연사: 민조홍 교수 (이화여대 수학과)
일시: 11월 27일 금요일 오전 11시.
제목 : The optimality of MILU-ILU preconditioner
장소: 온라인 강연
Meeting ID: 834 6601 3948
Abstract : MILU preconditioner is well known [15, 3] to be the optimal choice among all the ILU-type preconditioners in
solving the Poisson equation with Dirichlet boundary conditions by a standard finite difference method. However, it is less known which is an optimal preconditioner in solving the Poisson equation with Neumann boundary conditions. We review Relaxed ILU and Perturbed MILU preconditioners in the case of Neumann boundary conditions, and present empirical results which indicate that the former is optimal in two dimensions and the latter is optimal in two and three dimensions. There is little difference in coding the optimal preconditioners and the conventional ones. A slight code change from the conventional to the optimal can result in significant speed ups in computational time. In our fluid simulation, the speed up reached about 3.3 and 2.0 with respect to Jacobi and ILU, respectively. To the best of our knowledge, these empirical results have not been rigorously verified yet. We present a formal proof for the optimality of Relaxed ILU in rectangular domains, and discuss its possible extension to
general smooth domains and Perturbed MILU.