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26
votes
11answers
8k views

Robust algorithm for $2 \times 2$ SVD

What is a simple algorithm for computing the SVD of $2 \times 2$ matrices? Ideally, I'd like a numerically robust algorithm, but I'll like to see both simple and not-so-simple implementations. C code ...
0
votes
0answers
6 views

Explanation of Givens rotation in Jacobi Rotation SVD

I'm trying to implement Singular Value Decomposition (homework of sorts) via the Jacobi Rotation method (more info here, pages 11 and 12). I am stuck at the bullet saying (sorry for the picture, but I'...
0
votes
0answers
4 views

Is the Immersed Boundary (IB) method a Direct Numerical Simulation?

Is the IB method considered a Direct Numerical Simulation? A DNS code is the most detailed type of simulation and the most accurate but computationally expensive, right? What makes a simulation not a ...
2
votes
3answers
80 views

For traditional FEM and FVM, why can't we use mesh to represent geometry and use the mesh which represent the geometry to do the computation directly?

Isogeometric analysis [1] has the advantage of integrating geometric and mesh models using NURBS or Spline. At the same time, I would like to ask a question to my friends: for traditional FEM and FVM, ...
0
votes
0answers
69 views

How to debug segmentation faults in large problems?

I am sorry if this question seems like off topic or opinion based, but I was not sure how to go about it. I am currently working on a 100k x 100k positive definite linear system and trying to solve it ...
1
vote
0answers
24 views

Solving Lotka-Volterra Equations on Python [closed]

I'm trying to plot Lotka-Volterra Equations using Python. I am a real beginner when it comes to Python. I have these two equations: $$\frac{dR}{dt}=\alpha R-\gamma RF$$ and $$\frac{dF}{dt}=-\beta F+\...
2
votes
5answers
199 views

FEM and High Performance Computing

Suppose we want to solve an FEM problem in terms of HPC. What is the most usual way to do it: Using an open-source software like mfem,deal.ii etc.. or, Assembly the system by your own(read mesh file,...
4
votes
4answers
136 views

Can the mesh generation methods in FVM and FEM be totally based on the knowledge of the mesh generation theory in computer graphics?

The main references of mesh generation methods in computer graphics (CG) I found are discrete Differential Geometry [1] and a famous book "Polygon Mesh Processing" [2], while the "...
2
votes
2answers
104 views

What are the best ways to interpolate a vector field inside (convex) polygons?

I want to interpolate a vector field inside convex polygons in a polygonal mesh. For triangular meshes the scheme uses a piecewise constant interpolation in the triangle, discretized at the center of ...
3
votes
1answer
83 views

Scaling/Performance of Matlab's svds function (Lanczos bidiagonalization)

I have a simple Matlab script which aims to compute $k$ singular values of a matrix $A$. $A$ is a random dense square matrix of size $5000\times5000$, with 100 of its singular values constrained to ...
0
votes
1answer
57 views

Specifying mesh spacing for DFT in numpy

I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...
1
vote
1answer
323 views

Suitable finite difference method for a convection-diffusion system?

I am trying to solve a system of PDEs $H_{t} = \frac{0.3}{0.7} - \frac{0.005 B f(h(H))}{\theta} - \frac{0.3 f(h(H))}{0.7} + \frac{500}{0.7} (HH_x)_x + (HH_y)_y$ $N_t = \frac{N_{in} - 0.002 [N] B f(h(...
4
votes
0answers
72 views

Generally quadratic convex problem with one non-convex term

How would you approach a standard convex quadratic problem with convex constraints but one non-convex term ? Say $|x|^{0.4}$. $$\min_x \frac{1}{2} x^{T}Qx + g^Tx + c^T \mathrm{sign}(x) |x|^{0.4} $$ ...
-1
votes
0answers
32 views

Visible Deprecation Warning

Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify <...
2
votes
1answer
68 views

Is there a way to return a substring of a string using Convolutional Neural Networks?

I'm a PhD student in genetics and molecular biology working on an algorithm to identify if a DNA sequence is either a transposable element (TE) or not a TE using convolutional neural networks, and it'...
2
votes
2answers
603 views

Combined translational and rotational meshing in gmsh

For a flow simulation I am trying to reproduce a specific screw element design for an intermeshing co-rotating twin-screw extruder. I am using gmsh (v2.16) where the element is made from a 2D surface ...
1
vote
2answers
39 views

Job Scheduler for Local Machine

I am used to running calculations on a server/cluster, and we have used both PBS and SLURM. However, I am looking to run some calculations on my local machine. I would like to be able to schedule my ...
1
vote
1answer
21 views

Does 'Recombine' work for this geometry in Gmsh?

