Fast Finite Element Method Using Multi-Step Mesh Process

This paper introduces a new method for accelerating current sluggish FEM and improving memory demand in FEM problems with high node resolution or bulky structures. Like most of the numerical methods, FEM results to a matrix equation which normally has huge dimension. Breaking the main matrix equation into several smaller size matrices, the solving procedure can be accelerated. For implementing this matter, the meshing process should be changed. Here, a multi-step meshing process is proposed which consists of both posterior and main levels. The posterior level is used for separating matrix equations from each other and the main level for field computation in the problem. The proposed approach is compatible with other optimizing method for increasing speed in FEM. Therefore, combining this method with other methods creates a powerful asset for solving complex FEM problems. The results show that the proposed method speeds up FEM and decreases the memory capacity. In addition, it brings the facility of parallel computation which is of great importance in fast computational algorithm.