All Questions

About the flexible GMRES (fgmres), we know that it is a variant of right preconditioned gmres. And the robust command gmres in matlab as follows: ...

I'm trying to simulate the heat diffusion in a 3D piston. I marked the boundaries on GMSH. I have used a Dirichlet BC of 300 on the top face of piston. But the results look abnormal. There is a ...

tl;dr Using a Taylor-matched method to find coefficients for the discretized equation $ \mathbf{A} \vec{f}'' = \mathbf{B} \vec{f} $, a Fortran code has been implemented to find the second derivative ...

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 was recently reading some literature about evolutionary game theory and I got particularly interested in Moran process linked to prisoner's dilemma as a model of evolution of two sub-populations. ...

I have a bunch of data points in 3D that lie along a few planes. What would be the best approaches to estimate the normals of these planes? Edit: There are roughly equal number of points lying along ...

I want to learn a very simple PDE to gain physical and mathematical intuition—a PDE with just one spatial dimension $x$ and a time dimension $t$. And, I want to write code for it in Matlab and use a ...

In principle the PDE Toolbox in MATLAB can handle multi-domain 3D geometries as noted here. This feature and the associated function geometryfromMesh were introduced in MATLAB R2018a. The associated ...

I'm attempting to solve the Poisson equation in 3D for a magnetic vector potential in the presence of a current source. To validate my code, I'm initially looking to reproduce the model described in ...

Given an N-dimensional matrix A, I want to find an M<N dimensional index array I such ...

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 have a computer model with a number of parameters that need to be calibrated based on experimental results. It's also important to understand the sensitivity of the results to each parameter ...

I am trying to simulate a case in ANSYS FLUENT for combustion of methane and oxygen where oxygen enters the domain in the form of droplets. There is a change in temperature but there is no formation ...

I do not really get the point of null space usage for creating the prolongation operator for smoothed aggregation algebraic multigrid. I know what the null space is per definition and I know that the ...

I encountered some odd results when using the function fix() in Octave and Scilab. The following is input and output of the Scilab console but the exact same thing happens in Octave. I start with the ...

I have a cost function with 2 parameters. The variables are dependent on each other. So, if I just take a partial derivative with respect to one variable the slope is in terms of the other variable ...

According to [1] the one-dimensional Kohn-Sham equation is given by $$ \left( -\frac{1}{2} \frac{d^2}{dr^2} + \frac{l(l+1)}{2r^2} + V[\rho;r]\right) rR_{nl}(r) = \varepsilon_{nl} rR_{nl}(r) $$ where $$...

Consider the following system of nonlinear non-dimensional ODE : \begin{align*} \frac{d\bar{x}(\tau)}{d\tau}=\quad&\bar{x}\left[1-\bar{x}-\frac{\bar {y}_{1}}{\bar{m}_{1}\bar {y}_{1}+\bar{x}}-\...

According to [1] the Troullier-Martins pseudopotential for quantum number $l$ is computed by $$ V^{\textrm{KB}}_{\textrm{nonlocal},l}(r) = \frac{\vert{}V_{\textrm{nonlocal},l}(r)\Phi^{\textrm{PP},0}_l(...

I would like to know some GNU libraries or lists of downloadable Tersoff potentials. I couldn't find that many of them, and I also would like to know if there is a reason as to why this is the case.

Given matrix $K_{n \times n}, H_{n \times n},M_{n \times n}$, I want to solve for $B_{n \times n} $ and $V_{n \times 1}$ from the nonlinear system of equations: \begin{aligned} &H_{i j}=\frac{B_{i ...

Anyone have an idea for a DCP (disciplined convex programming) representation of the concave function $x\sqrt{1-x}$, which is has domain $[0,1]$? The Taylor series about $x=0$ is $$x - \frac{x^2}{2}...

I have the following matrix $$ A = [x_1, x_2, ..., x_n], $$ where $x_i \in \mathbb R^n$. But I know the relationship that \begin{align} x_2 = s_2 x_1 \\ x_3 = s_3 x_3 \\ ... \end{align} where $s_i$...

I have a matrix $A\in \mathbb{C}^{N\times N}$ and I need to calculate $||A^{-1}||_{2}$ efficiently. Can it be done without having to evaluate the inverse explicitly? In general, I am looking for ...

I am working on implementing the Fourier beam propagation method in C++. I am really more of a programmer than a physicist but I think I have a good understanding of what I am trying to do. Here is ...

