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I have a sparse square matrix $A$ with size $n \times n$ and number of nonzero entries $nnz$. The goal is making a sub-matrix $B$ with $s$ nonzeros which are randomly chosen from $A$. Duplicates are ...

I'm looking for a comparison between the Jacobian-Free Newton-Krylov (JFNK) method performance compared to the conventional CFD nonlinear solution methodologies like SIMPLE. Does anyone know if such ...

package com; import java.util.Scanner; class Good { public Good() { ...

I have been trying to get Matlab to solve the following integral for a while (just to be clear when I say "solve" I mean "spit out a number"): ...

Consider the integer lattice in $2d$, namely the set $\mathbb{Z}^2 = \{(x,y): x,y\in \mathbb{Z}\}$, and let $u:\mathbb{Z}^2 \to \mathbb{R} $ be a function defined on some bounded subset of $\mathbb{Z}^...

I'm trying to find the global stiffness matrix for the truss example in the picture given, but I'm a bit confused. I know the matrix should be 8x8, but I don't understand how. My understanding is ...

I have two sets of exponential data (temperature measurements) of the form T(t)=$-e^{-kt}$. k is a constant that determines the rate of temperature change. 1 temperature measurement was taken every 10 ...

I'm looking for resources on fast, numerically stable pairwise euclidean distance algorithms. In particular, suppose $A \in \mathbb{R}^{M \times D}$ and $B \in \mathbb{R}^{N \times D}$ are two sets of ...

I am interested in solving a large number of small linear systems of equations, $Ax=b$, with $A$ either $2\times2$ or $3\times3$. Assuming none of these systems are actually singular, is there ...

Let the PDE be defined as \begin{align} & \begin{cases} u_t = v_x \\ v_t = u_x \end{cases}\; \; -1 \lt x \lt 1, t \ge 0 \\ & u(-1,t) = u(1,t) = 0 \end{align} Initial conditions for $u$ and $...

I have been working with an algorithm, which uses additions of floating point vectors, (sparse matrix of floats)x(dense vector of floats) dot products I recently found out that I can get the same ...

Consider Poisson’s equation $$- \Delta u = f{\rm\qquad{ in }}\;\Omega $$ with following mixed boundary cconditions $$u = g{\rm\qquad{ on }}\;\Gamma \subset \partial \Omega $$ $$\frac{{\...

I understand what the matrix looks like for the coefficients of A1 and B1. Can someone fill in the entries in the matrix for the additional coefficients (a2, b2) etc., if I want to include more terms ...

When solving a linear system $Ax=b$ where $A=B^TCB$ do I need to form $A$ explicitly by two matrix-matrix multiplications or is there another more simple way? $C$ is a NxN matrix and not always ...

I need to calculate a matrix $A$ (at least some elements of it, see below) as defined by the following equation $$ A=B(\mathbb{1}-B)^{-1} $$ where B is a square matrix of dimension $N$ and $\mathbb{...

I am cross posting this question to the mathermatics stack exchange. please find it either at this link, https://math.stackexchange.com/q/2952989/430980, or below: I have a question concerning the ...

can someone explain to me what is meant by constraint propagation in simple words? I am studying the optimization theory on optimal power flow where I have encountered this terminology but I am unable ...

MKL and FFTW offer 1-D FFTs that can operate on many inputs simultaneously - in other words, they can batch-transform the columns of some input matrix. Is the performance of these multi-transforms ...

In Yurii Nesterov's Introductory Lectures on Convex Optimization, there is a bound for the total number of iterations for some process. See page 109: $$\left[\frac{1}{\ln(2(1-\kappa))} \ln\frac{t_0-t^...

Ideally, I would like to get the symbolic/algebraic integral of the function and plot the resulting surface in 3d. I am not sufficiently versed in SciPy to know if this is even really possible.

I am implementing the advection equation $u_x+(1/c)u_t=0$ following a Crank-Nicholson finite difference scheme. The equation for this is \begin{eqnarray*} -\frac{\gamma}{4} w_{n-3 j+1} + w_{n-2 j+1} ...

I'm coding an iterative algorithm of constrained continuous optimisation. An augmented Lagrangian algorithm (outer) calls a bound-constrained L-BFGS-B algorithm (inner), which calls a line search ...

Howe to DataSet/DataTable merges with another DataSet/DataTable in c# with MySql 5.7.2.So other DataSet joins the ende of the first DataSet, not the top

If $A$ has eigenvalue $\lambda_A$ $$B = I - c\frac{I-rA}{I-\bar{r}A}$$ How to derive the eigenvalue $\lambda_B$? $$\lambda_B=1-c\frac{1-r\lambda_A}{1-\bar{r}\lambda_A}$$ where $c, r, \bar{r}$ are ...

Consider the implicit ODE $$ M(y)\dot{y} = F(t,y) $$ If $M$ is non-singular for all $y$ How to use the forward-Euler method to numerically solve for $y$ without inverting $M(y)$? I only came out ...

