A Large scale finite element analysis using domain decomposition method on a parallel computer

A parallel finite element analysis based on a domain decomposition technique (DDT) is considered. In the present DDT, an analysis domain is divided into a number of smaller subdomains without overlap. Finite element analyses of the subdomains are performed under the constraint of both displacement continuity and force equivalence among them. The constraint is satisfied through iterative calculations based on either the Uzawa algorithm or the Conjugate Gradient (CG) method. Owing to the iterative algorithm, a large scale finite element analysis can be divided into a number of smaller ones which can be carried out in parallel.

The DDT is implemented on a parallel computer network composed of a number of 32-bit microprocessors, transputers. The developed parallel calculation system named the ‘FEM server type system’ involves peculiar features such as network independence and dynamic workload balance.

The characteristics of the domain decomposition method such as computational speed and memory requirement are first examined in detail through the finite element calculations of homogeneous or inhomogeneous cracked plate subjected to a tensile load on a single CPU computer.

The ‘speedup’ and ‘performance’ features of the FEM server type system are discussed on a parallel computer system composed of up to 16 transputers, with changing network types and domain decompositions. It is clearly demonstrated that the present parallel computing system requires a much smaller amount of computational memory than the conventional finite element method and also that, due to the feature of dynamic workload balancing, high performance (over 90%) is achieved even in a large scale finite element calculation with irregular domain decomposition.