Modeling multicomponent reactive transport on parallel computers using Jacobian-Free Newton Krylov with operator-split preconditioning

Abstract

Modern multicomponent reactive transport models necessitate the use of parallel computation due to extreme memory and processing demands. Innovative parallel algorithms are needed to fully exploit the advanced computational power provided by today's supercomputers within these models. In order to take advantage of available high-performance computing, we have developed the parallel reactive transport model PARTRAN. This three-dimensional, finite volume model is built upon the versatile PETSc library developed at Argonne National Laboratory. PARTRAN is capable of using either conventional techniques (Jacobian-based) or the Jacobianfree, Newton-Krylov method to solve the fully coupled, nonlinear system of equations representing complex geochemical transport processes in the subsurface. The use of Newton-Krylov eliminates the necessity of computing and storing a Jacobian, resulting in considerably less computation and memory use. While one disadvantage of Jacobian-free Newton-Krylov is the need for efficient matrix-free preconditioning, we develop an innovative operator-split preconditioning method to address this shortfall. In this paper, we provide a brief overview of PARTRAN and its implementation of the Jacobianfree, Newton Krylov technique. We evaluate the parallel performance of the model in detail, comparing the performance of the Newton-Krylov method with conventional Jacobian-based and operator-split methods. The Jacobian-free, Newton-Krylov method demonstrates excellent parallel performance based on runtime, scalability and efficiency, in comparison to the conventional methods.