All Questions
11,503
questions
3
votes
1
answer
156
views
Any FEM book recommendations that focus on stability and proofs on error bounds?
Everything from descrete stability proofs for steady state and time dependent problems. energy stability, stability of mixed methods, nonlinear problems, vector valued problems in fluid/structural/EM, ...
- 506
2
votes
2
answers
84
views
Getting singular matrices for lid driven cavity problem
I was trying to solve the lid driven cavity problem using the galerkin method with SUPG stabilization. I was using GMRES method as my solver and I am also getting a solution. And the solution looks ...
- 21
0
votes
0
answers
55
views
LBFGS-B initial gradients too high?
I'm optimizing a geometrical shape for electromagnetic performance. The shape is constrained with bounds, say between 0.2 and 0.8, whereas the parameters are all between 0.2 and 0.8.
I am interested ...
- 1
0
votes
0
answers
49
views
How to solve the heat equation using the spectral method (Chebyshev's differentiation matrix), with constant flux boundary condition on both sides?
I am trying to solve a 1d heat equation with a constant flux boundary condition on the right-hand side and a zero flux boundary condition on the left-hand side. I've gained a lot of insight from ...
- 1
1
vote
0
answers
44
views
Mathematica Package for validating effective string theory solution
I am asking for Mathematica package that given an input of:
symmetric matrix $G_{\mu\nu}$, antisymmetric matrix $B_{\mu\nu}$ and a scalar function $\Phi$
will check whether it is a solution to the one-...
2
votes
0
answers
48
views
trust region method for linearly-constrained convex optimization
I'm interested in the problem of minimizing a convex function $f(x)$ for $x$ living in some Banach space $X$, subject to the linear constraint $Kx = g$ where $K : X \to Y^*$ for some other space $Y$.
...
- 10.4k
0
votes
0
answers
30
views
Covariant Euler-Lagrange Computation - Mathematica
Does anybody know of a software (or software package) that can solve the Euler-Lagrange equations for a manifestly-covariant field Lagrangian density? Mathematica has a "Variational Methods" ...
1
vote
0
answers
66
views
Deriving order of accuracy and interpreting a given discretization scheme when underlying method ( finite difference/volume) not known
If a spatial grid is given with time levels like this:
to solve the following model problem
Now consider the following discretization schemes:
Scheme 1
Scheme 2
Usually, to determine order of ...
- 445
1
vote
0
answers
53
views
Particular linear systems: sparse matrix + column
I am trying to understand a limitation in a routine in the interval arithmetic software Intlab. From matrices starting from a given size (in my particular problems),...
- 1,077
0
votes
0
answers
36
views
Lumped (diagonal) vs. consistent (non-diagonal, symmetric) mass matrix in Nastran
I've been tinkering with DMAP to explore the procedure followed by Nastran when solving a complex modes analysis.
I've reached a passage I cannot understand: at some point Nastran formulated what it ...
2
votes
0
answers
92
views
An alternative to Levenberg–Marquardt algorithm
When trying to solve for a (over)determined non-linear least square method:
$$\underset{x}{\min}||f(x)||^2_2, f: \mathbb{R}^n \rightarrow \mathbb{R}^m, x\in \mathbb{R}^n, m\geq n$$
we use the Gauss-...
- 21
0
votes
1
answer
78
views
Derivative using torch.fft oscilates on the boundary
I was trying to use the torch.fft to compute derivatives. The issue is that even for a simple example ($f = \sin(x)$), I have weird oscillations on the boundaries.
...
- 35
1
vote
1
answer
117
views
On the calculation of the first m generalized eigenvectors
This is a classic generalized eigenvalue/eigenvector problem:
$$
A\,\vec{x}=\lambda\,B\,\vec{x}
$$
which, however, is characterized by:
$A,B$ are real, symmetric and positive definite matrices of ...
- 113
8
votes
2
answers
217
views
How to find a computational bottleneck
I am a PhD student and my lab has developed a code to run simulations. It relies on external libraries and code my lab has written. I've run a strong scaling study which shows poor performance, see ...
- 81
3
votes
3
answers
132
views
inverse problem of predicting parameters of ODEs driven by data
Consider a system of ODEs
\begin{align}
u' = f(u,v)\\
v' = g(u,v)
\end{align}
with some unknown parameters in $f$ and $g$, where primes denote time derivatives. No data of $u(t)$ or $v(t)$ are ...
- 317