Hi, Jed, Thanks for your quick reply and have a nice day. My problem is to solve a hybrid FEM-BEM problem, so one sub-matrix from BEM is fully dense and one from BEM-FEM is partially dense. I managed to used a multi-level fast multpole method to compute the product of my entire system matrix with a given vector. And I can find a quite good problem dependent approximation B to my system matrix *A*.
My next purpose to speed up the convergence rate of GMRES using this operator *B*. In my code, the expensive of storage of the far field interaction from BEM part is avoided. And I can explicitly form the sparse matrix *B*. So, could I ask you: how to give the sparse matrix *B* to petsc?. Because *B* is sparse, I prefer to fully LU decomposition to solve the preconditioned problem *B*z=c. Best wishes Zhengyong On Tue, Apr 3, 2012 at 11:28 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote: > On Tue, Apr 3, 2012 at 14:25, RenZhengYong <renzhengyong at gmail.com> wrote: > >> I have a question to ask for your suggestions which is to solve Ax=b >> using GMRES, >> here A is partially dense. Using petsc, I successfully used the >> matrix-free approach to solve >> it so that the expensive storage of A is avoided. My question is could I >> offer an matrix B >> (which is sparse matrix and good approximation to A) so that the >> convergence rate of >> GMRES can be speed up. >> > > Certainly, but the challenge is to find this other operator. You could try > sparse approximate methods to approximate either the operator or its > inverse. Other approaches would typically involve further knowledge of your > problem. > -- Zhengyong Ren AUG Group, Institute of Geophysics Department of Geosciences, ETH Zurich NO H 47 Sonneggstrasse 5 CH-8092, Z?rich, Switzerland Tel: +41 44 633 37561 e-mail: zhengyong.ren at aug.ig.erdw.ethz.ch Gmail: renzhengyong at gmail.com -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120403/6ad0a0c3/attachment.htm>
