Preconditioned Krylov equation solvers in elastoplastic boundary element analysis

Nonlinear elastoplastic boundary element analysis (BEA) involves an algebraic subproblem requiring the solution of dense nonsymmetric matrix equations with an evolving right hand side vector. When multiple right hand side vectors are present, direct matrix triangular factorization techniques have been the compelling choice, amortizing the work of a single matrix factorization over the sequence of multiple fast 'solutions' of the resulting triangular systems. Recently, the superior performance of preconditioned Krylov equation solvers in linear BEA has also been documented. In this paper, the superior performance of preconditioned Krylov equation solvers is shown to be extendable to elastoplastic BEA. This is accomplished by exploiting the strategic reuse of the preconditioner, its factorization, and the Krylov vectors computed in the solution for the first right hand side vector, in the subsequent solution of matrix equations with multiple 'nearby' right hand side vectors. The details associated with this strategy are given, and the computer resources required in three dimensional elastoplastic BEA are used to quantify the computational efficiency associated with this new algorithm.