Parallel Discrete Complex Image Method for Barnes-Hut Accelerated Capacitance Extraction in Multilayered Substrates

Abstract

From the results of the previous section it is apparent that kernel evaluations by means of interpolation from a pre-existing database is much more time-efficient for computing both the near-interactions and the matrix-vector product. In fact, the Best-MEM method provides completely unacceptable computational time and should not even be considered as an option unless the computational environment possesses severe memory limitations. On the other hand, for large, multiscale geometries involving millions of unknowns, it may not be possible to store the entire kernel database. In these cases, it is our recommendation to select po(p) larger than the radius of near interactions. In this way, the near-matrix-fill time will remain unchanged and both memory levels and MVP times will be acceptable. Obviously, for distributed systems with significant amounts of memory, computational time will benefit if as much of the database is stored as memory permits.