Numerical solutions of two-dimensional Laplace and biharmonic equations by the localized Trefftz method

DOI10.1016/j.camwa.2020.09.023OpenAlexW3097747139MaRDI QIDQ2019559

Weichung Yeih, Yan-Cheng Liu, Chia-Ming Fan, Cheng-Yu Ku, Chiung-Lin Chu

Publication date: 21 April 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2020.09.023

zbMATH Keywords

biharmonic equationLaplace equationmeshless methodmultiply-connected domainlocalized Trefftz method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Stokes and related (Oseen, etc.) flows (76D07) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items

Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material, A meshless collocation method for solving the inverse Cauchy problem associated with the variable-order fractional heat conduction model under functionally graded materials, Localized singular boundary method for solving Laplace and Helmholtz equations in arbitrary 2D domains, A space-time generalized finite difference method for solving unsteady double-diffusive natural convection in fluid-saturated porous media

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On choosing the location of the sources in the MFS
• Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations
• Element-free Galerkin methods for static and dynamic fracture
• A meshless collocation method based on the differential reproducing kernel interpolation
• Indirect Trefftz method for boundary value problem of Poisson equation.
• The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics
• Resolution of three-dimensional Stokes fluid flows using a Trefftz method
• A new method of fundamental solutions applied to nonhomogeneous elliptic problems
• A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Analysis of three-dimensional interior acoustic fields by using the localized method of fundamental solutions
• Solving the inverse Stokes problems by the modified collocation Trefftz method and Laplacian decomposition
• Generalized finite difference method for solving two-dimensional non-linear obstacle problems
• A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain's Characteristic Length
• Application of symmetric indirect Trefftz method to free vibration problems in 2D
• Trefftz method: A general theory
• Trefftz method: An overview
• The Trefftz method as an integral equation