All Questions

I have the following matrix: $$ C = \pmatrix{A & B} $$ where $B$ is dense and $A$ has significant sparse structure. $A$ is a B-spline collocation matrix so each row has some number of zeros, ...

So I have discitized the Crank Nicolson Method for diffusion equation, but I don't understand how to put it into matlab. Since the solution isn't separable how is it inputted?

... or is it for a normal binary search tree ( not ordered ). I was reading this post here: https://medium.com/basecs/demystifying-depth-first-search-a7c14cccf056 and I noticed that the in-order ...

Homework disclaimer... The task: We are using the following algorithm to solve the quadratic equation $x^2+2px+q=0$: $x_1=|p|+\sqrt{p^2-q}\mathtt{;}$ $\mathtt{if}\,p>0\,\mathtt{then}\,...

I'm trying to calculate higher order (e.g., m=0, n=46) Zernike moments for some image. However, I'm running into a problem ...

I'd like to know how to deal with a divergence when trying to solve the Poisson equation for electrostatics with a simple spectral method. I'm not sure how to best state my problem, so I'll explain ...

I am looking for a software where I can check the properties of for instance, real gases like helium, and observe the molecular movements of that gas visually. I want to have a chance to create a ...

I am using ParMetis do the repartitioning of the adaptive mesh. However, ParMetis cannot guarantee that the result partition is a contiguous mesh. Hence, I need to check if there are any non-...

In my calculation (of a simple heat equation, for testing) using the newton method I tried to replace the full jacobian matrix with an approximation vector, i.e. replacing $J$ in $$J(u)\delta u=-F(u)$...

Is there a faster way to check whether $A\in\mathbb{R}^{n\times n}$ is positive definite on $b^{\bot}:=\{x\in \mathbb{R}^{n}: x\cdot b=0\}$ than ...

Consider the nonlinear least-squares minimization of a vector of $n$ residuals $\mathbf{f}$ in $p$ parameters $\mathbf{x}$: $$ \min_{\mathbf{x}} || \mathbf{f}(\mathbf{x}) ||^2 $$ This can be done with ...

I am a super n00b beginner, I have been teaching myself python concepts for the last couple of months using juptyer notebook, and lessons in CFD & similar subjects that I am conceptually familiar ...

I am trying to solve a simple optimal control problem using the Hamilton-Jacobi-Bellman equation, numerically in Python. This is proving to be rather difficult as I end up having to solve the ...

I am using a piece of code to study magnetohydrodynamics and I have encountered a problem. The code is solving the ideal MHD equations, i.e. the Euler equations with the Lorentz force and Faraday's ...

Given an infinite set C. Prove that C is decidable if and only if there is a function computable, total, injective and growing whose image is C. I can undertand why it needs to be a function ...

I have 5 at most 4th order polynomials in 5 variables, $$p_i(x_1,x_2,x_3,x_4,x_5) \qquad i = 1, \ldots, 5$$ where all coefficients are either rational or floating point. I'd would like to get the ...

I have an explicit FD (Finite Difference) code for diffusion/heat on a PDE in a cuboid domain, and it works fine. I would like to update the discretized equations and change the code so as to solve ...

I want to obtain the algebraic values of, for example, Hermite polynomials using SciPy but in a recursive manner. Using Maple, for example, these can be defined as ...

I am currently working on a numerical algorithm involving a lot of floating point arithmetic, involving some badly conditioned problem sets. I am using the relation $|x - y| / (\max(|x|, |y|, 1)) \...

Preliminaries: and  I wrote Maple code for above. Download the Maple code for Above:   Now, we can calculate the Matrix    as follows  for $k=2, M=3$, Question:  How can we write (Maple or ...

One can use GMRES as it is, but there is also a version of GMRES called k-step restarted GMRES, which is used for large matrices, where $k$ is some fixed number of steps after which we take a new $x_0$...

Most algebraic multigrid methods are scalar or variable based. This means that the initial grid size is identical to the number of unknowns of the problem. It has been stated, that this approach is ...

At how fine time resolution do modern computer simulations run at? Do they need to measure ms, ns (and if ns, then at what accuracy)? This sprang to my mind when I was considering, what's the ...

void printNum(int num); int main(void) { int num = 6; printNum(int num); return 0; } vois printNum(int num) { printf("%d", num); }

I have a set of $K$ keywords. Each of this keywords can have set of bids from $1\$,\dots,N\$$. For each bid for a keyword, it will get a specific amount of clicks and a specific cost. Clicks and Cost ...

I want to create a sinusoidal wave surface in Gmsh whose peak is tilted towards the right side. I have created this symmetrical wave using the simple sine wave equation in Gmsh but the original ...

