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Hi I am trying to solve a set of pde converted into ODE and DAE using central finite difference method. I have used the MATLAB 'solve' command to determine the coefficients of fictitious nodes for ...

I am puzzled by the Wikipedia entry discussing many online algorithms for computing the sample variance, including the Welford's online algorithm. In particular, the sample variance $s_n^2$ can be ...

Do you know any way to call scipy.integrate.odeint, solve_ivp, or any python solver directly within a Matlab code? I have tried ...

I want to plot a numerical integral function of some function $f$ using scipy and matplotlib. How can I do this? I tried the ...

I have been struggling for two days with the following problem. I would like to do a $d$-dimensional interpolation over some data. I tried first to use polyharmonic splines, but when the size of data ...

Original Stack Overflow Question: https://stackoverflow.com/questions/65683788/indexerror-index-31-is-out-of-bounds-for-axis-1-with-size-31?noredirect=1#comment116218335_65683788 PDE: u_t = u_xx + u(...

I am using the Galerkin method (Discontinuous to be precise) to discretize in space the scalar linear wave equation and the explicit second order centered finite difference scheme to discretize in ...

I am not sure whether this question belongs here, but I would like to give it a try and benefit from the experience of the people at scicomp.SE. From my experience, the software quality in ...

This question is a specialization of full rank update to cholesky decomposition, to which I hope to get a more positive answer. When calculating the minus log of the multivariate normal distribution, ...

I am trying to numerically solve the following equation: $\frac{\partial^{2} \phi}{\partial t^{2}}-\frac{\partial^{2} \phi}{\partial x^{2}}+V(x) \phi(x, t)=0$ On some domain, with: $\phi(x, 0) = I(x)$ ...

I want to construct a gauss integration for the weight function $w(x) = x^{1/2}$ for $$\int_{0}^{1}x^{1/2}f(x)dx = a_{1}f(x_{1})+a_{2}f(x_{2})$$ Solving \begin{align*} a_{1}+a_{2} =& \int_{0}^{...

Say you have a tensor $T$ and the components are represented by a 3 by 3 by 3 matrix. And you want to use that tensor to map a vector $u$ into a new vector $s$, both of which are 3 by 1 column vectors....

I have read different approaches on how to solve pdes in parallel which are discretized using finite element method. For example: Non-overlapping domain decomposition approach as mentioned in https://...

I believe, I have a parametric nonlinear optimization problem. The non-convex constraints depend on some parameters, and I seek a solution that satisfies these constraints for all parameters in a ...

I want to approximate $uu'$ with a finite difference. On the one hand, it seems to be $$(uu')_i=u_i\frac{u_{i+1}-u_{i-1}}{2\Delta t}=\frac{u_iu_{i+1}-u_iu_{i-1}}{2\Delta t}$$ On the other hand, $$(uu')...

I have got a mesh of triangles (for a finite element code) that I'd like to partition into polygons, much better if convex. I tried metis and it is very complicated but powerful if one knows about ...

I work for a school who is looking to split students into two groups for COVID related reasons. Ultimately we need to split the students by class section and try to keep families to be in the same ...

I am applying optim() function in R to obtain maximum likelihood estimates of the fixed effects and random effects in a model with bivariate random effects. The ...

I'm doing CFD simulations for blood flow in unstructured grids. My boundary condition at the outlets is called three-element Windkessel which basically calculates the pressure by solving this ODE: $$...

Let $A \in \mathbb{R}^{m \times n}$ where $m \geq n$. Let $B$ and $\tau$ be the result of applying LAPACK's dgeqrfp method (R on the upper right triangle, and the ...

I've been working on a finite element code on unstructured methods, which I've parallelized using the Schur complement method. Here's a summary of how I did it: Assign each triangle of the mesh to a ...

The usual story of Givens rotations vs Householder reflections is that Householder reflections are better if you want to map a long vector to $e_1$, while Givens is better if you want to map a 2-...

I have been trying to figure out what I did wrong for the last two days. I do not know if I actually did something wrong or if the error is supposed to be this large in usual leapfrog problems. I ...

Assume we have an IVP $y'(t) = f(t,y)$, and that $\partial_t f$ and $\nabla f$ are cheap to compute. Assume further that more derivatives are not cheap to compute, or inaccessible for some reason, ...

I would like to have an algorithm that interpolates the values attached to nodes in a concave mesh mesh. To be me precise, assume we have a point cloud P (e.g. in 3 dimensions) and a list of edges E ...

Problem I'm trying to calculate CPU / GPU FLOPS performance but I'm not sure if I'm doing it correctly. Let's say we have: A Kaby Lake CPU (clock: 2.8 GHz, cores: 4, threads: 8) A Pascal GPU (clock: ...

