Static and quasi-dynamic load balancing in parallel FDTD codes for signal integrity, power integrity, and packaging applications

The finite-difference time-domain (FDTD) method is a robust technique for calculating electromagnetic fields, but practical problems, involving complex or large geometries, can require a long time to calculate on any one single-processor computer. One computer with many processors or many single-processor computers can reduce the computation time. However, some FDTD cell types, e.g., PML cells, require more computation time than others. Thus, the size and shape of the individual process allocations can significantly influence the computation time. This paper addresses these load balancing issues with static and quasi-dynamic approaches. The message-passing interface (MPI) library is applied to a three-dimensional (3D) FDTD code. Timing results including speedup and efficiency, are presented for trials run on a cluster of sixteen processing nodes and one server node. Two examples are shown in this paper, a power bus with 16 decoupling capacitors and a five layer power distribution network. In such models, the problem size and complexity make modeling with a serial code impractical and time consuming for engineering. Models with several million cells take days to run, but proper implementation, including load balancing, can reduce this execution time to hours on a sufficiently powerful cluster.