I am struggling to recombine the remaining triangular cells into unstructured quadrangular ones in this geometry using Gmsh. Do I need to add auxiliary lines somewhere or do some geometries just don't ...
2
votes
0answers
83 views
+50

Flux sign and face normal confusion in finite volume method

I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) $\nabla. (k\nabla T) = 0$, using finite volume method, however, I am having some ...
1
vote
0answers
34 views

How to speed up the Mixed-Integer Quadratic Program process?

Currently, I am solving a problem in the format: M is an integer as well. The problem that troubles me is that X is a vector in {0,1} with a size of 7000. I use the solver in https://github.com/...
0
votes
0answers
8 views

Finding the plot of input parameters in COMSOL [closed]

Can anyone help me find out the plot of the input waveform f0 which is present in parameters1 (having a central frequency of 40MHz)? I needed to know the waveform type(sinusoidal, delta, etc.). The ...
2
votes
1answer
74 views

FFTW on subarray with MPI

With the guru interfaces of FFTW, I can apply transforms only to parts of a multidimensional array by modifying the fftw_iodim ...
11
votes
2answers
29k views

What is the fastest algorithm for computing the inverse matrix and its determinant for positive definite symmetric matrices?

Given a positive definite symmetric matrix, what is the fastest algorithm for computing the inverse matrix and its determinant? For problems I am interested in, the matrix dimension is 30 or less. ...
0
votes
0answers
50 views

4th Order Adams-Moulton Method C++

I am trying to solve an ODE using 4th Order Runge Kutta and the 4th Order Adams-Moulton Method. I iterate over a couple of thousand timesteps and it seems to hold fine when the values are constant(...
2
votes
3answers
190 views

Is the imaginary part needed in this problem?

Before jumping into my question, let me contextualize it. I'm doing numerical simulations of a Helmholtz scattering problem $$\Delta p + \kappa^2 p = 0\, .$$ The incident pressure wave $p^{inc}$ will ...
1
vote
0answers
35 views

implementation of shell elements in a topology optimization algorithm

I am working on developing a topology optimization solver based on the finite element method and I want to add a triangular shell element in it. I used the classic finite element method but I didn’t ...
-1
votes
0answers
43 views

python plot exhibiting delta function behaviour but it was not supposed to do it

I'm currently trying to plot the photoionization cross-section in a semiconductor. The photoionization process is an optical transition of an electron in the ground state to higher subbands in a ...
2
votes
1answer
52 views

How to extract connected components from persistence diagram?

From the given point cloud (Fig. 1), I use Scipy-TDA to extract persistence diagram (Fig. 2). What I'm interested in is to extract 3 circles. For example, I'd like to know 3 center points and labels ...
11
votes
3answers
1k views

Rule of thumb for sparse vs dense matrix storage

Suppose I know the expected sparsity of a matrix (i.e. the number of non-zeros / total possible number of non-zeros). Is there a rule of thumb (perhaps approximate) for deciding whether to use sparse ...
3
votes
1answer
68 views

Solve two-player game - minimize the l-infinity norm of a matrix-vector product

I have a matrix $M$ with non-negative real entries, and I would like to minimize the objective function $$\Phi(v) = \|Mv\|_\infty,$$ where $v$ is constrained to be a probability vector, i.e., $v_1+\...
0
votes
1answer
31 views

Why is Time evolving block decimation so efficient?

I have a short question about Time evolving block decimation (TEBD). During a lecture I was told that this method is very efficient in evolving 1D quantum spin systems with only nearest neighbor ...
1
vote
2answers
227 views

Jacobians with automatic differentiation

I have an objective function F: Nx1 -> Nx1, where N>30000. There are many sparse matrix/tensor multiplications in this function, so taking an analytic Jacobian by paper and pen is cumbersome. ...
2
votes
1answer
67 views

Computing Series of $ke^{-(x - h)^2}$

I asked this question on the Computer Science stack exchange (https://cs.stackexchange.com/questions/128710/faster-computation-of-ke-x-h2), but it appears that it is more appropriate in Computational ...
1
vote
0answers
30 views

What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money 𝑚 to spend over 𝑟 different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
2
votes
1answer
88 views

Why is $1/r^2$ force law giving spiral trajectory?

