Computational Science Stack Exchange
Computational Science Stack Exchange

Most Popular

more tags
1500 questions
7
votes
4 answers

Algorithm for high quality 1/f noise?

How can I generate arbitrarily high quality $1/f$ noise, for use in a model? My model involves a lot of feedback, over a large number of iterations, with a very high bandwidth, so I'd like the $1/f$ noise to be as "ideal" as possible. Assuming…
Seth
  • 173
  • 1
  • 4
7
votes
3 answers

Nearest positive semidefinite matrix to a symmetric matrix in the spectral norm

So I have a symmetric matrix $A$ and I would like to solve the optimization problem, $$\hspace{2.5mm}\text{Minimize}\;\; \|A-S\|_2$$ $$\hspace{-5mm}\text{Subject to}\;\; S\geq0.$$ $A$ is given and $S$ is the variable. I can put this straight into my…
Set
  • 503
  • 2
  • 14
7
votes
2 answers

How can I obtain a one dimensional finite difference formula for $U_{xx}$ with unevenly spaced nodes?

I know that if I had evenly spaced points, I can use $U_{xx}\approx \frac{U_{i-1}-2U_{i}+U_{i+1}}{dx^2}$. But if my gridpoints are unevenly spaced, I assume that I can obtain the finite difference formula in the following way: $D^-[D^+(U)]$,…
Paul
  • 12,045
  • 7
  • 56
  • 129
7
votes
1 answer

Online resources for reviewing graphics cards for GPGPU

Can anyone recommend a site that maintains up-to-date reviews of graphics cards for GPGPU use? Most benchmarks focus on gaming performance, whereas I am interested in the performance of scientific applications like FFTs, linear algebra, and…
Emre
  • 333
  • 1
  • 7
7
votes
3 answers

Largest eigenvalue of FD discrete Laplacian

Is there good approximation for largest (in magnitude) eigenvalue for discrete Laplacian ($\nabla^2$) obtained from nonuniform structured grid (like that)? Of course, one can always use general methods such as Lanczos or Power Iteration, but I am…
Alexander
  • 1,111
  • 1
  • 8
  • 15
7
votes
2 answers

Solution blows up when using Runge-Kutta to solve simultaneous ODEs for liquid film equations

This is a continuation of a problem I asked over at physics exchange and math exchange. Basically I have two ODEs that I am solving in order to calculate the radial and tangential velocity of liquid dispensed on the center of a disk rotating at…
Derek
  • 173
  • 6
7
votes
5 answers

Adjoint method for optimization problem

I am interested in the adjoint method for shape optimization problems. However, I couldn't find a helpful introduction. So I come here and look forward to some enlightening advices. Could you direct me to any textbooks, published papers or free…
newbie
  • 249
  • 1
  • 3
7
votes
1 answer

Will upgrading to a 64 bit OS help me any?

Assuming that I am running Intel MKL (BLAS, LAPACK), is there any difference in performance if I run it on a 32 or 64 bit OS? (Of course, assuming that my hardware remains the same). My processor is a 64 bit Intel i3. But am currently running…
Inquest
  • 3,394
  • 3
  • 26
  • 44
7
votes
1 answer

Performance of adding eight numbers sequentially vs. in a tree

The simplest way to add 8 numbers would be something like this, sum = one + two + three + four + five + six + seven + eight; This (in C) would add one and two, and add the result to three and do the same till eight. Instructions for adding…
kesari
  • 287
  • 2
  • 7
7
votes
1 answer

float128 in linear algebra

Is there any paper or research concerning float128 arithmetics applied to linear algebra problems(e.g. iterative solvers, decompositions etc.)? How much benefit is really there in comparison with double? How much slower is it? I've discovered this…
Alexander
  • 1,111
  • 1
  • 8
  • 15
7
votes
1 answer

Why should I renormalize physical variables?

I am working with legacy physical codes and I develop new ones based on the output of them. They all use their own internal normalization of variables (for example all distances are divided by the physical size of the simulation box) which leads to…
Vincent
  • 343
  • 1
  • 8
7
votes
1 answer

Jacobi iteration to reduce the quadratic function

Given certain function $f(X)$ which is quadratic in $X\in\mathbb{R}^{n\times d}$, $$\frac{1}{2}tr(X^TAX) - tr(Y^TBX)$$ for positive definite weighted Laplacian matrices $A, B\in\mathbb{R}^{n\times n}$, i.e. the diagonal elements are negative…
usero
  • 1,663
  • 2
  • 14
  • 27
7
votes
1 answer

What is numerical damping in the context of time-dependent FEM solvers?

Comsol Multiphysics (a popular FEM package) includes two time-stepping algorithms (IDA aka BDF, and Generalized-alpha), described in their documentation as follows (quoted here under Fair Use; emphasis mine): • IDA was created at the Lawrence…
Evgeni Sergeev
  • 171
  • 1
  • 3
7
votes
3 answers

Tanh-sinh quadrature numerical integration method converging to wrong value

I'm trying to write a Python program to use Tanh-sinh quadrature to compute the value of \begin{equation} \int_{-1}^1 \frac{dx}{\sqrt{1-x^2}} \end{equation} but although the program converges to a sensible value with no errors in every case, it's…
ThomasNicholas
  • 171
  • 4
7
votes
4 answers

Finite Difference Method Stability

The diffusion equation is: $ \frac{\partial T}{\partial t} = \alpha \left( \frac{\partial^2 T}{\partial x^2} \right) $ An explicit finite difference approach can be used to solve this, forward in time and central differences in space.…
zed111
  • 201
  • 2
  • 7
1 2 3
…
99 100