The 232nd R-CCS Cafe - part 1

Numerical solution of partial differential equations for multi-physics problem consists of nonlinear and linear solvers, where large sparse matrix obtained by discretization scheme needs to be solved. Sometimes, condition number of such sparse matrix becomes very large due to multi-physical component unknowns or supplemental unknowns to treat constraints, e.g. incompressiblity and boundary conditions in flow problems or mechanical problems. To deal with such system, sparse direct solver based on factorization is a robust tool but its computational complexity is not so small. Then it is now requested to accelerate the computing speed by using mixed precision arithmetic. In this talk, a new factorization algorithm based on a hybrid approach of direct and iterative solvers, which keeps the same accuracy of the solution by using lower precision arithm