A scalable VLSI algorithm for the fourth-order elliptic problem

The work presents a parallel scalable VLSI algorithm for solving the first fourth-order elliptic boundary value problem on a rectangle. The VLSI complexity AT/sup 2/ of the algorithm (A-area, T-time) is expressed in terms of the problem size n/sup 2/ (the number of discretization points) and the VLSI array size p/sup 2/ (the number of processing cells). The algorithm is based on the semidirect procedure where in each iteration two discretized Poisson equations occur. The design is of a scalable form where one VLSI block performs all operations of the semidirect cycle. Its length and height is O(plogp) and O((n/sup 2//p) logn+plogp) respectively. One iteration of the semidirect process costs O((n/p)/sup 2/logn) parallel time steps. The number of iterations required to obtain a solution with an initial error reduced by O(n/sup -2/) is O(/spl radic/(nlogn)). Hence, the global estimation of this algorithm is O((n/sup 7/log/sup 5/nlogp)/p/sup 4/+(n/sup 5/1og/sup 4/nlog/sup 2/p)/p/sup 2/) in AT/sup 2/ complexity measure.