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.

我们提出了一种非迭代方案，用于解决具有任意数量自由度的一般线性静止原边值问题。主要目标是将具有任意几何形状的域的有限元方法性能与与其低计算成本相关的有限差分方法效率相结合。我们应用域分解方案来定义矩形子域（2D 情况）或矩形六面体子域（3D 情况）。有限元网格以规则区域中的元素为正方形（2D 情况）或立方体（3D 情况）的方式生成。合适的重叠方案允许有限元法用于非规则元素的区域，而有限差分法可用于规则元素的区域（2D 情况下的正方形或 3D 情况下的立方体）。