An integral equation-based numerical method for the forced heat equation on complex domains

DOI10.1007/s10444-020-09804-zzbMath1452.65272arXiv1907.08537OpenAlexW3080356318MaRDI QIDQ2200076

Anna-Karin Tornberg, Fredrik Fryklund, Mary Catherine A. Kropinski

Publication date: 15 September 2020

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.08537

zbMATH Keywords

heat equationboundary integral methodYukawa potentialRothe's methodquadraturecomplex domainsmodified Helmholtz equationfunction extension

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical integration (65D30) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)

Related Items (8)

An adaptive kernel-split quadrature method for parameter-dependent layer potentials ⋮ The smooth forcing extension method: a high-order technique for solving elliptic equations on complex domains ⋮ Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects ⋮ An integral equation method for the advection-diffusion equation on time-dependent domains in the plane ⋮ An FMM Accelerated Poisson Solver for Complicated Geometries in the Plane Using Function Extension ⋮ Viscous transport in eroding porous media ⋮ Spectrally accurate solutions to inhomogeneous elliptic PDE in smooth geometries using function intension ⋮ A fast, high-order scheme for evaluating volume potentials on complex 2D geometries via area-to-line integral conversion and domain mappings

Uses Software

• Matlab
• DLMF
• rbf_qr

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