All Questions

I am doing a text classification task with R, and I obtain a document-term matrix with size 22490 by 120,000 (only 4 million non-zero entries, less than 1% entries). Now I want to reduce the ...

What is the theoretical convergence rate for an FFT Poison solver? I am solving a Poisson equation: $$\nabla^2 V_H(x, y, z) = -4\pi n(x, y, z)$$ with $$n(x, y, z) = {3\over\pi} ((x-1)^2 + (y-1)^2 + (...

Multi-physics simulation involves coupling multiple "physics", often with different space and/or time scales. Additionally, the single-physics codes are often written by different teams. The most ...

Quiet a lot of insight can be gained form experience, I was just wondering if anybody has seen something similar to this before. The plot shows the initial condition (green) for the advection-...

Following from my previous question I am trying to apply boundary conditions to this non-uniform finite volume mesh, I would like to apply a Robin type boundary condition to the l.h.s. of the domain (...

I'm from the field of accelerator physics, specifically related to circular storage rings for synchrotron light sources. High energy electrons circulate around the ring, guided by magnetic fields. ...

Many numerical methods for hyperbolic PDEs are based on the use of Riemann solvers. Such solvers are essential for accurately capturing shock waves. There are a range of such solvers available for ...

I'd like to be independent of commercial software for my scientific work. I find a dependence an commercial packages such as Matlab and its toolboxes unsatisfactory, because I do not know if I will ...

After doing some mathematics related to the stability of elements in 3D Stokes problem I was slightly shocked to realize that $P_2-P_1$ is not stable for an arbitrary tetrahedral mesh. More precisely, ...

I have a data set $x_{1}, x_{2}, \ldots, x_{k}$ and want to find the parameter $m$ such that it minimizes the sum $$\sum_{i=1}^{k}\big|m-x_i\big|.$$ that is $$\min_{m}\sum_{i=1}^{k}\big|m-x_i\big|.$$...

I have a linear system of equations of size mxm, where m is large. However, the variables that I'm interested in are just the first n variables (n is small compared to m). Is there a way I can ...

I wish to simulate the behaviour of a double-pendulum-like system. The system is a 2-degrees-of-freedom robot manipulator that is not actuated and will, therefore, behave mostly like a double-pendulum ...

I need simple explanation of the Multigrid Method or some literature about this. I am familiar with iterational methods including BiCGStab,CG,GS,Jacobi and preconditioning, but I am a beginner with ...

Let x, y be two floating-point numbers. What's the right way to compute their mean? The naive way ...

When applying the classical formula for the angle between two vectors: $$\alpha = \arccos \frac{\mathbf{v_1} \cdot \mathbf{v_2}}{\|\mathbf{v_1}\| \|\mathbf{v_2}\|}$$ one finds that, for very small/...

I have a mixed integer programming problem. And I am current using GLPK as my solver. But I found that GLPK is good for Linear Programming problem, but for Mixed Integer programming, it requires much ...

There are numerous FD schemes for the advection equation $\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}=0$ discuss in the web. For instance here: http://farside.ph.utexas.edu/teaching/...

There is a system of linear constraints ${\bf Ax} \leq {\bf b}$ . I wish to find a strictly positive vector ${\bf x} > 0$ that satisfies these constraints. That means, $x_i > 0$ is required for ...

what are state of art methods for numerical solution of ODEs with discontinuous right side? I'm mostly interested piecewise-smooth right side functions, e.g. sign. I'm trying to solve the equation of ...

I have a very basic notion about interval arithmetic (IA), but it seems to be a very interesting branch of computational science both theoretically and practically. It is clear that the obvious ...

Sorry for the long post but I wanted to include everything that I thought was relevant in the first go. What I want I am implementing a parallel version of Krylov Subspace Methods for Dense Matrices....

What is counterpoise correction exactly ? Can you explain when it is needed and why ?

In methods like gmres or bicgstab it could be attractive to use another Krylov method as a preconditioner. After all they are easy to implement in a matrix-free way and in a parallel environment. For ...

