All Questions
11,503
questions
0
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0
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7
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Projecting the initial state on a Discontinuous Galerkin basis
Context
I want to solve a 1D Burgers equation with a discontinuous Galerkin approach on the space-time domain $(x,t)\in [0,1]^2$. I want to project the function $u(x) = e^{-\frac{(x-0.5)^2}{0.02}}$ ...
- 37
1
vote
1
answer
1k
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 <...
4
votes
2
answers
383
views
Solving a generalised eigenvalue problem with non-square matrices
I need to solve a generalised eigenvalue problem of the form
$$A\mathbf{x}=\lambda B \mathbf{x}$$
where $A$ and $B$ are $m \times n$ complex matrices, that are not symmetric with $m>n$.
I am aware ...
- 11.8k
2
votes
1
answer
523
views
Overflows and underflows in Python
I’m writing some Python code using NumPy. Since I got an overflow warning, I decided to check for underflows as well at all places in the code, using ...
- 2,117
0
votes
0
answers
17
views
Why does Energy -> temperature conversion failed to converge in my OpenFOAM simulation [closed]
How can I resolve this issue?
I want some help in resolving it. Thanks.
0
votes
1
answer
56
views
How to properly use ARPACK's dsaupd and dseupd?
In Rust, I am trying to solve an eigendecomposition problem through ARPACK. I made the following subroutine for this purpose:
...
- 273
0
votes
0
answers
79
views
Guidelines for finding a preconditioner for a matrix that is "near" singular
Given a large non-symmetric non-sparse matrix $A=(a_{m,n})$ with the property that the columns of $A$ are "close", making the matrix very ill-conditioned and near singular. For example, ...
- 8,702
0
votes
0
answers
21
views
formula for the elliptical orbit of the magnetic field in a current carrying circular loop [closed]
In a circular current carrying loop the magnetic field lines form elliptical orbits if I have constant value for current and a point let's say at r distance from the center of th current carrying loop ...
2
votes
3
answers
261
views
Computing Tangential Derivative using the Dirichlet value
Let $\Gamma$ be a smooth boundary of a domain $\Omega$. Let $u = g$ on $\Gamma$. How can I compute the tangential derivative of the function $u$ using the information that $u = g$ on $\Gamma$? Please ...
- 2,267
-1
votes
1
answer
68
views
optimal gradient algorithm to determine best $α_k$
Let's consider an optimal-step gradient algorithm and assume that:
$g(α) := f(X_k - α∇f(X_k)) = 2α^2-4α+17$, how can we determine the optimal $α_k$?
Here is my simple solution:
$g(α) = 2α^2-4α+17$
$g'(...
- 2,267
0
votes
1
answer
65
views
step-fixed algorithm to minimize f, which step to ensure convergence?
If we want to apply the fixed-step gradient algorithm to the minimization of $f(x) = \frac{1}{2}(Ax, x)$ where $A$ is a symmetric 2x2 matrix with eigenvalues $\lambda_1 > \lambda_2 > 0$, for ...
- 2,267
0
votes
1
answer
43
views
step-fixed algorithm first iterates
let us have the fixed-step gradient algorithm, with $p = 2$ and we assume that for $X = (x, y)$,
$∇ f(X) = \begin{pmatrix}
x -1\\
y -2
\end{pmatrix}$
Let me assume we intialize with $X_0 = (0,0)$ what ...
- 2,267
2
votes
1
answer
66
views
When does linear system have linearly growing singular values?
Suppose $W$ is a large matrix where $i$th smallest singular value grows as $O(i)$. What kind of matrix can $W$ be?
For instance, this appears to hold for random matrix with IID entries and for lower-...
1
vote
1
answer
57
views
What are some good medium matrices with known eigenvectors?
I am trying to test if an eigendecomposition I have is working properly. For this I would like some matrices that are 10x10 (ish) with trivial (or known) eigenvectors and eigenvalues so that I can ...
- 11.8k
2
votes
1
answer
158
views
How to add damped constraint force to constrained dynamics simulation?
I have implemented a constraint dynamics physics simulation as proposed by Andrew Witkin et al 1990, but I cannot get the initial constraint "snapping" correctly.
I implemented
$$ JWJ^{T} \...
- 514