9/11/2022 Friday  10h40 to 11h05

Atsushi Suzuki



RIKEN Center for Computational Science

Dissection sparse direct solver with mixed precision arithmetic for smaller memory footprint abstract

Sparse direct solver is the most robust linear solver for finite element methods where the stiffness matrix may be sometimes singular due to artificial boundary conditions by mathematical modeling or by numerical algorithm. It is better to use direct solver especially for designing phase of numerical algorithm for new physical models. I will present a factorization procedure in a hybrid way by decomposing the coefficient matrix into a union of moderate part where factorization by single precision is acceptable and of hard part where the corresponding Schur complement may be singular, which is performed automatically during factorization phase. The last Schur complement is generated by iterative solver and overall solution has same accuracy as the standard factorization but memory footprint is drastically reduced thanks to lower precision arithmetic.