A VLSI multigrid poisson solver amenable to biharmonic equation

Abstract

A VLSI parallel algorithm for solving discretized Poisson equation on an N×N grid is proposed. A standard multigrid algorithm is adopted which allows a parallel solution of this problem in T=O(logN) time steps. A special network consisting of N × N processor elements and of O(NlogN) interconnection lines in each direction results in a design the area of which is O(N2log2N). Thus, the AT2 estimation for this Poisson solver is O(N2log4N) which improves the best result known until now by factor of O(N/logN). An application of the multigrid Poisson solver is made to a VLSI semidirect biharmonic solver. The VLSI layout needs an area A=O(N3logN) and the time of algorithm is O(√Nlog2N). The total complexity for the VLSI biharmonic solver is AT2=O(N4log5N) which is of the same order as for the best algorithms developed until now.