In- and out-of-core BEM equation solver with parallel and non-linear options

An algorithm for solving large BEM equation sets arising when using the substructuring option is described. The solver is based on a frontal solution philosophy. This feature along with a special ordering scheme for the unknowns minimizes the effect of the fill-in. The condensation of unknowns is carried out in two loops running over all substructures. Within the first loop all unknowns associated with nodes at the external surface of the body are eliminated. The remaining interfacial unknowns are condensed within the second loop. The software has a built-in mechanism of recognizing whether the given step of condensation of unknowns can be carried out in-core or out-of-core. This limits the usage of slow direct access files to the necessary minimum. The implemented multiple right-hand side option makes the solver suitable for non-linear applications. Examples of such applications in non-linear heat transfer problems and plasticity are discussed. A parallelized version of the solver uses the parallel virtual machine (PVM) software and is portable to many computer systems. The parallelization is based on a concept following the block solver philosophy. The parallel solver might be run on computer clusters consisting of processors of different power. A special load equivalencing algorithm has been developed to assign proper task to computers of different power. The solver has been run in an industrial environment to solve problems of about 100 thousand unknowns. Numerical examples are included.