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1500 questions
11
votes
3 answers
Applying Dirichlet boundary conditions to the Poisson equation with finite volume method
I would like to know how Dirichlet conditions are normally applied when using the finite volume method on a cell-centered non-uniform grid,
My current implementation simply imposes the boundary condition my fixing the value of the first…
boyfarrell
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11
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1 answer
Are there any heuristics for optimizing the successive over-relaxation (SOR) method?
As I understand it, successive over relaxation works by choosing a parameter $0\leq\omega\leq2$ and using a linear combination of a (quasi) Gauss-Seidel iteration and the value at the previous timestep... that is
${u}^{k+1} =…
Paul
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11
votes
1 answer
Why are interior point methods difficult to warm start?
I often encounter the general adage that interior point methods are difficult to warm start. Is there an intuitive explanation behind this advice? Are there situations in which one can expect benefits from warm starting in an interior point method?…
Christopher Johnson
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11
votes
1 answer
Library for Fourier transform on triangle lattice
I am looking for reasonably fast implementations of the discrete Fourier transform (DFT) on a 2D triangular or hexagonal lattice.
I would appreciate pointers to such implementations (especially ones easily usable from Python or Mathematica), and…
Szabolcs
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11
votes
2 answers
What is the underlying structure of scientific code performance?
Consider two computers with different hardware and software configurations. When running the exact same serial Navier-Stokes code on each platform it takes x and y time to execute one iteration for computer 1 and 2, respectively. In this case,…
Isopycnal Oscillation
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11
votes
2 answers
Numerical method for equation solving that works on stochastically computed functions
There are many well known numerical methods for solving equations of the type
$$ f(x) = 0, \quad x \in \mathbb{R}^n,$$
e.g. bisection method, Newton's method, etc.
In my application $f(x)$ is calculated with a stochastic method (the result is an…
Szabolcs
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11
votes
1 answer
How can one parallelize a multigrid method for solving a linear system of equations?
As I understand it, the multigrid method solves a linear system by solving a coarser version of the same problem (there by eliminating low frequency error) then projecting back to the fine grid to smoothen out the high frequency errors. For large…
Paul
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11
votes
5 answers
How to deal with complexity in numerical code, for example, when dealing with large Jacobian matrices?
I am solving a non-linear system of coupled equations, and have calculated the Jacobian of the discretised system. The result is really complicated, below are (only!) the first 3 columns of a $3\times 9$ matrix,
(The complexity arises, in part,…
boyfarrell
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11
votes
3 answers
Are there any libraries out there that implement block Krylov subspace methods?
Question
Are there libraries out there that implement block Krylov subspace methods? (I was not able to find any from a simple Google search.)
Background
Right now, I am working with a code that solves several systems of the…
Geoff Oxberry
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11
votes
3 answers
Volume of 3D convex hull of small point sets all on the hull
I have a question that is similar to this one asked before except in 3D, and I only need the volume, not the actual shape of the hull.
More precisely, I'm given a small set of points (say, 10-15) in 3D, all of which are known to lie on the convex…
Victor Liu
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11
votes
2 answers
Data structures for finite volume code: Arrays vs Classes
I have to write a finite volume code for Magnetohydrodynamics (MHD). I have written numerical code before but not at this scale. I just wanted to ask which will be a good choice, using a data structure (object orientated approach) with classes or…
0b1100001
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11
votes
3 answers
Testing if two 12x12 matrices have the same determinant
I am given a $12 \times 12$ matrix $Q$ that is symmetric, invertible, positive definite and dense. I need to test if $$\det(Q) = \det(12I-Q-J) \; \; (1)$$ where $J$ is the all ones matrix.
I am currently doing this with the armadillo library but it…
Jernej
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11
votes
3 answers
N-dimensional Delaunay Tesselation Software Libraries
I have a set of known points/nodes irregularly spaced in N-Dimensional space (N>=2), and I would like a way to generate the Delaunay triangulation of these points, and return the corresponding elements.
Are there any existing meshing libraries that…
mirams
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11
votes
3 answers
Complex numerical analysis
What numerical analysis situations become more/less stable, have faster/slower convergence, or are otherwise quite different when dealing with functions of complex variable instead of functions of a real variable?
vtt
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11
votes
3 answers
Best Methodologies for Managing a Mesh in Parallel Finite Element Computation?
I am currently developing a domain decomposition method for the solution of the scattering problem. Basically I am solving a system of Helmholtz BVPs iteratively. I discretize the equations using finite element method over triangular or tetrahedral…
midurad
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