Preconditioned conjugate gradient and finite element methods for massively data-parallel architectures

Abstract

For the computational solution of the Navier's partial differential equations of elasticity on general domains, a finite element discretization and its implementation on a massively data-parallel (CM-2) architecture was investigated. The discretization led to irregular finite element grids in order to accomodate general domains in applications. The presence of irregular grids required us to develop and implement new communication software that could handle very general and irregular finite element grids. The resulting algebraic equations for those grids were found to be very amenable to element-to-processor mappings on data parallel supercomputers if implemented in conjunction with conjugate gradient iterative solvers. These iterative solvers were then accelerated by the use of local type preconditioners to enable the robust solution of large scale problems.