zaiki@uunet.UU.NET (Koji Zaiki) (07/11/90)
How do you do ? I read the news from you about multigrid and conjugate gradient method(CG) for parallel processing. I've developed the CG program for our parallel computer ADENA. The ADENA is a parallel MIMD computer and its architecture concept is based on ADE(Alternating Direction Edition) with no memory conflict. This machine is developed by us. Until now, it has been shown that the three-dimensional simulations of natural phenomena such as an air pollution or tidal waves are successfully solved by the vectorized ICCG and ILUBCG methods using the vector processors. But these algorithms were not efficiently executed by parallel computers. Now consider to solve the following equation. A * u = f. where A is the coeficient matrix, u is the answer. In general, the iteration process is described as C*( u(n+1)-u(n) ) = - tau(n+1) *( A*u(n) - f ) where the matrix C is an approximate factorization of the matrix A. The ADENA computer allows massively parallel computation of the splitting-up operator method, which is a generalization of the ADI method. In my algorithm, the matrix C is given as follows: C = (D+A1)*D'*(D+A2)*D'*(D+A3) A = D + A1 + A2 + A3 where D is diagonal elements in the matrix A. A1, A2, and A3 are off- diagonal elements in the x-, y-, and z-directions, respectively. D' is the inverse of D. This algorithm is useful for the finite difference scheme. And now, we are looking for FEM for parallel processing. If you have any idea or information about FEM for parallel processing or other PPCG, please email. 1990, 7, 11 Koji Zaiki VLSI device research laboratory Semiconductor research center Matsushita Electric Industrial Co., Ltd. email zaiki@sd11.src.mei.co.jp