Application of conformal mappings and the numerical analysis of conditioning of the matrices in Trefftz method for some boundary value problems

DOI10.1016/j.enganabound.2018.09.010zbMath1404.65289OpenAlexW2896703854WikidataQ129087197 ScholiaQ129087197MaRDI QIDQ1634606

R. Kuras, Mariusz Borkowski

Publication date: 18 December 2018

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2018.09.010

zbMATH Keywords

conformal mappingill-conditioningTrefftz methods2D potential problem

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) General theory of conformal mappings (30C35) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Schwarz-Christoffel-type mappings (30C30)

Related Items

Applications of the Trefftz method to the anti-plane fracture of 1D hexagonal piezoelectric quasicrystals

Uses Software

• Schwarz-Christoffel
• SC Toolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Conformal mapping for the efficient MFS solution of Dirichlet boundary value problems
• Conformal mapping of the unit circle or of the upper half plane onto a polygon
• A numerical conformal mapping method for harmonic mixed boundary value problems
• Singularities and treatments of elliptic boundary value problems.
• An effectively modified direct Trefftz method for 2D potential problems considering the domain's characteristic length
• Application of a direct Trefftz method with domain decomposition to 2D potential problems
• Conformal mapping for the efficient solution of Poisson problems with the Kansa-RBF method
• A numerical conformal transformation method for harmonic mixed boundary value problems in polygonal domains
• Circulant matrix and conformal mapping for solving partial differential equations
• Treatment of harmonic mixed boundary problems by conformal transformation methods
• Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping
• Survey of trefftz-type element formulations
• Schwarz-Christoffel Mapping
• Trefftz method: An overview
• All well-posed problems have uniformly stable and convergent discretizations