I have written a program to solve for Newton's 2nd Law of motion for a given force law, in 2D polar coordinates. It is known that if the force law is of the form $k/r^2$,we get conic sections as ...
2
votes
1answer
70 views

GPGPU/FPGA programming for Combinatorial Analysis

Recently, I have taken an interest in performing combinatorial analysis for the game of 21 (blackjack) and attempted to use my AMD APU to try and thread the program via the 4 cores on the chip. ...
0
votes
0answers
49 views

FEM Meshing artifact at nodes with fewer neighbors

I wrote a 2D-FEM solver to solve some diffusion process and wanted to verify my code with a test problem. The input was $f(x,y) = x^2+y^2$ and I applied the stiffness matrix on it to get $\Delta f = 4$...
1
vote
1answer
47 views

Implementation of sparse matrix SVD for GPU

I have a sparse matrix $W$ which is almost-squared ($N+1 \times N$) and I would like to know the eigenvalues of $A = W^T W$. $A$ is Hermitian so the eigenvalues are real-positive valued. The usual ...
1
vote
2answers
63 views

How do I speed up this function evaluation in matlab?

Half the run time of my code right now is evaluating a big function over many, many points, it takes maybe about 20 seconds per evaluation The function consists of a bunch of simple operations that ...
6
votes
1answer
334 views

When and when not to use automatic differentiation

I am just learning (more) about automatic differentiation (AD) and at this stage it kind of seems like black magic to me. The second paragraph of its Wikipedia article makes it sound too good to be ...
-1
votes
0answers
29 views

Image segmentation network to extract questions from an image of a test paper?

This is the sample document -> I want to extract questions along with the options. There are other question papers as which have questions with diagrams in them. I want to be able to extract them ...
0
votes
0answers
29 views

Numerical simulation for a bounded process. Is slight deviation a “normal” fact?

Suppose I have to numerically simulate a process $\{y_t\}$ such that $y_t\geq0$ $\forall t\in\mathbb{N}$, with $t$ denoting time-step. Let's suppose I use MonteCarlo with $\mathscr{N}$ simulation ...
1
vote
0answers
29 views

Discretization formula for a system of two differential equations. “Solution to one of these is the initial condition of the other”. In which sense?

Consider the following stochastic differential equation \begin{equation} dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1} \end{equation} where $A$, $B$ and $C$ are parameters ...
2
votes
1answer
30 views

How do you construct a self-similar binary structured-tree?

Please excuse me if this question somehow looks trivial or not really interesting, but I recently have a hard time to convince someone else that my algorithm for constructing a self-similar binary ...
0
votes
1answer
31 views

Integrating Matrix Elements TypeError: f() takes 1 positional argument but 3 were given

I'm working on a linear variational problem for a general PIB and I keep encountering the same problem, and I know its a rather simple solution. Any suggestions? ...
0
votes
3answers
66 views

How to determine global stiffness matrix is constrained or not

Background In solid fem, we often solve $$\mathbf{Ku}=\mathbf{p}$$ where $\mathbf{K}$ is global stiffness matrix, $\mathbf{u}$ is displacement, $\mathbf{p}$ is global load vector. If displacement not ...
2
votes
0answers
56 views

OpenMP inconsistently segfaulting

I parallelized my code with openMP, and now have this bug in my code that's really odd. If it's the first time I run on a computer, it segfaults, but if I run the program again it runs fine. I've ...
0
votes
2answers
168 views

Different questions about “Inverse Physics problems”

I am in a context of forecasts in astrophysics. Don't be too rude if questions seem to you stupid or naive but rather indulgent, I am just looking for better undertsand all these numerical methods of ...
1
vote
1answer
73 views

How to write a code of 2D ADI method in matlab?

I tried to write a code for the alternating direction implicit (ADI) method in 2D, but I got stuck. My equation is: $$\frac{\partial U(t,x,y)}{\partial t} = 2\Delta U(t,x,y) -10(\frac{\partial U(t,x,y)...
4
votes
2answers
438 views

Help understanding and implementing fast multipole method for N-body

I've been trying to understand the Fast Multipole Method but not really getting anywhere. It seems like the fastest mainstream N-body simulation algorithm, and I would like to implement it in an ...

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