Trefftz-type procedure for Laplace equation on domains with circular holes, circular inclusions, corners, slits, and symmetry - Kołodziej, Jan A.; Uściłowska, Anita (Computer Assisted Methods in Engineering and Science, 1997)
The purpose of the paper is to propose of a way of constructing trial functions for the indirect Trefftz method as applied to harmonic problems possessing circular holes, circular inclusions, corners, slits, and symmetry. In the traditional indirect formulation of the Trefftz method, the solution of the boundary-volume problem is approximated by a linear combination of the T-complete functions and some coefficients. The T-complete Trefftz functions satisfy exactly the governing equations, while the unknown coefficients are determined so as to make the boundary conditions satisfied approximately. The trial functions, proposed and systematically constructed in this paper, fulfil exactly not only the differential equation, but also certain given boundary conditions for holes, inclusions, cracks and the conditions resulting from symmetry. A list of such trial functions, unavailable elsewhere, is presented. The efficiency is illustrated by examples in which three Trefftz-type procedures, namely the boundary collocation, least square, and Galerkin is used.