All Questions

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 ...

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 ...

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 ...

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 ...

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+\...

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 ...

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. ...

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 ...

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 ...

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 ...

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. ...

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 $\Delta f = 4$...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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? ...

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 ...

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 ...

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 ...

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)...

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 ...

Consider a function $f(t)$ and its Fourier transform $F(\omega)$. The amplitude of the Fourier transform $F(\omega)$ depends on the frequency $\omega$ and thus also depends on the scale of the $t$-...

I have used different variants of the Laplacian operator (div grad) using 4, 8, 12, 20 and 24 of the closest points. I get problems due to the chosen coordinate system and the discretization of the ...

I am trying to solve a problem with 2D Convection-Diffusion equation with U = Concentration ($mg/m^{2}$) using Implicit Upwind Finite Difference Method like this $$ \frac{\partial U}{\partial t} + ...

I am transferring a finite element code from Matlab to Python. A problem occurs at the last step when I try to solve the displacement $U = F/K$. I have checked that the calculated $F$ and $K$ are same ...

Consider a potentially high-dimensional (say, $N$ up to 20) integral of the form $$ \int_0^\infty \rho_1(x_1)\rho_2(x_2) \cdots \rho_N(x_N) \bigg(x_1+x_2+\cdots+x_N -K\bigg)^+ \, dx_1 \cdots dx_N. $$ ...

I use python for my algorithm which uses only one core and I need more processing speed. I have i7 6700K CPU with 8 cores. How to convert them to one core to have a total performance of 8 cores? ...

I am trying to model a linear elastic material in Abaqus using UMAT. For my application, I need to rotate the 6x6 compliance matrix for a given set of eigenvectors (or a rotation matrix). I came ...

I have a function $$ f(z) = \frac{1}{(z-z_1)(z-z_2)(z-z_3)(z-z_4)} $$ All of $\{z_1,z_2,z_3,z_4\}$ are simple poles. The residues for this function are given as $$ \text{Res}(f(z),z_i)= \lim\limits_{z\...

I was wondering if anyone could enlighten me about the convergence properties of the truncated newton method in case of a non-positive definite hessian $\nabla^2 f = H$. From the Book 'Numerical ...

I have a multiple CPU system weakly connected and memory access is slow when one CPU accesses the others memory. The CPUs uses NUMA. How can I make TensorFlow adjust to this or does it per default?

I have a question about implementing traction boundary conditions in 2D and 3D linear elasticity. Consider the picture above. I want to apply traction boundary conditions on the boundary in red. My ...

I have a physical model which takes $\sim50$ parameters and gives $\sim2000$ outputs taking tens of minutes to run. I need to optimize these parameters to give outputs as close as possible to data. ...

This was so much easier in Python (so much so that I'm considering going back to matplotlib for data analysis). But really, trying to figure out ROOT and Boost graph library and mathgl makes me want ...

What are the pros of Fourier-Galerkin spectral methods while solving PDEs? Here's the one that came in my mind first: Easy implementation: using this method, differentiation operator computation is ...

I have found a toy implementation of RK-Dopri(4,5), written in Python. I am concerned however, about line 118: y = y + h * (b1*K1+b3*K3+b4*K4+b5*K5+b6*K6) Has the ...

I came across this paper by Simoncini and Popolizio that deals with acceleration techniques in the context of rational Chebychev approximation for the exponential. The problem is to solve efficiently ...

I want to compress an array of time series floating point data as much as possible. Currently the only algorithm I've found for this is XOR compression which works well, but doesn't compress the data ...

I apologize in advance if this post is at all ignorant or elementary, I am a pure mathematician who is newly getting into the world of scientific computing. For my research, my advisor would like me ...

In his talk "What is a good linear finite element?", Shewchuk states that small dihedral angles in linear tetrahedra elements cause ill-conditioning of the stiffness matrix. Do small dihedral angles ...

I have a point $y \in \mathbb{R}^d$ and a convex polyhedron $\mathcal{P}$ given as the intersection of half-spaces: $$\mathcal{P} = \{x \in \mathbb{R}^d \mid a_1 \cdot x \le b_1, \dots, a_n \cdot x \...

Can you provide a jargon-free (as much as possible) explanation of what is meant by "dense ODE systems", and "sparse ODE systems"? Some hints I have gotten from Googling: dense ...

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 ...

I have a transformation matrix which takes in the elastic constants from the local $rtl$ coordinates and then converts the elastic constants to the global $xyz$ coordinates via a rotation about the $z$...

The Q2-P1 element is one of the popular finite elements for incompressible flow problems in the mathematics community. For this element, the velocity field is approximated using bi-quadratic shape ...

Let $A$ be the well known tridiagonal matrix coming from the 1D Finite difference discretization of the Laplacian, with stencil $\frac{[1 \quad-2 \quad 1]}{h^2}$. The system $Ax = b$ is very large, so ...