Improved Matrix Solver for Multiphysics Modeling Based on a Novel Reusable Shifted Laplace Preconditioner

In the process of multiphysics coupling computations under frequency-domain electromagnetic (EM) field excitation, it is very challenging to solve a sequence of slowly varying EM linear systems. This paper proposes a novel solution framework, based on a reusable shifted Laplace preconditioner, which reduces the computational resources remarkably, by minimizing the number of preconditioner inversion operations in the preconditioned Krylov subspace method. Initially, the direct method is employed to solve the first EM finite element matrix, and the resulting LU matrices are stored for future use. Then, this LU decomposition serves as the shifted Laplace preconditioner for subsequent systems, which are solved iteratively using the Krylov subspace method. If the number of iterations for a system exceeds a predefined threshold, the direct method is applied to the next linear system to update the preconditioner. This iterative-direct approach continues until all linear systems in the sequence are resolved. Our solver’s accuracy and efficiency are evaluated against commercial software and standard direct methods, demonstrating superior performance. The effectiveness of our approach is further validated through multiphysics simulations of a real-world packaged balun for mmWave antenna, manifesting significant computational improvements.