A dual reciprocity multiwavelet Galerkin method for the numerical solution of Poisson׳s equation

A dual reciprocity multiwavelet Galerkin method is developed for the solution of Poisson׳s equation in this paper, which combines the dual reciprocity boundary element method (DRBEM) and the multiwavelet Galerkin method (MGM). The DRBEM is used to transform the domain integral in the boundary element formulation of Poisson׳s equation into the boundary of the domain, which is based on compactly supported positive definite radial basis function. Then, the MGM is employed for solving the resulting boundary integral equation, in which Alpert multiwavelets are employed to construct the trial and test functions of Galerkin variational formulation. Because of the use of multiwavelets, the resulting system matrix can be approximated by a sparse matrix. Compared to the DRBEM based on radial basis functions, the present method reduces the memory spaces and computational costs of the system matrix significantly. Numerical results show the efficiency of the present method.