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1500 questions
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votes
2 answers

Periodic Green's functions in integral equation methods in different frequency regimes

I'm asking about the solution of the Helmholtz equation on a periodic domain with piecewise constant wavespeed in different frequency regimes. One possible approach is to solving this problem is to write down integral equations on the boundary…
Victor Liu
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4 answers

Prolonging PBS job

It is quite painful to discover that a few-day long job is going to be prematurely killed due to an error in setting walltime limit for it. Is there a way to change it for a running PBS job?
mbq
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Efficient Gravitational Field Implementation

I asked a similar question on physics.stackexchange, being ignorant about this website. I am basically looking for an efficient way to implement gravitational fields. I have a huge 2D space, with thousands of objects in it. I then need to simulate…
Jeroen
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Radial integration of expensive function with Bessel weights

I need to calculate the integral $$I = \int_0^R f(r)J_n\left(\frac{z_{nm}r}{R}\right)rdr$$ where $J_n$ is the $n^{\mathrm{th}}$ order Bessel functions of the first kind, $z_{nm}$ is its $m^{\mathrm{th}}$ zero and $f(r)$ is a real function which is…
jtravs
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2 answers

Solving a generalised eigenvalue problem

I have a generalized eigenvalue problem in the standard form $\lambda \mathbf{B} \mathbf{x} = \mathbf{A} \mathbf{x} $, resulting from a finite difference discretization of a coupled system of two linear stability equations, so the system is large…
Davide
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The effect of decoupling a coupled system of PDEs

I asked a somewhat similar question previously but perhaps it might have been too specific for anyone to really answer. Here is a bit more general of a question that I am struggling with. Consider the following…
Justin Dong
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WELL pseudo-random number generations

I've used MT19937 in a test harness to generate uniformly (unsigned) 32-bit [0, $2^{32}$- 1] values, based on the original Authors' mt19937.c implementation, to generate an (essentially inexhaustible) supply of statistically random stream of…
Brett Hale
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1 answer

FDTD Poynting Vector

I'm attempting to validate my FDTD code against Meep by calculating the Poynting vector field across a simulation consisting of a monochromatic point source within a box (no boundary conditions (Dirichlet) so everything just bounces off the domain…
3Dave
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What is the best way to multiply a diagonal matrix (in fortran)

What is the best way to compute: $$ Y = D X $$ where $D \in \mathbb{R}^{m\times m}$ is diagonal and $X \in \mathbb{C}^{m \times n}$ is general. I am mostly interested in these two cases: $m >> n$, $m > 10^7$ $n >> m$, $m < 10^4$ Options I can…
Max Hutchinson
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Quasi Monte Carlo in Matlab

I want to use Quasi Monte Carlo to try and improve the convergence of a simulation I am running. The random numbers are simply to produce the observation errors for a standard linear regression model, which is then estimated using a number of…
Bazman
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Gauss-Seidel, SOR in practice?

When I learned about SOR, it was mostly given as one of the first examples of iterative methods, and then later the iterative methods that I would end up using would be Krylov subspace methods. Are any of the iterative methods like Gauss-Seidel and…
Kirill
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3 answers

Optimizing matrix-vector multiplication for many small matrices

I'm looking at speeding up matrix-vector products but everything I read is about how to do it for very large matrices. My case, the matrices are small but the number of times it must be done is very large. What methods, if any, are there to…
tpg2114
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5 answers

Computational Complexity of 2D Convolution

I am using image filtering for an image processing algorithm I'm developing. I'm using a predefined Matlab function to do the convolution, but I'd like to know what the computational complexity is for this algorithm. The simple way of thinking of…
jake
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1 answer

Second derivative of the Associated Legendre functions

I would like to compute, as part of the solution of the Laplace equation using the Fast Multipole Method, the second derivative of the associated legendre functions of the first kind . Specifically, I am looking for C implementations or just the…
rivendell
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4 answers

precision vs matrix condition number

I have an application in which I am computing a quantity which is approximated by an average over $M$ points. In theory, the average converges to the correct quantity when $M$ is infinite. In practice, the computation involves a $M\times M$…
yannick
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