All Questions
11,503
questions
12
votes
2
answers
2k
views
Is there an open source set of ODE solvers for C that use the native C99 complex type?
I've been using GSL as the foundation of many of my simulations, but it's a little bit overkill for my purposes and it defines its own complex type for legacy reasons. Rather than code my own Runge-...
- 491
43
votes
18
answers
3k
views
Where can one obtain good data sets/test problems for testing algorithms/routines?
In evaluating the quality of a piece of software you are about to use (whether it's something you wrote or a canned package) in computational work, it is often a good idea to see how well it works on ...
18
votes
4
answers
649
views
Which methods can ensure that physical quantities remain positive throughout a PDE simulation?
Physical quantities like pressure, density, energy, temperature, and concentration should always be positive, but numerical methods sometimes compute negative values during the solution process. This ...
- 25.7k
14
votes
1
answer
461
views
What spatial discretizations work for incompressible flow with anisotropic boundary meshes?
High Reynolds number flows produce very thin boundary layers. If wall resolution is used in Large Eddy Simulation, the aspect ratio may be on the order of $10^6$. Many methods become unstable in this ...
- 25.7k
34
votes
4
answers
2k
views
Why is local conservation important when solving PDEs?
Engineers often insist on using locally conservative methods such as finite volume, conservative finite difference, or discontinuous Galerkin methods for solving PDEs.
What can go wrong when using a ...
- 25.7k
15
votes
3
answers
947
views
What is a scalable preconditioner for high-frequency Helmholtz?
Standard multigrid and domain decomposition methods do not work, but I have large 3D problems and direct solvers are not an option. What methods should I try?
How are my choices affected by the ...
- 25.7k
7
votes
3
answers
582
views
Does there exist an arbitrary-precision convex optimization solver?
I have a relatively simple convex optimization problem that involves less than 100 variables but contains a terribly ill-conditioned matrix. I have tried CVX and CPLEX; even though both can typically ...
- 16.6k
18
votes
1
answer
1k
views
When should implicit methods be used in the integration of hyperbolic PDEs?
Numerical methods for solving PDEs (or ODEs) fall into two broad categories: explicit and implicit methods. Implicit methods allow larger stable timesteps but require more work per step. For ...
- 16.6k
25
votes
4
answers
2k
views
When is a high order method useful for computational fluid dynamics simulations?
Many numerical approaches to CFD can be extended to arbitrarily high order (for instance, discontinuous Galerkin methods, WENO methods, spectral differencing, etc.). How should I choose an ...
- 16.6k
17
votes
2
answers
963
views
How can I choose a good Riemann solver when numerically solving a system of hyperbolic PDEs?
Many numerical methods for hyperbolic PDEs are based on the use of Riemann solvers. Such solvers are essential for accurately capturing shock waves. There are a range of such solvers available for ...
- 16.6k
16
votes
1
answer
5k
views
How can I estimate the condition number of a large sparse matrix using PETSc?
I have a PETSc Mat and would like to estimate its condition number.
- 25.7k
10
votes
1
answer
210
views
Polynomials that are orthogonal over curves in the complex plane
Various important sets of polynomials (Legendre, Chebyshev, etc.) are orthogonal over some real interval with some weighting. Are there known families of polynomials that are orthogonal over other ...
- 16.6k
23
votes
1
answer
15k
views
Why is Newton's method not converging?
I am using PETSc's nonlinear solver package SNES to solve a system of nonlinear equations obtained by discretizing a partial differential equation. How can I determine why the solver is not converging ...
- 25.7k
18
votes
2
answers
332
views
Is there an efficient algorithm for matrix-valued continued fractions?
Suppose I have a matrix equation recursively defined as
A[n] = inverse([1 - b[n]A[n+1]]) * a[n]
Then the equation for A[1] looks similar to a continued fraction,...
- 487
5
votes
1
answer
112
views
What are some good ICA packages for physiological data, like MEG?
EEGLab doesn't work well due to the data being from a Neuromag MEG. Any thoughts for alternatives?
- 231