I'm searching for lower bounds of bilinear forms arising in FEM for elliptic second order PDEs with mixed boundaries. I did some research and found: $$\max_{v_{h}\in\mathcal{V}_h(\mathcal{\Omega})}a(...

I am looking for a mathematical explanation for the singularity caused by a Dirichlet boundary condition partially imposed at a boundary. For instance $$ \nabla^2u=0 ~ \text{in}~\Omega $$ where $\...

If one had to code up a new dynamical system for a research group at a university, and the university has a Matlab total headcount license so that one could code in Matlab, are there any benefits to ...

I wonder if there is any study that compares the performance of kd-tree vs brute-force nearest neighbor search on GPU. Post #4 on this page suggests that kd-tree may not be the optimal algorithm for ...

I have written Poisson solvers using two different methods: A classic Jacobi scheme and one using the multigrid solver Hypre. I made up a couple of test cases ensuring the validity of those solvers. ...

Due to my previous question, where I asked about flux calculation in lattice Boltzmann (LB) method here, I have more or less same question for deviatoric stress tensor calculation due to pseudo-...

I am trying to implement a numerical solver and am having troubles dealing with boundary conditions, especially in the corners. I have a 2D mesh, and on the left I have a Dirichlet condition, on the ...

I am parallelizing code to numerically solve a 5 Dimensional population balance model. Currently I have a very good MPICH2 parallelized code in FORTRAN but as we increase parameter values the arrays ...

I am creating a C++ Physics Simulation where I need to move an rigid body through an acting force field. Problem: simulation does not conserve energy. Quesiton: abstractly, how is conservation of ...

I have some discrete data, non-equispaced in $x$, $y=f(x)$. I want to use a numerical finite difference method to calculate the second derivatives of $y$, at some point. I am using the Fornberg ...

I have a 32 cores machine, and I need to run 16 different dynamics simulations in parallel on it. I want the 16 jobs to run in parallel, not sequentially, on the same machine. The 16 dynamics input ...

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 ...

My PDE simulation program written in Fortran has to make about 2 million variable time steps. But with each time step it slows down more and more, so that if it initially makes 1000 time steps per ...

I am looking find a way of efficiently generating a random, undirected subgraph $G_s$ with $N$ vertices, using a subset of edges from an exisiting undirected graph $G$, also of size $N$, where the ...

I have a task to plot average temperature profile at each cross-section in the axial direction of a combustion chamber. I have $x$, $y$, $z$ coordinates data in excel as well as the corresponding ...

I am trying to simulate a robot manipulator dynamics in SciLab. Basically, I generated a step function that has constant acceleration for half of the time and then the same acceleration but negative ...

For context: Gelfand's formula for the spectral radius is $\lim_{k\rightarrow \infty}|A^k|^{1/k}$ where $|\cdot|$ is any well-defined operator norm. I naively coded a function to calculate the $k$th ...

I am trying to solve Stokes problem using Finite element method. My question is how to impose that total pressure over the surface is zero to remove the constant pressure mode?

I want to solve the convex optimization as follows: \begin{align} \underset{X_1,X_2}{\min} &\ -\frac{1}{N}\sum_{i=1}^N\log\det\left(I+H_i^HX_2H_i\right)-\log\left[1+h^H(X_1+X_2)h\right]\\ &\...

I am trying to compute the convolution of two characteristic functions over a Cartesian mesh. First, I define my Cartesian mesh of the interval $[0,1]$ as follows $$ x_{i} = i \Delta x, i = 0, 1, 2\...

The computation of Troullier-Martins pseudowavefunctions has been described in [1]. The pseudowavefunction $R^{\textrm{PP}}_l$ is defined by $$ R^{\textrm{PP}}_l(r) = \left\{ \begin{array}{ll} R^{\...

Prewitt gradient operator Show that the Prewitt gradient operator can be obtained by fitting the least-squares plane through the 3 × 3 neighborhood of the intensity function. Hint: Fit a plane to ...

I am trying to write a neural network from scratch for the purposes of having the entire architecture available for me to mess around with. In doing so, I am trying to completely understand back-...

I'm supposed to solve the following partial differential equation in python using Runge-Kutta 4 method in time. $$ \frac{\partial}{\partial t}v(y,t)=Lv(t,y) $$ where $L$ is the following linear ...

So I've found some interesting linear algebraic research areas that's both pure-ish, with a numerical bent to it, too -- e.g. inverse eigenvalue problems have both interesting theoretical and ...