Unconditionally stable concurrent procedures for transient finite element analysis

Abstract

A new class of algorithms for transient finite element analysis which is amenable to an efficient implementation in parallel computers is proposed. The suitability of the method for parallel computation stems from the fact that, given an arbitrary partition of the finite element mesh, each subdomain in the partition can be processed over a time step independently and simultaneously with the rest. Both element-by-element and coarse partitions of the mesh are discussed. For the former, the proposed algorithms are shown to have the structure of an explicit scheme. In particular, no global equation solving effort is involved in the update procedure. However, in contrast to explicit schemes the proposed algorithms are shown to be unconditionally stable over a certain range of the algorithmic parameters. In structural dynamics problems, good accuracy is obtained with a constant time step integration. For heat conduction problems accuracy limitations suggest the use of a step-changing technique. When this is done, numerical tests indicate the good behavior of the method. The case in which the mesh is partitioned into a small number of subdomains, typically as many as processors in the computer, is also explored in detail. Good accuracy is obtained over a wide range of time steps. Finally, extensions to second- and higher-order accuracy methods are discussed.