures in three-dimensional space
• Quadrature by expansion: a new method for the evaluation of layer potentials
• A Nyström method for weakly singular integral operators on surfaces
• A robust and non-singular formulation of the boundary integral method for the potential problem
• A fast algorithm for simulating vesicle flows in three dimensions
• A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
• A Nyström method for boundary integral equations in domains with corners
• Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning
• On the fast matrix multiplication in the boundary element method by panel clustering
• Double exponential formulas for numerical integration
• A fast integral equation method for solid particles in viscous flow using quadrature by expansion
• A plane-wave singularity subtraction technique for the classical Dirichlet and Neumann combined field integral equations
• A high-order algorithm for obstacle scattering in three dimensions
• On the numerical solution of a hypersingular integral equation in scattering theory
• The Euler-Maclaurin formula in presence of a logarithmic singularity
• New identities for fundamental solutions and their applications to non-singular boundary element formulations
• Convergence analysis of a high-order Nyström integral-equation method for surface scattering problems
• Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis
• On the evaluation of layer potentials close to their sources
• Fast construction of the Fejér and Clenshaw-Curtis quadrature rules
• A collocation method for a hypersingular boundary integral equation via trigonometric differentiation
• Ein numerisches Verfahren zur Lösung des Neumannschen Außenraumproblems für die Helmholtzsche Schwingungsgleichung
• Über eine Methode zum räumlichen Neumannschen Problem mit einer Anwendung für torusartige Berandungen
• A Method for Computing Nearly Singular Integrals
• Evaluation of Layer Potentials Close to the Boundary for Laplace and Helmholtz Problems on Analytic Planar Domains
• The Exponentially Convergent Trapezoidal Rule
• Non-singular boundary integral methods for fluid mechanics applications
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• On the extraction technique in boundary integral equations
• Hybrid Gauss-Trapezoidal Quadrature Rules
• High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions
• Surface scattering in three dimensions: an accelerated high–order solver
• A Grid-Based Boundary Integral Method for Elliptic Problems in Three Dimensions
• The Exponential Accuracy of Fourier and Chebyshev Differencing Methods
• Fast High Order Accurate Solution of Laplace’s Equation on Irregular Regions
• Spectrally Accurate Quadratures for Evaluation of Layer Potentials Close to the Boundary for the 2D Stokes and Laplace Equations
• Solving Boundary Integral Problems with BEM++
• A Fast Accurate Boundary Integral Method for Potentials on Closely Packed Cells
• Nearly Singular Integrals in 3D Stokes Flow
• A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces
• A fast algorithm for particle simulations
• A fast, high-order algorithm for the solution of surface scattering problems: Basic implementation, tests, and applications
• Numerical quadratures for singular and hypersingular integrals

This page was built for publication: Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D