I am trying to identify the weak form of PDE in structural mechanics. I read a lot of papers where they are using the elliptic boundary value problem \begin{equation} \int\limits_{\Omega} \delta \...

I have noticed a subset of lapack selected-eigenvalue solvers with the suffix vx and vr. dsyevx/vr, zheevx/vr etc. The function preambles (along with this previous stack exchange question) say they ...

I am working on an FEA mesh of hexahedron elements. The elemental level calculations involve finding the surface normals and area for each surface of a hex element. I preferred the vector cross ...

I'm having two sets of grids. One is uniform and another one is not uniform. I will calculate the derivative in uniform grid points and I like to transfer(map) the derivative to the non-uniform grid ...

I am fairly new to FEM and FEinCS. I worked through the relevant examples of the FEinCS Tutorial (https://fenicsproject.org/tutorial/ and http://hplgit.github.io/INF5620/doc/pub/fenics_tutorial1.1/) ...

I need to create a sub-communicator (mi_comm_world_2) based on a bigger mpi communicator (mpi_comm_world). In particular, after ...

I am searching for a prime of this form: $$(2^k - 1) 10^d + 2^{k-1} - 1$$ where $d$ is the number of decimal digits of $2^{k-1} - 1$, which is congruent to 6 mod 7. I reached k=565.000 and there is ...

Nonlinear ODE Statement I would like to use scipy to solve the following: u'' + (u')^2 = sin(x) u(0)=0, u(1)=1 where u = u(x). Approach I am looking at the ...

I am trying to understand the meshless methods as described in https://arxiv.org/pdf/1409.7395.pdf. I'm having trouble understanding the following step: (Page 7, just after equation 17) Now, rather ...

For a 3D array A to be conjugate symmetry, then A = conj(A([1 nx:-1:2],[1 ny:-1:2], [1 nz:-1:2])) for A having size nx,ny,nz. I will be so happy if I get help on this.

In an attempt to create three-dimensional volumes with inclusions in Gmsh I stumble upon a problem which was non-existent in the two-dimensional case. I'm using the OpenCASCADE geometry kernel ...

I'm trying to solve this question whose growth function is given as: Pk = (r^k) * P0 Where pk = [0.19 0.36 0.69 1.3 2.5 4.7 8.5 14] k = [1 2 3 4 5 6 7 8] The unknowns I'm trying to solve for is r ...

Compared to the transient PDE for linear elasticity, the steady equations appear to less well-conditioned. Are they inherently ill-conditioned without the transient term? The condition number for ...

I have an array of length L with N zeros, and L-N non-zero values. I have another array of length N. I would like to put the values of the shorter array into the positions of the longer array which ...

The question is pretty much the title. Note that I have lots of experience using open-source meshing tool, e.g. Gmsh and OpenFoam blockMesh & snappyHexMesh. Nevertheless, I have no idea on how to ...

There are a lot of algorithms which seem to have been supplied an official number, such as Algorithm 76, Hierarchical clustering using the minimum spanning tree. Another example is Algorithm 123, ...

I'm trying to implement a simulation for geodesics in Kerr black holes using Matlab. I used the ode's of this paper $$ p_r = \frac{\Sigma}{\Delta} \dot r $$ $$ p_\theta = \Sigma \dot \theta $$ $$ \...

I have a training set of a bunch of three element tuples in the form of (x, y, z) where x, y, and z are all continuous real valued scalars. Given a future x value (which will likely be close but not ...

I am poking at reproducing some fundamental research in group-theory. In particular, I want to reproduce the OEIS sequence #1. The crux of the problem is not generating potential groups, this can be ...

The original post was on stackoverflow : I transfert it here. I have to solve numerically the advection equation with periodic boundaries conditions : u(t,0) = u(t,L) with L the length of system to ...

I am running a 4node simulation of a cantilever beam. I calculated the convergence rate for different mesh sizes ( 4x2 8x4 16x8 32x16) and it was 1.7 not 2. what the reasons that might effect the ...

I have encountered an linear programming problem as follows: $$\max_{x\in\mathcal F_n}~ c_n^t\cdot x_n,\quad \quad \quad \quad \quad \quad (\ast)$$ where $\mathcal F_n:=\big\{x_n\in\mathbb R^{512n^...

I'm given a matrix. How do I find the nearest (or a near) positive definite from it? The matrix can have complex eigenvalues, not be symmetric, etc. However, all its entries are real valued. The ...

I am working on a program which takes values computed at the quadrature points from the finite element method and extrapolates them to the nodal points. I am working with a 10 node tetrahedral element ...