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Questions tagged [matrix-free]

For questions about matrix-free methods, which only require computing matrix-vector products, rather than storing the whole matrix explicitly.

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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 ...
user90189's user avatar
  • 109
4 votes
1 answer
161 views

Is there a way to generate a matrix-free decomposition for a matrix-free operator?

Hypothetical question for some code that I'm writing. Suppose I have an matrix-free linear operator $A$, i.e. the only thing I know about it is the forward action $v \mapsto Av$. For simplicity, let's ...
TrostAft's user avatar
  • 141
7 votes
0 answers
288 views

Matrix-free FEM references

I've seen that many people are using matrix-free fem codes in my community (mechanical engineering). I have to admit that I googled a bit and I didn't manage to find a good reference for the subject. ...
FEGirl's user avatar
  • 385
4 votes
0 answers
212 views

High quality constrained optimization C++ library with matrix free second order solver?

I'm working with large scale constrained optimization problem. Some of my constraints can be non linear. Currently i'm using IPOPT. Quality is good by my Hessian computation too slow. It seems that i ...
Daiver's user avatar
  • 225
3 votes
1 answer
128 views

Parallel, matrix-free estimate of the trace

What would be the best way to estimate the trace of a large, distributed matrix, if one only know its action on a vector throug a parallel "matvec" routine? In the application I am interested in, the ...
Christine Darcoux's user avatar
1 vote
2 answers
733 views

Implementation of the Jacobian-free Newton method

In my calculation (of a simple heat equation, for testing) using the Newton method, I tried to replace the full Jacobian matrix with an approximation vector, i.e. replacing $J$ in $$J(u)\delta u=-F(u)...
arc_lupus's user avatar
  • 553
2 votes
2 answers
163 views

Memory/speed tradeoff for many small matrix inverses

Problem In the case of a finite element code, I have many small (order of 30x30) matrix inverses (or LU factorizations), one per finite element. These matrix inverses never change and must be applied ...
user3482876's user avatar
0 votes
1 answer
248 views

Fast computation of square root inverse of matrix, matrix being determined from Ax=b form

I have an equation of the form $J^Te=f$, where $e$ and $f$ are known vectors and $J$ is an unknown matrix. How can I efficiently compute $J^T(JJ^T)^{-1/2}e$ ? My motivation to address this problem ...
user3619023's user avatar
8 votes
2 answers
705 views

Matrix free finite elements method for visualization in process tomography

I am Computer Scientist and now I am interested in matrix multiplication on GPUs. My research are focused on matrix free finite elements method where I multiply sparse matrix. Sparse matrix could ...
Konrad's user avatar
  • 95
1 vote
1 answer
449 views

Solver library for matrix-free linear equation system

I will have to solve a large linear system. I'm now looking for a solver that works "matrix-free" (So that I just have to specify a matrix-vector product, but not the matrix). As far as I understand (...
Michael's user avatar
  • 1,463
9 votes
2 answers
761 views

Applying matrix square root inverse in matrix-free regime

Let $A$ be a large symmetric positive definite matrix, and suppose that we can efficiently apply $A$ and have a fast solver to apply $A^{-1}$, but we do not have access to the matrix entries for ...
Nick Alger's user avatar
  • 3,133