"Zhenglun (Alan) Wei" <zhenglun.wei at gmail.com> writes: > Dear folks, > I hope you're having a nice day. > For the Poisson solver in /src/ksp/ksp/example/tutorial/ex45.c, I used > the ksp_type = CG to solve it before; it converges very fast with > pc_type = gamg. However, I was trying to check if the matrix generated > by the 'ComputeMatrix' is symmetric by using "ierr = MatIsSymmetric(B, > tol, &flg);". It shows that this matrix is not exact a symmetric one by > setting tol = 0.0. Yet, the matrix is 'symmetric' if the tol > 0.01.
The matrix does not enforce boundary conditions symmetrically. > Does this mean that, even if the matrix is not exact symmetric, the CG > could still be used. You happen to be iterating in a "benign" space in which the operator is SPD. > This brings me a question. Can the CG be used to solve an actual > unsymmetric matrix as long as 'MatIsSymmetric' returns a 'PETSC_TRUE' > value with certain tolerance. No. > Is there any rule of thumb for this tolerence? Also, as a > preconditioner, does 'gamg' only work for symmetric positive-definite > matrix? or it works for any matrix or even with GMRES? It works for many moderately non-symmetric, certainly for something that only has non-symmetric boundary conditions.
