Many large-scale scientific simulations require the solution of nonlinear partial differential equations (PDEs). The effective solution of such nonlinear PDEs depends to a large extent on efficient and robust sparse linear system solution. In this paper, we show how fast and reliable sparse linear solvers can be composed from several underlying linear solution methods. We present a combinatorial framework for developing optimal composite solvers using metrics such as the execution times and failure rates of base solution schemes. We demonstrate how such composites can be easily instantiated using advanced software environments. Our experiments indicate that overall simulation time can be reduced through highly reliable linear system solution using composite solvers.
- Composite methods
- Large-scale PDE-based simulations
- Newton-Krylov methods
- Sparse linear solution
ASJC Scopus subject areas
- Hardware and Architecture
- Computer Networks and Communications