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In this talk, I will introduce a Cartesian grid based boundary integral method for the Stokes equation on complex domains.The method solves the partial differential equations in the framework of boundary integral method (BIM), taking advantage of the stability property of BIM.But it is kernel-free in the sense that the method does not need to know any analytical expression for the kernel of the boundary integrals involved or the fundamental solution of the Stokes equation.Thus it is not limited to the applications that the traditional BIM applies to.