A Wavelet Interpolation Galerkin Method for the Solution of Boundary Value Problems in 2D Electrostatic Field
Xu Meng · Journal of Hebei University of Technology · 2001
This paper presents a new method for the numerical solution to partial difference equations named a wavelet interpolation Galerkin method, in which autocorrelation functions of Daubechies's compactly supported wavelets are taken as the Riesz's basis with interpolation properties for the solution space. It is discussed to precondition the coefficient matrix and to treat the domain with several media. Then external wavelets are used to deal with mixed boundary conditions, which simplifies the disposal of boundary conditions and improves the accuracy of approximate solutions. Applied for the numerical computation of boundary value problems in 2D electrostatic field, some results show its validity. And results from finite element method are also given.