Computational Science Stack Exchange
Computational Science Stack Exchange

Most Popular

more tags
1500 questions
10
votes
4 answers

Reference request: Rigorous analysis of algorithms for PDE and ODE

I'm interested in suggestions for book references on the subject of numerical PDE and ODE, in particular, a rigorous analysis of such methods in a manner written for professional mathematicians. It does not have to be extremely comprehensive in the…
Christopher A. Wong
  • 275
  • 1
  • 8
10
votes
2 answers

Are 8 Gauss points required for second order hexahedral finite elements?

Is it possible to get second order accuracy for hexahedral finite elements with fewer than 8 Gauss points without introducing unphysical modes? A single central Gauss point introduces an unphysical shearing mode, and the standard symmetric…
Geoffrey Irving
  • 3,969
  • 18
  • 41
10
votes
5 answers

Best choice of solver for a large sparse symmetric (but not positive definite) system

I am presently working on solving very large symmetric (but not positive definite) systems, generated by some certain algorithms. These matrices have a nice block sparsity which can be used for parallel solving. But I can't decide whether I should…
Soumya
  • 131
  • 1
  • 1
  • 5
10
votes
2 answers

Extracting diagonal of an approximately diagonal matrix when we don't know its entries

What is a good way to extract the diagonal from a symmetric matrix that is already almost diagonal, but where you don't have the matrix elements (only the ability to apply it to vectors)? Further constraints are, (1) applying the n-by-n matrix…
Nick Alger
  • 3,143
  • 15
  • 25
10
votes
1 answer

Least absolute deviations solving using the Barrodale-Roberts-algorithm: Premature termination?

Please excuse the longish question, it just needs some explanation to get down to the actual problem. Those familiar with the mentioned algorithms probably could jump directly to the first simplex tablau. To solve least absolute deviation problems…
Thilo
  • 241
  • 2
  • 7
10
votes
2 answers

Where can I find a good reference for the stability properties of several methods of solving parabolic PDEs?

Right now I have a code that uses the Crank-Nicholson algorithm, but I think that I would like to move to a higher-order algorithm for timestepping. I know that the Crank-Nicholson algorithm is stable in the domain I want to work in, but I am…
Dan
  • 3,355
  • 3
  • 21
  • 47
10
votes
1 answer

Boundary conditions in fluid simulation

I'm working on a 2D fluid sim using vortex particles/"vortons" as described in Fluid Simulation for Video Games. Which I think is the same things as the "discrete vortex method". Basically you represent the fluid with a collection of particles…
Jay Lemmon
  • 583
  • 3
  • 10
10
votes
1 answer

Energy conservation in the solution of the Helmholtz equation

This might be a silly question, but I know very little about the theoretical properties finite elements, so here goes. Suppose you were to solve the Helmholtz equation (let's say in 2D) with a spatially varying wave speed using finite elements. For…
Victor Liu
  • 4,480
  • 18
  • 28
10
votes
4 answers

Relevance of fixed-point and arbitrary precision computations

I see very few non-floating point computing libraries/packages around. Given the various inaccuracies of floating point representation, the question arises why there aren't at least some fields where this increased accuracy might be worth the…
Milind R
  • 607
  • 5
  • 16
10
votes
2 answers

Connections between Differential Forms and the second order Finite Volume Method

Reading today about the theory of differential forms, I was left impressed how much it reminded me of second order Finite Volume Method (FVM). I'm struggling to figure out is thinking this way just trivial or is there some deeper connection. Well,…
Johntra Volta
  • 1,403
  • 9
  • 14
10
votes
6 answers

Where does Python fit into the picture within computational science field?

So I've been debating whether or not I should bother learning Python. From speaking with my professors, Matlab seems to be the common language used in applied mathematics/computational science as far as academia is concerned; while in industry, my…
TheRealFakeNews
  • 593
  • 1
  • 4
  • 16
10
votes
2 answers

What does it mean for a basis set to be "correlation consistent" ?

Some basis sets are said to be "correlation consistent". What does it mean in practice ?
Stefano Borini
  • 1,599
  • 3
  • 16
  • 20
10
votes
1 answer

Solving a simple Ax=b system in parallel with PETSc

I am new to the PETSc package. I have a ~4000x4000 matrix A in matrix-market format and I want to get PETSc to solve this using multiple processors. I know how to solve the system on a single processor, but I don't know how to distribute the…
smilingbuddha
  • 645
  • 5
  • 10
10
votes
3 answers

Literature references for modeling current and future energy costs of floating-point operations and data transfers

I am searching for the most important literature and slide references for modeling current and future energy costs of floating-point operations and data transfers across the CPU, memory, network, and storage. I have marked this question as a…
Aron Ahmadia
  • 6,951
  • 4
  • 34
  • 54
10
votes
3 answers

What is this regularization technique?

I'm currently working on understanding some very old code. They are trying to solve an underdetermined system and the comments say that they want the minimum norm solution. The system they solve is: $A x = b$, with $A \in \mathbb{R}^{5 \times n} (n…
Thijs Steel
  • 1,693
  • 8
  • 16
1 2 3
…
99 100