Parallel Matrix-Free Implementation of Frequency-Domain Finite Difference Methods for Cluster Computing

Full-wave 3D electromagnetic simulations of complex planar devices, multilayer interconnects, and chip packages are presented for wide-band frequency-domain analysis using the finite difference integration technique developed in the PETSc software package. Initial reordering of the index assignment to the unknowns makes the resulting system matrix diagonally dominant. The rearrangement also facilitates the decomposition of large domain into slices for passing the mesh information to different machines. Matrix-free methods are then exploited to minimize the number of element-wise multiplications and memory requirements in the construction of the system of linear equations. Besides, the recipes provide extreme ease of modifications in the kernel of the code. The applicability of different Krylov subspace solvers is investigated. The accuracy is checked through comparisons with CST MICROWAVE STUDIO transient solver results. The parallel execution of the compiled code on specific number of processors in multi-core distributed-memory architectures demonstrate high scalability of the computational algorithm. Keywords— finite difference frequency domain (FDFD), finite integration technique, matrix-free method, parallel programming, computational electromagnetics.