Analiza teoretyczna oraz numeryczna wybranej hybrydowej nieosobliwej metody Trefftza na przykładzie dwuwymiarowego zagadnienia Poissona, Cz. 2
Journal Title: Autobusy. Technika, Eksploatacja, Systemy Transportowe - Year 2017, Vol 214, Issue 12
Abstract
The aim of this paper is theoretical and numerical analysis of one of the nonsingular Trefftz method. Two-dimensional boundary value problem governed by Poisson’s equation is taken as the example. Domain boundary equation is obtained from one of the variational formulation. In this paper the original one is considered. By proper selection of the base functions one can simplify the problem by limiting the calculations to the boundary of the analyzed domain only. The solution of the problem is assumed as the superposition of regular Trefftz functions, which satisfy the differential Laplace’s equation. Taking the same functions as the weighting functions one obtains equations of the O-S;T-T methods (Galerkin version). The first part of the paper contains the theoretical analysis of the O-S;T-T methods and shows how to implement it to solve the Poisson’s problem. The second part of the paper is devoted to Poisson’s problem in the domain divided into subdomains (hybrid method). Direct method of subdomains coupling is presented and implemented for solving two boundary value problems.
Authors and Affiliations
Dorota Borkowska
Keywords
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