TL,DR What is the accepted best practice in scientific computing circles for storing large quantities of hierarchically structured data? For example, SQL does not play nicely with large sparse ...

I need to do a simulation for my thesis project involving some piezoelectric nanoparticles in a fluid beamed with ultrasounds. I'm looking for a software for such simulation and for now it seems me ...

I am trying to evaluate Reynolds number in Ansys CFX 2020 R2 using CCL/Perl script on different domains in a radial turbine. But for that, I need to define the Characteristic length. So I define the ...

I need to generate an image with 11x11 pixels having in the center of the image a square of 5x5 pixels, with the gray level of the background 0 and the gray level of the square is 50. I need to ...

I want to construct a gauss integration for the weight function: $$w(x) = x^{1/2}$$ $\in(0,1)$ of the form: $$\int_{0}^{1}x^{1/2}f(x)dx = w_{1}f(x_{1})+w_{2}f(x_{2})$$ \begin{align*} w_{1}+w_{2} =...

I've spent the whole day trying to figure out what is the correct way to impose (and implement) periodic boundary conditions $u(0,t)=u(1,t)$ for all $t>0$ for the simple advection equation $u_t + v ...

I want to know summation of some small numbers, such as {e^-1000, -e^1001, e^1002...} If all numbers are positive, I can use log-sum-exp algorithm. But unfortunately, negative numbers are also ...

I implemented a rather simple SPH simulation using a cubic-spline-kernel and a simple non-iterative pressure solver as described in this PDF in equation 9. I followed algorithm 1 of that paper (...

I have a problem with computing gradient of each node in finite element method. I can get the value of each node. But how can I get the gradient? I know $u = \sum u_i \phi_i$ where $\phi_i$ are the ...

I realized an usual way to scale an N-body problem for an N-body simulation is by choosing units such that gravitational constant $G = 1$, but I'm probably doing it the wrong way. Suppose I simply ...

Given the location of $n$ points on a 2D plane ($P_1, P_2, \ldots, P_n$); and the location of a special point $X$. Find three points $P_i,P_j,P_k$ ($i \neq j \neq k$) such that point $X$ is inside the ...

I would like to generate a 3D hexahedral mesh starting from a STL file using Gmsh 4.8.0. I followed these steps: Opened a STL file: file->open Added a volume: Modules -> Geometry -> ...

Inspired by this answer, I tried to understand when floating point errors come into visibility and to check it also comparing the plot of the numerical solution with Explicit Euler with the analytical ...

I'm looking for a relatively straightforward but robust MPI-based parallel n-body application implementation in C/C++ -- ideally one that's off the shelf and has been used in other papers before. A ...

I want to generate the parameter, for a Poisson distribution, from a lognormal distribution. Has there been literature on if this is proper in probability & statistics, or are there nuances to ...

I want to solve the following Cauchy problem \begin{equation} y' = y^2 + \frac{t^4 - 6t^3 + 12t^2 - 14t + 9}{(1+t)^2} \end{equation} with initial condition: $y(0) = 2$ for $t \in [0,1.6]$ using a 3 ...

Looking at previous S.E answers, we have a formula for this: The theoretical peak FLOP/s is given by $$ \text{Number of Cores} * \text{Average frequency} * \text{Operations per cycle} $$ After ...

Before we start, a small disclaimer: I am not a computer scientist, and the field of isosurfaces is new to me, so hopefully, the question is phrased clearly:) Otherwise, let me know, and I will (try ...

Consider the half-planes $\{x \leqslant 2\}$ and $\{x+y \leqslant 3\}$. These two half-planes are coded with the R package 'rcdd' as follows: ...

I'm looking for an open-source automatic meshing tool or library able to generate full or dominant hexahedral mesh starting from a provided arbitrary model i.e. a surface triangular mesh stored in STL ...

I know that, in general, finite volume (FV) methods are more (numerically) diffusive than spectral methods. However, I can't find any information on how the advection scheme changes that. For example, ...

Let us suppose that I have a full cycle LCG, following the standard equation Hence, as it has a full cycle, it will have a period of m, and will output values ranging from 0 to m. However, I want to ...

I'm trying to solve a system of ODEs using the BDF order 4 method. I find the first 3 points using RK4, then for the implicit part of the BDF, I use Newton-Raphson iteration. Unfortunately my solution ...

I'm numerically modelling flows around various geometric 2D shapes. Is there a good source/cookbook of equations that approximate these? Some examples are Rectangle: $(x-a)^n+(y-b)^n < r^n$ where ...