A scheme for the analysis of primal stationary boundary value problems based on FE/FD multi-method

摘要

We present a non-iterative scheme for solving general linear stationary primal boundary value problems with an arbitrary number of degrees of freedom. The main goal is to combine the finite element method performance for domains with arbitrary geometry with the finite difference method efficiency related to its low computational cost. We apply a domain decomposition scheme to define rectangular subdomains (2D case) or rectangular hexahedral subdomains (3D case). A finite element mesh is generated in such a way that the elements in the regular regions are squares (2D case) or cubes (3D case). A suitable overlap scheme allows the finite element method to be used in regions of non-regular elements, while the finite difference method can be used in regions with regular elements (squares for 2D case or cubes for 3D case). We present six computational simulations showing the best performance in the CPU time of the proposed scheme compared to the classic finite element method while maintaining solution accuracy.