I would like to say first that am new at using Calculix. I'm using Abaqus/CAE to create a cup deep drawing simulation and everything worked perfectly but my objective is to run the same exact ...

I am currently implementing classical density functional theory for a radially symmetric system. In mathematical terms, I am searching for a function $f(r)$ that minimizes a functional $\Omega[f]$. ...

I need help writing a code in Matlab to solve cubic equations using Vieta's... Very new to programming, so this is what I have so far: By means of a translation and rescaling, the general cubic can ...

I set up two one-way wave equations for constant velocity $c$ in one-dimension. When I implement them I get a highly unstable (divergent) solution. I wonder if someone could give me a suggestion about ...

I am new with OpenFOAM, and I will have to modify ShockTube tutorial of OpenFOAM rhoCentralFoam solver. Where can I find the information about this tutorial? Searching in Google has only led me to ...

I adapted this FEniCS code for my problem and I'm wondering if there is any good resource about how to choose the penalty parameter $\alpha$? Best case would be, if I can define it through some ...

I need to load data from a .txt file (<3KB) in Matlab. The structure of the data is as follows: s_0.4 2.00869311294470 1.90140098201689 4.00117387799144 2.73028990891229 ... ...

In a lot of the computational solid mechanics papers that I've come across, boundary conditions are typically implemented as a traction boundary condition or a Dirichlet boundary condition. But in ...

I have a model about a fluid being extruded on a moving bed as in the 3D printing process. The model is a boundary-value problem where the right boundary is the point where the fluid attaches to the ...

Problem Solving a non-linear system of equations. The number of variables is the same as the number of equations. When I fix a set of variables (say $\vec{y}$) and keep another set free (say $\vec{...

I have a TTree in ROOT with 1000 events and 15 variables associated to each of them. I would like to convert this in its entirety to an hdf5 dataset. How do I organise my data in HDF5 Groups such that ...

I need to optimize affine transformations for of a set of triangles using energy function based on the connectivity. The energy of an edge $e_j$ between triangles $T_a, T_b$ is given by $$ E_j = \...

The partial differential equation, \begin{align} \dfrac{\partial f}{\partial x} + a(x)\dfrac{\partial f}{\partial y} = 0 \qquad & f(0,y) = f(L_1,y) = c_0e^{-y} \\ & f(x,0) = c_0 \;,\; f(x,L_2) ...

What are common methods to choose pivot blocks in Block LU (for non-SPD/non-Diagonally Dominant Matrices)?

I am working on a multi-commodity flow problem where for a graph $G=(V, E)$, some flows are permitted to be split and some flows should strictly follow one path. I have formulated this problem as ...

I am using a second-order finite difference in space and time approximation for the 1D wave equation. No source but initial data: $I(x)=\mathrm{e}^{-400 (x-0.5)^2}$. Velocity $c=1$, $nx=501$, $nt=...

I have found that in unstructured mesh, discretizing the laplacian operator with finite volumes requires special care, as given in An Introduction to Computational Fluid Dynamics: The Finite Volume ...

I have a vague understanding of the compatibility equations for linear elasticity. They appear to be necessary in obtaining a unique displacement field. However, why is it that, in my papers I've come ...

Many dense linear algebra decompositions (QR, SVD...) on an $m\times n$ matrix have cost $$ O(\max(m,n)\min(m,n)^2) $$ when implemented in practice on a computer. Is there a colloquial name or a more ...

I have the following problem: $$\begin{bmatrix}A &B \\C& D\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}\lambda I_m & 0 \\ 0& \mu I_n\end{bmatrix}\begin{bmatrix}x \\y\...

I want to minimize a function $f(z) = z^H A z + c_1^T \theta + c_2^T \log(r)$ where $z = r e^{i\theta}$, $z\in \mathbb{C}^n$, $A \in \mathbb{R}^{n\times n}$ is symmetric positive definite, and $c_1, ...

I am developing a FEM fluid solver using the Taylor-Hood algorithm, i.e. quadratic interpolation for velocity, and linear for pressure. I have developed the code for 2-D quadrilaterals and triangles, ...

Writing this comment reminded me of something I noticed years ago about evaluating Bessel functions of the first kind $J_n(x)$ in Excel. (BESSELJ) I don't use Excel now but at the time I'd checked ...

How well do explicit Runge-Kutta "tableau" methods compare to the state of the art ODE solvers and when do they fail? I've been reading Butcher's ODE book and he does a good job at introducing ...

I need to solve the following equation: $$ \begin{pmatrix} \frac{\omega^2}{c^2}\varepsilon_x-\mu_z^{-1}k_y^2-\mu_y^{-1}k_z^2 & \mu_z^{-1}k_xk_y & \mu_y^{-1}k_xk_z\\ \mu_z^{-1}k_xk_y &\...