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3
votes
2answers
198 views

A numerical GMRES example

I'm having trouble understanding how GMRES works. I've read the part in Saad's book and a few others but still I am confused. Can someone provide me a numerical example to understand it better? Or if ...
4
votes
1answer
119 views

What factors are relevant when deciding between GMRES and schur complement solves?

Suppose I have a linear system $$ \left\lbrack \begin{array}{cc} M_1& S\\ S^{\mathrm{T}}& M_2 \end{array} \right\rbrack \left\lbrack \begin{array}{c} X\\ Y\end{array} \right\rbrack= \...
0
votes
0answers
314 views

MATLAB: code for restarted gmres

I have a question about Matlab and restarted gmres. I would like to use gmres.m provided here. This code seems to be a popular for the scientific computation ...
1
vote
1answer
136 views

OpenMP threaded nonlinear solver for complex numbers

Problem: I have translated Jacobian-Free Newton-Krylov solver written by C. T. Kelley to Fortran and now want to parallelize it on shared-memory system with OpenMP. In addition, I want to precondition ...
4
votes
1answer
884 views

High quality flexible GMRES (FGMRES) implementation

What are the best FGMRES implementations in various languages/frameworks? In particular, are there any good quality Matlab implementations? I am referring to the variation of GMRES where a changing ...
0
votes
1answer
106 views

GMRES: Making the matrix square without solving for boundaries

How do we define the matrix for GMRES, if we do not want to solve the boundary elements but only the interior ones. I am using pentagonal elements so in a row there are 6 elements (cell itself + 5 ...
11
votes
2answers
402 views

preconditioning a krylov method with another krylov method

In method like gmres or bicgstab it could be attractive to use another krylov method as a preconditioner. After all they are easy to implement in a matrix-free way and in a parallel environment. For ...
2
votes
1answer
291 views

Not enough memory for GMRES

After realizing that Gauss-Seidel is extremely slow for my simulation, i wanted to try GMRES and luckily found the C++ code here without diving into the theory. The size of the matrix in my case is <...
1
vote
0answers
68 views

Petsc solver problem

I have to resolve the linear equation Ax = B in which A is not symmetrical, either definite positive. I used the solver GMRES of Petsc. It seems to work well but with the same configuration (initial ...
3
votes
0answers
400 views

GMRES implementations

I am looking for simple GMRES implementations. Unfortunately, I have a few requirements: should be C or Fortran, Fortran preferred needs a license that permits inclusion in an MIT/BSD licensed ...
13
votes
3answers
2k views

Problems where Conjugate gradient works much better than GMRES

I am interested in cases where Conjugate gradient works much better than GMRES method. In general, CG is preferable choice in many cases of SPD (symmetric-positive-definite) because it requires less ...
3
votes
2answers
103 views

Parameter selection difficulty in GMRES

we are using a first order implicit finite volume code for simulation of incompressible flows. At its core, the code utilizes a (non-preconditioned) GMRES method for solving linear systems given in ...
1
vote
1answer
800 views

GMRES Matlab 'tol' parameter

I need to use GMRES solver in MATLAB, and I need to play around with the codes parameters and I had a very simple question about its usage. The documentation of the solver here mentions a parameter <...
7
votes
5answers
5k views

Best choice of solver for a large sparse symmetric (but not positive definite) system

I am presently working on solving very large symmetric (but not positive definite) systems, generated by some certain algorithms. These matrices have a nice block sparsity which can be used for ...
2
votes
0answers
442 views

Cusp Library performance worse than PETSC (GMRES 200 iterations) Why?

I wanted to compare the speeds of the GMRES implementations in the CUSP and the PETSc libraries. The matrix (A) used for testing was a 3d Laplacian matrix obtained by using the 7 point stencil on a ...