This project develops the Multigrid Machine (MGM), a highly parallel VLSI architecture for the solution of partial differential equations (PDEs) using the multigrid methods. The mutigrid methods are one of the most efficient solution methods for PDEs and are inherently parallel. The MGM is developed using the super-copresser methodology, which has been applied to realize special-purpose VLSI architectures for sorting, matrix multiplication, and the solution of PDEs using finite difference methods. The MGM is a synchronous architecture highly suited for VLSI implementation and is able to solve problems of arbitrary dimensions. The MGM developed with cost-effective supercomputer performance will influence many domains which require high-speed solution of PDEs. Its development will allow new knowledge to be gained in the use of synchronous parallel arrays to implement asynchronous iterative algorithms and the design of new parallel multigrid algorithms for VLSI implementation. The flexible software emulator and timing model for the MGM will be useful for studying many other domains in which multi- level algorithms are effective.