I came across a puzzling remark in the paper P. J. van der Houwen, The development of Runge-Kutta methods for partial differential equations, Appl. Num. Math. 20:261, 1996 On lines 8ff on page 264, ...

Suppose I have two VTK files, both in structured grid format. The structured grids are the same (they have the same list of points, in the same order), and there is a field, call it "Phi", in each VTK ...

I am trying to understand some results and would appreciate some general comments on tackling nonlinear problems. Fisher's equation (a nonlinear reaction-diffusion PDE), $$ u_t = du_{xx} + \beta u ...

There seem to be two main kinds of test function for no-derivative optimizers: one-liners like the Rosenbrock function ff., with start points sets of real data points, with an interpolator Is it ...

In my research department we plan a small seminar on the new c++20 language standard. There are exhaustive lists online presenting the new features of the language standard, some of which will be of ...

In semiconductor simulation, it is common that the equations are scaled so they have normalised values. For example, in extreme cases electron density in semiconductors can vary over 18 order of ...

Standard multigrid and domain decomposition methods do not work, but I have large 3D problems and direct solvers are not an option. What methods should I try? How are my choices affected by the ...

I've had a glimpse of Numerical Analysis (majorly, Numerical Methods like root finding, quadratic equations and other preliminary stuff) in my Calculus class but now, I find myself wanting more ...

The meta seemed to suggest that career advice is ok . . . so here goes. I have a couple of close friends in the ML and mathematical modeling fields just finishing PhD's and starting out on the job ...

As far as I am aware, multigrid solvers use iterative smoothers such as Jacobi, Gauss-Seidel, and SOR to dampen the error at various frequencies. Could a Krylov subspace method (like conjugate ...

I have taken a basic introduction to Finite Element Method, which did not emphasize a sophisticated understanding of a 'weak formulation'. I understand that with the galerkin method, we multiply both ...

Which approaches are used in practice for estimating the condition number of large sparse matrices?

I regularly compete in so called "Programming Contests", where you solve difficult algorithmic problems with your own code and problem solving skills during a limited time-frame. For referential ...

Sometimes while optimizing code it is required to time certain portions of the code, I have been using the following for years but was wondering if there is a simpler/better way to do it? ...

I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of planets in a system (or any objects, for that matter). All the bodies are circles in an Euclidean ...

Specifically I want to extend work involving B3LYP started with Gaussian 03 but continued with GAMESS-US. The energies provided by the default B3LYP methods are not the same. There is a discussion ...

Question: Suppose that you have two different (factored) preconditioners for a symmetric positive definite matrix $A$: $$A \approx B^TB$$ and $$A \approx C^TC,$$ where the inverses of the factors $B, ...

I am looking for some open source implementation (any of Python, C, C++, Fortran is fine) of rational approximation to a function. Something along the article [1]. I give it a function and it gives me ...

I am running molecular dynamics (MD) simulations using several software packages, like Gromacs and DL_POLY. Gromacs now supports both the particle decomposition and domain decomposition algorithms. ...

My research group focuses on molecular dynamics, which obviously can generate gigabytes of data as part of a single trajectory which must then be analyzed. Several of the problems we're concerned ...

I am teaching a numerical analysis survey class and am seeking motivation for the BFGS method for students with limited background/intuition in optimization! While I don't have time to prove ...

I'm developing some larger code to perform eigenvalue computations of huge sparse matrices, in the context of computational physics. I test my routines against the simple harmonic oscillator in one ...

I wonder what has happened to polynomial preconditioners. I am interested in them, because they appear to be comparatively elegant from a mathematical perspective, but as far as I have read in surveys ...

I have a PETSc Mat and would like to estimate its condition number.

Computational Science people: I originally posted this question at Math Stack Exchange and someone commented that I might get "much better" answers here: I am a novice at numerical methods and ...

I am interested in solving the Poisson equation using the finite-difference approach. I would like to better understand how to write the matrix equation with Neumann boundary conditions. Would someone ...

I was reading this on Math SE. The basic question is : Assume that someone wishes to study something advanced; one way to do this would be to start off from basics and build up. But the "bigger ...