Questions tagged [gmres]
Refers to the (G)eneral (M)inimal (RES)idual algorithm, which is a popular Krylov subspace method for solving linear systems.
16 questions with no upvoted or accepted answers
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How to construct an effective preconditioner for this particular problem
A quick introduction to my problem
I am currently developing a method for simulation of water waves in three dimensions based on potential flow theory. The computational bottleneck of the method is ...
- 125
5
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Preconditioning technique for large sparse non-hermitian matrix
I am attempting to solve a computational acoustics problem that involves solving an underlying sparse matrix. The size of the problem varies with grid size (3D) and fill-in's obviously make direct ...
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Comparing block versus non-block Krylov methods for handling multiple right-hand-sides
Suppose I wish to solve a linear system $AX=B$ iteratively where $A$ is an $m\times m$ matrix and $X,B$ are $m \times s $ matrices (not single vectors). Instead of solving $s$ independent systems I'm ...
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Preconditioned residual converges, but true residual doesn't
I'm using Albany w/ Trilinos to solve an elasticity problem with thermal expansion mismatch. I'm using block GMRES with MueLu preconditioning. It works for problem size of several million dofs, but ...
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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 ...
- 782
3
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52
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Preconditioned GMRES for nearly diagonalizable systems
I have been working with a matrix $A$ and preconditioner $P\approx A^{-1}$ that I've then applied GMRES to the (left) preconditioned linear system
\begin{equation}
P^{-1}Ax=P^{-1}b
\end{equation}
$P^{-...
- 189
3
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235
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How to obtain smallest eigenvalues with Arnoldi iteration
I understand that the Arnoldi iteration produces a basis which tends to include in its span the eigenvectors corresponding to eigenvalues of large magnitude (hence the analogy between the last vector ...
- 91
3
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Solving PDEs: What is the best way to deal with non-banded/dense jacobians?
I have a system of PDEs describing atmospheric chemistry and transport. I use finite-differences to make my system of PDEs into a system of ~10,000 ODEs. I then integrate the ODEs forward in time with ...
- 317
3
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How to reproduce the numerical examples in Prof. Saad's Book about Krylov subspace methods?
After reading Prof. Saad' Book, "Iterative methods for Sparse Linear Systems, 2nd version", I want to do the numerical examples about the Krylov subspace methods not only to reproduce the results in ...
- 981
2
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602
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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 ...
- 645
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Struggling to understand the Householder Arnoldi Algorithm
I have spent almost three frustrating weeks trying to understand the Householder GMRES algorithm. I understand the basic GMRES algorithm the maths of Householder transformations used in QR ...
- 325
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105
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Matrix Free alternatives in dealii
I am implementing a Fast Multipole Method (FMM) in deal ii.
I do not want to store a dense matrix, but lower rank matrices and to use matrix free methods. By now, I store the elements of the low-rank ...
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How to compute the computational cost and storage of the Full Orthogonalization Method?
About the analysis of Full Orthogonalization Method (FOM) in Prof. Saad's book, wrote as follows:
Algorithm 6.4 (FOM):
\begin{array}{l}
r_0=b-Ax_0,\beta=\|r_0\|_2,v_1 = r_0/\beta\\
Define \quad H_m ...
- 981
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110
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Help with debugging block GMRES
I have written block version of GMRES by referring [1] and MATLAB implementation of gmres. I need to write it for complex matrices. My block implementation when run on single RHS is giving correct ...
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220
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Arnoldi Decomposition Algorithm
I try to get into GMRES via Arnoldi-Decomposition. For my understanding, I Implemented the Arnoldi-Decomposition in python.
...
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GMRES implementation does not converge for singular Hermitian problems
I've just implemented the GMRES algorithm based on chapter 4 of Fundamentals of Numerical Mathematics for Physicists and Engineers using the problems in Numerical Analysis by Timothy Sauer for ...
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