Reducing sparse nonlinear eigenproblems by automated multi-level substructuring

A parallel additive Schwarz preconditioned Jacobi–Davidson algorithm for polynomial eigenvalue problems in quantum dot simulation

“…The GMRES iterations are referred to the iterations used by GMRES to solve the correction equation. The subdomain problems (13) are solved by an incomplete LU decomposition. For simplicity of implementation, the actual partitioning and overlapping size are determined internally by PETSc.…”

“…The quality of subdomain solve: Let l be the level of fill-ins in ILU(l), which is used to solve the subdomain problems (13). We choose l = 0,1,2, or 3.…”

“…Furthermore, to save computational cost and memory use in practice, local subdomain problems(13) are solved by an inexact solver incomplete LU (ILU). The ILU solver performs an incomplete LU decomposition and then performs a forward and backward substitution using the incomplete factors.Algorithm 2.…”