Improvements in linear system solutions to Finite Element Method

This work presents a flexible implementation of Finite Element Method (fFEM) to disassembly and assembly only elements of the linear systems whose properties were modified. It is important resource in problems where the runtime with FEM should be reduced. In this case, the first run store main global characteristics to be reused in next executions. This technique uses Biconjugate Gradient Stabilized iterative method with ILU preconditioner and direct method to solve linear systems. The evaluation of this entire solution was performed to solve an optical waveguide grating in time domain and a straight waveguide in frequency domain. The results present good performance in frequency domain, reducing the runtime. For this reason, this work suggests the possibility to integrate these improvements with some metaheuristics to optimize electromagnetic devices as future work.