2007c): A MRIEM for solving the Laplace equation in the doubly-connected domain. CMES: Computer Modeling in Engineering & Sciences

Abstract: A new method is developed to solve the Dirichlet problems for the two-dimensional Laplace equation in the doubly-connected do-mains, namely the meshless regularized integral equations method (MRIEM), which consists of three portions: Fourier series expansion, the Fred-holm integral equations, and linear equations to determine the unknown boundary conditions on artificial circles. The boundary integral equations on artificial circles are singular-free and the ker-nels are degenerate. When boundary-type meth-ods are inefficient to treat the problems with com-plicated domains, the new method can be appli-cable for such problems. The new method by us-ing the Fourier series and the Fourier coefficients can be adopted easily to derive the meshless nu-merical method. Several numerical examples are tested showing that the new method is powerful