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

摘要

Provided that the boundary value problem can be equivalently solved in conformally transformed domain, one can consider its mapping into unit disk domain. The problem can be solved for the new geometry and the solution can be retransformed back to the original problem domain. The paper presents this approach in order to validate whether it can be applied for improving ill-conditioning of the matrices and solutions obtained in indirect Trefftz methods.