Solving Large Sparse Linear Systems to End-to-end Accelerator Structure Simulations

摘要

This paper presents a case study of solving very large sparse linear systems in end-to-end accelerator structure simulations. Both direct solvers and iterative solvers are investigated. A parallel multilevel preconditioner based on hierarchical finite element basis functions is considered and has been implemented to accelerate the convergence of iterative solvers. A linear system with matrix size 93,147,736 and with 3,964,961,944 non-zeros from 3D electromagnetic finite element discretization has been solved in less than 8 minutes with 1024 CPUs on the NERSC IBM SP. The resource utilization as well as the application performance for these solvers is discussed.