I am trying to solve a series of the linear equations Ax=b. A is a large sparse positive definite matrix, in n*n. And b is a vector, in n*1. Among this equations, "A" matrix are the same, while the vector "b" are different. They both come from finite element method (e.g. same geometry and different loadings in structral machanics). I used to apply the PCG (preconditioned conjugate gradients) iterative method with an incomplete Cholesky preconditioner to solve every one of them. I would like to know whether I could get some accelerating idea from the same property of matrix "A"?
To note some details,
1. At first, I think I'd better get the inverse of "A" directly. Then I could calculate all the solution of these equations easily. But I found it is impossible to get the inverse of a large sparse positive definite matrix. I learned that It is very expensive and less precise.
2. The only way I could use now is to run the PCG iterative method with an incomplete Cholesky preconditioner parallelly. It takes large RAM.
3. I may make a preconditioner with smaller "droptol" for matrix "A". All the PCG would converge faster with it as below. But this step is very slow.
tol = 1e-6;
L1 = ichol(A, struct('type','ict','droptol',tol));
Any suggestion would be appreciated. Thank you.