A clustered reduced communication element by element preconditioned conjugate gradient algorithm for finite element computations

The clustered element by element preconditioned conjugate gradient (EBE-PCG) method can be effectively used to solve problems with symmetric positive definite matrices such as those arising in ANTARES-3D, a metal forming finite element (FE) simulation package. Efficient parallelization of this application on distributed memory multiple instruction multiple data (MIMD) parallel computers require automatic partitioning of the finite element domain into clusters of elements and solving the compute intensive parts of these clusters concurrently while minimizing inter-processor communication. Such domain decomposition of the FE graph is accomplished by creating an element interaction graph (EIG) and partitioning the EIG into sub-graphs using the Kernighan-Lin partitioning heuristic. In order to minimize the communication overhead during the solution of the linear systems of equations, a clustered reduced communication EBE-PCG formulation is developed and used. Performance measurements for a blade forging are reported