Solving the nonlinear Poisson-type problems with F-Trefftz hybrid finite element model

Date

2012

Authors

Wang, Hui
Qin, Qing Hua
Liang , Xing-Pei

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

A hybrid finite element model based on F-Trefftz kernels (fundamental solutions) is formulated for analyzing Dirichlet problems associated with two-dimensional nonlinear Poisson-type equations including nonlinear PoissonBoltzmann equation and diffusionreaction equation. The nonlinear force term in the Poisson-type equation is frozen by introducing the imaginary terms at each Picard iteration step, and then the induced Poisson problem is solved by the present hybrid finite element model involving element boundary integrals only, coupling with the particular solution method with radial basis function interpolation. The numerical accuracy of the present method is investigated by numerical experiments for problems with complex geometry and various nonlinear force functions.

Description

Keywords

Keywords: Boundary integrals; Complex geometries; Diffusion-reaction equation; Dirichlet problem; Fundamental solutions; Hybrid finite element methods; Hybrid finite elements; Nonlinear force; Nonlinear Poisson-Boltzmann equation; Nonlinear Poisson-type equation; N Fundamental solution; Hybrid finite element method; Nonlinear Poisson-type equation; Radial basis function

Citation

Source

Engineering Analysis with Boundary Elements

Type

Journal article

Book Title

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Restricted until

2037-12-31