title: Limits for computational electromagnetics codes imposed by computer architecture
abstract: The algorithmic complexity of the innermost loops that determine the complexity of algorithms in computational electromagnetics (CEM) codes are analyzed according to their operation count and the impact of the underlying computer hardware. As memory chips are much slower than arithmetic processors, codes that involve a high data movement compared to the number of arithmetic operations are executed comparatively slower. Hence, matrix-matrix multiplications are much faster than matrix-vector multiplications. It is seen that it is not sufficient to compare only the complexity, but also the actual performance of algorithms to judge on faster execution. Implications involve FDTD loops, LU factorizations, and iterative solvers for dense matrices. Run times on two reference platforms, namely an Athlon 900 MHz and an HP PA 8600 processor, verify the findings
keyphrases: computational electromagnetics codes computer architecture algorithmic complexity innermost loops operation count computer hardware memory chips data movement matrix-matrix multiplications matrix-vector multiplications FDTD loops LU factorizations iterative solvers dense matrices CEM codes