Parallel Iterative FEM Solver with Initial Guess for Frequency Domain Electromagnetic Analysis

Abstract

The finite element method is a key player in computational electromagnetics for designing RF (Radio Frequency) components such as waveguides. The frequency-domain analysis is fundamental to identify the characteristics of the components. For the conventional frequency-domain electromagnetic analysis using FEM (Finite Element Method), the system matrix is complex-numbered as well as indefinite. The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps. However, such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver. It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency. Overall, it is hard to adopt conventional iterative solvers even though the system matrix is sparse. A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper. In this implementation, the previous solution of the iterative solver of Matlab (Matrix Laboratory) employing the preconditioner is used for the initial guess for the next step's solution process. The overlapped parallel stage using Matlab's Parallel Computing Toolbox is also proposed to alleviate the cold starting, which ruins the convergence of early steps in each parallel stage. Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.

Extracting Resistance, Inductance, and Capacitance Matrices Using Finite Element Method

“…이러한 전자기 수치해석 기법의 하나인 유한요 소법(finite element method, FEM)은 곡면과 같은 기하학적 으로 복잡한 구조의 해석이 가능하며, 비균질성 매질의 해석에 강점을 가진다. 게다가, 유한요소 과정을 통해 얻 게 되는 행렬은 0을 많이 포함하고 있는 sparse matrix가 되기 때문에 계산 부하가 적으며, 반복법 및 분할 알고리 듬을 적용한 병렬 연산을 적용하기에 적합하다는 장점이 있다 [10], [11] .…”

Extracting Resistance, Inductance, and Capacitance Matrices Using Finite Element Method

“…이러한 전자기 수치해석 기법의 하나인 유한요 소법(finite element method, FEM)은 곡면과 같은 기하학적 으로 복잡한 구조의 해석이 가능하며, 비균질성 매질의 해석에 강점을 가진다. 게다가, 유한요소 과정을 통해 얻 게 되는 행렬은 0을 많이 포함하고 있는 sparse matrix가 되기 때문에 계산 부하가 적으며, 반복법 및 분할 알고리 듬을 적용한 병렬 연산을 적용하기에 적합하다는 장점이 있다 [10], [11] .…”