A multiwavelet Galerkin method for Stokes problems using boundary integral equations

A multiwavelet Galerkin method for the simulation of two-dimensional incompressible viscous fluid flow in primitive variables is developed in this paper. This method combines a Galerkin variational formulation of the boundary integral equation based on single layer potential to the Stokes equation with the trial and test functions constructed by Alpert multiwavelets. Due to the use of multiwavelets and compression strategies, the present method reduces the computational complexity of system matrix from O(N2) to almost O(N) (where N is the number of unknowns). In order to compute the double integrals with logarithmic kernel more efficiently, the analytical formulae to calculate the inner integrals are presented in this paper and then the Gaussian quadrature is used for the outer integrals. Some numerical examples are given to demonstrate the availability of the method.