Most Popular

1500 questions
22
votes
4 answers

Numeric Quadrature with Derivatives

Most numerical methods for quadrature treat the integrand as a black-box function. What if we have more information? In particular, what benefit, if any, can we derive from knowing the first few derivatives of the integrand? What other…
MRocklin
  • 3,088
  • 20
  • 29
22
votes
1 answer

BDF vs implicit Runge Kutta time stepping

Are there any reasons for why one should choose high order implicit Runge Kutta (IMRK) over BDF time stepping? BDF seems much easier to me as $q$ stage IMRK needs $q$ linear solves per time step. Stability for BDF and IMRK looks to be a moot…
user107904
  • 607
  • 4
  • 13
22
votes
1 answer

Alternatives to hdf5

I've been using HDF5 for years, but as the size of the dataset grows I'm starting to experience the same problems listed here http://cyrille.rossant.net/moving-away-hdf5/ Can you point me to a format like HDF5 with - Good support for parallel…
M. G.
  • 321
  • 2
  • 4
22
votes
2 answers

A good finite difference for the continuity equation

What would be a good finite difference discretization for the following equation: $\frac{\partial \rho}{\partial t} + \nabla \cdot \left(\rho u\right)=0$? We can take the 1D case: $\frac{\partial \rho}{\partial t} + \frac{d}{dx}\left(\rho…
tiam
  • 864
  • 7
  • 18
22
votes
7 answers

Analyzing Numerical Error in C++ Function

Suppose that I have a function that takes as input several floating-point values (single or double), does some computation, and produces output floating-point values (also single or double). I am working primarily with MSVC 2008, but also plan to…
user_123abc
  • 323
  • 2
  • 6
21
votes
3 answers

Binary vs. ASCII file size

I need to write some data from a computation, that will be read later by Paraview (.vtu or vtk file). When it comes to file size , should I go for the ASCII format or the Binary format ?
SAAD
  • 636
  • 2
  • 7
  • 20
21
votes
2 answers

What is pseudo time-stepping?

While reading some literature on PDE solvers I came across the term pseudo time-stepping today. It seems to be a common term, however I failed to find a good definition or an introductionary article for it. Hence: What is pseudo time-stepping, and…
Florian Brucker
  • 970
  • 1
  • 8
  • 21
21
votes
4 answers

F2Py with allocatable and assumed shape arrays

I would like to use f2py with modern Fortran. In particular I'm trying to get the following basic example to work. This is the smallest useful example I could generate. ! alloc_test.f90 subroutine f(x, z) implicit none ! Argument Declarations…
MRocklin
  • 3,088
  • 20
  • 29
21
votes
1 answer

How does the performance of Python/Numpy array operations scale with increasing array dimensions?

How do Python/Numpy arrays scale with increasing array dimensions? This is based on some behaviour I noticed while benchmarking Python code for this question: How to express this complicated expression using numpy slices The problem mostly involved…
Nat Wilson
  • 438
  • 3
  • 8
21
votes
4 answers

For which statistical methods are GPUs faster than CPUs?

I have just installed a Nvidia GT660 graphic card on my desktop and, after some struggle, I manage to interface it with R. I have been playing with several R packages that use GPUs, especially gputools, and I was comparing the time taken by my GPU…
Jugurtha
  • 707
  • 4
  • 12
21
votes
1 answer

Diagonal update of a symmetric positive definite matrix

$A$ is a $n \times n$ symmetric positive definite (SPD) sparse matrix. $G$ is a sparse diagonal matrix. $n$ is large ($n$ >10000) and the number of nonzeros in the $G$ is usually 100 ~ 1000. $A$ has been factorized in the cholesky form as…
luogyong
21
votes
2 answers

Numerically stable way of computing angles between vectors

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/acute angles, there is a loss of precision and the…
astrojuanlu
  • 1,187
  • 2
  • 12
  • 25
21
votes
2 answers

Algorithms for a many-to-many generalized assignment problem

I can't seem to find any literature on algorithms which can be used to solve a many-to-many generalized assignment problem (GAP), i.e. models where not only can more tasks be assigned to one agent, but multiple agents can also be assigned to one…
Gerrit Jan
  • 311
  • 1
  • 3
21
votes
3 answers

Parallel I/O options, in particular parallel HDF5

I have an application that can be trivially parallelized but its performance is to a large extent I/O bound. The application reads a single input array stored in a file that is typically 2-5 GB in size (but I expect this number to grow in the…
khinsen
  • 1,731
  • 11
  • 8
21
votes
4 answers

How to determine the amount of FLOPs my computer is capable of

I would like to determine the theoretical number of FLOPs (Floating Point Operations) that my computer can do. Can someone please help me with this. (I would like to compare my computer to some supercomputers just to get an idea of the difference…
Ol' Reliable
  • 313
  • 1
  • 2
  • 7