Top new questions this week:
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I am considering the problem of simulating the evolution of an interface given as a curve in 2D (or surface in 3D) that evolves according to a velocity specified at the interface of the form:
$$\vec{v}...
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I have the following energy functional of $p$-Laplacian equation:
$$
E(u) = \frac{1}{p} \int_{\Omega} |\nabla u|^p dx
$$
for $2.8 \leq p \leq 5$.
My goal is to minimize the energy functional by using ...
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This question is mainly an inquiry about the usefulness of Discontinuous Galerkin (DG) for the time-independent transport equation of the form
$$\sigma u+\beta\cdot\nabla u =f,\;\;\;\text{on }\Omega\...
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I have been trying to calculate the matrix inverse of some large matrix with entries ranging by orders of magnitude. I tried to use the matrix decomposition to simplify the computation, where a matrix
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Is the spatial second derivative of the strain energy of a hyperelastic material positive definite in general?
If this is not a general property of hyperelastic materials are there techniques for ...
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Crossposted at MathOverflow
Consider a quadratic programming problem with the following format:
$$
\text{min} Q(x) = c^Tx+\frac{1}{2}x^TDx \\
$$
$$
\text{s.t.} Ax\leq b, \\
x\geq 0
$$
where $D$ is a $...
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Greatest hits from previous weeks:
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Suppose I have two VTK files, both in structured grid format. The structured grids are the same (they have the same list of points, in the same order), and there is a field, call it "Phi", in each VTK ...
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In FEM classes, it's usually taken for granted that the stiffness matrix is positive definite, but I just can't understand why. Could anyone give some explanation?
For instance, we can consider the ...
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Suppose I'm using a linear congruential pseudo-random number generator (PRNG). Given a seed $x_0$, the multiplying factor (a), the shift factor (c) and the modulus factor (m), how can I determine the ...
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For a project, I have to implement these two methods and compare how they perform on different functions.
It looks like the conjugate gradient method is meant to solve systems of linear equations of ...
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Suppose
$$\begin{align*}
\min A &\mathrm{vec}(U) \\
&\text{subject to } U_{i,j} \leq \max\{U_{i,k}, U_{k,j}\}, \quad i,j,k = 1, \ldots, n
\end{align*}$$
where $U$ is a symmetric $n\times ...
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I am working on a project that I need to add a regularization into the NNLS algorithm. Is there a way to add the Tikhonov regularization into the NNLS implementation of scipy [1]?
[2] talks about it, ...
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Which one is better: FORTRAN or Python? And I guess that in both cases you need Gnuplot, am I right?
I'm working on a Windows machine at the moment.
I'd like to use it to get numerical solutions for ...
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