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1500 questions
6
votes
2 answers
How can I reduce the communication bottleneck of a parallel explicit finite difference scheme?
Suppose i was trying to solve a parabolic PDE (heat equation) on a rectangular domain using an explicit finite difference scheme. I am storing my solution vector in a matrix form (because it closely resembles the shape of the domain). I know that…
Paul
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6
votes
2 answers
Books/Resources on Sparse Optimization?
I'm looking to learn more about Sparse Optimization and apply it to machine learning problems. Could you please recommend some books/resources on this topic? Both theoretical and applied are fine.
hattoriace
- 63
- 3
6
votes
2 answers
matlab eigs: wrong eigenvalues for tridiagonal matrix
I try to compute eigenvalues of the tridiagonal matrix coming from finite difference scheme. For small mesh size, eigs works well. But for large size it fails. Here is an example where eigs fails. Is there any other way to reliably compute a few…
cfdlab
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- 19
6
votes
2 answers
What are the most common dense matrix storage formats?
I'm looking to write some code to read in a dense matrix from a file, and I was wondering what are the most common storage formats that my code should support?
srabidoux
- 69
- 1
6
votes
1 answer
Are there high order symplectic methods for $y'=f(y)$?
Are there high order energy-conserving or symplectic methods for solving $y'=f(y)$?
Maesumi
- 163
- 5
6
votes
1 answer
Advice on solving a coupled physics problem
I am taking a shot at solving a coupled physics problem. I have this matrix formed:
$\mathbf{J}=\begin{bmatrix}
\mathbf{A} & \mathbf{B}\\
\mathbf{C} & \mathbf{D}
\end{bmatrix}$
where $\mathbf{A}$ and $\mathbf{D}$ represent two different physics,…
user2183232343
- 63
- 5
6
votes
1 answer
Code to numerically integrate a system of first-order ODEs
I need to solve the following system of differential equations.
When I have the solutions for $n_f$ and $v$, I need to find and plot $J=-e_\cdot n_{f} \cdot v$.
I wrote a code in matlab with all ODEs like this:
function systemSolve
…
CarlosCr
- 61
- 3
6
votes
2 answers
Need an example of convection-dominated problem to test on FreeFEM++
Can you all give me (at least) one example about convection-dominated problem in order that I can test it (them) on FreeFEM++. If possible, please give me specific examples (it/they contain(s) full equations, boundary condition, initial condition,…
Anh-Thi DINH
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- 8
- 14
6
votes
2 answers
Finite-volume method: can Dirichlet boundary conditions be applied to the integral form?
I would like to apply Dirichlet conditions to the advection-diffusion equation using the finite-volume method. This answer, "How should boundary conditions be applied when using finite-volume method?"
emphases the benefit of staying with integral…
boyfarrell
- 5,409
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- 35
- 67
6
votes
1 answer
How to do co-simulation with two FMU models
I have two FMU developed with different simulation tools. I would like to connect them through some variables and run a co-simulation with an open source tool as OpenModelica. This co-simulation has to be rather tight as both FMU have…
Koldo
- 95
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- 5
6
votes
1 answer
What efficient algorithms are there to generate arbitrary dimensional meshes of simplices?
I know that delaunay triangulation can be extended into arbitrary dimensions by solving the convex hull problem in $(p+1)$ dimensions and projecting the lower hull into dimension $p$ to obtain a mesh in dimension $p$. However, this approach is…
Paul
- 12,045
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- 56
- 129
6
votes
2 answers
Computing smallest eigenvectors of a sparse matrix, having its inverse
I'm a bit confused by the vast amount of literature on solving eigenvalue problems. I have a sparse (large) matrix which I have already factored (by Cholesky or LDU). I would like to compute few eigenvectors of this matrix associated to the smallest…
Tom
- 465
- 4
- 14
6
votes
3 answers
Algorithm for Principal Eigenvector of a Real Symmetric 3x3 Matrix
I have a 3x3 covariance matrix (so, real, symmetric, dense, 3x3), I would like it's principal eigenvector, and speed is a concern. Is there a fast algorithm for this specific problem? I've seen algorithms for calculating all the eigenvectors of a…
anjruu
- 203
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6
votes
1 answer
ENO-WENO Schemes: Are ENO-WENO schemes non oscillatory for all kinds (linear/non linear) of problems?
Is there an rigorous proof of ENO-WENO schemes being non oscillatory?
0b1100001
- 531
- 2
- 10
6
votes
2 answers
How many bits to unambiguously represent fixed-point division?
Suppose I have a function which divides an $m$-bit unsigned integer $a$ by an $n$-bit unsigned integer $b$ and returns the quotient as a fixed-point number with $t$ fractional bits, truncating towards zero. So I have $f(a,b)= 2^{-t}\lfloor…
Sneftel
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