All Questions
11,504
questions
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-...
- 2,695
0
votes
0
answers
44
views
Solve beam equation with elastic term using scipy solve_bvp
I want to solve the beam equation with distributed load and elatic term (which depends on how much the beam interact with the terrain) :
$$
EI\frac{d^4w}{dx^4}+k*(w(x)-t(x))=q(x)
$$
where $q(x)$ is a ...
- 35
1
vote
0
answers
35
views
Understanding this code to truncate the SVD
In Brunton's and Kutz's data-driven science and engineering book, page $19$, is a description of one way to truncate the SVD of a given matrix
I want to understand what the code for the variable <...
- 111
2
votes
2
answers
164
views
(Isoparametric) Mapping of physical coordinates to their equivalent parametric coordinates on a reference element
I have some experiece with finite element methods (FEM), in general. However, I mainly worked with Cartesian grids -- i.e. using orthogonal (non-curved) elements.
Recently, I became interested in a ...
- 125
0
votes
0
answers
46
views
1D FDTD simulation of plane wave propagation and the Courant stability condition
I'm currently trying to simulate a simple case of wave propagation in free space before adding in more complexities, and already I'm stumped. I understand the Courant stability condition. However, I ...
- 1
2
votes
1
answer
52
views
Good references for the P3/P1dc element
I am struggling to find some good references for the P3/P1dc element (cubic element for velocity and linear piecewise discontinuous for pressure) for the Stokes/Navier-Stokes equations.
Is there a ...
- 964
0
votes
2
answers
80
views
Source for scalability challenge for number of finite element nodes per process
Context
In distributed simulation of a finite element mesh with $N$ nodes and $P$ processes, a professor stated to me that "achieving good scaling for more than 25,000 finite element nodes per ...
- 265
0
votes
0
answers
33
views
Fastest way to calculate the eigenvector with the largest eigenvalue for a 3*3 positive-definite matrix [duplicate]
As stated in the title: I have a 3 by 3 positive-definite matrix $M$. What I need is the eigenvector corresponding to the largest eigenvalue, since I am calculating the solution to maximize the value ...
- 101
0
votes
1
answer
38
views
Estimating the rate of convergence of Projected Gradient Descent on constrained polynomial objectives
I am estimating the order of convergence of Projected Gradient Descent (GD) on quadratic polynomials with random coefficients independently drawn from Uniform(-1,1) and bounded by a unit hypercube. I'...
- 23
3
votes
0
answers
47
views
Datasets for inverse heat transfer problems
I was wondering if there is an available, real-life known inverse heat transfer problem dataset to benchmark oneselfs algorithm, as in MNIST for deep learning. Talking about... (well in this case I ...
- 181
1
vote
1
answer
50
views
Solving TOV equations that describes neutron stars in modified f(R, T) gravity
Sorry for the long post, tldr at bottom.
I'm trying to use standard RK4 code in C/C++ to solve a coupled system of 2 modified TOV equations in f(R,T) gravity and reproduce some of the results of this ...
- 23
3
votes
2
answers
156
views
Finding ALL Eingenvalues of a Sparse Integer Matrix
I would like to find ALL Eingenvalues of a huge, very sparse integer matrix. This matrix has a lot of known properties, e.g. that it is symmetric and nearly tridiagonal, with very few (max. ca. 4 per ...
0
votes
0
answers
59
views
How to correctly discretize volume elements in different geometries?
I am solving a reaction-diffusion problem in one dimension for a catalyst particle to get the internal effectiveness factor ($\eta$),as given below:
$$ \eta = \frac{\int_0^{V_p}{R_i\ dV}}{R_i^{surf}\...
- 23
0
votes
0
answers
43
views
Rule-Based Link Prediction for Social Network [migrated]
Relevance to Site
I believe this question is suitable for the Computational Sciences Stack Exchange site as it pertains to the implementation of a graph algorithm. According to this widely accepted ...
5
votes
1
answer
344
views
Time integration of first-order ODE with higher-order information
Suppose I wish to derive a numerical integrator for the first-order ODE $$x'(t)=F(x(t)).$$ By differentiating both sides of the expression in $t$, I can write a second-order relation also satisfied ...
- 1,393