All Questions
2,721
questions with no upvoted or accepted answers
14
votes
0
answers
532
views
Sequential approach to solving coupled PDEs
I'm dealing with a coupled system of three transient, non-linear convection-diffusion equations. Let's just say to simplify the problem that they take the following form:
$$
-\nabla\cdot(D_{1}(u_{2},...
- 937
14
votes
0
answers
452
views
Operator Splitting methods for DAEs
After doing some research, I've found that most of the literature on operator splitting methods (e.g. Strang Splitting, Fractional Step, etc.) are specifically designed for a standard problem type of ...
- 12k
13
votes
0
answers
729
views
Fast Eigenvalue and SVD Solver for Structured Matrices
I am looking for a fast Eigenvalue and SVD solver for small dense structured matrices (Hankel and Toeplitz). I have searched for efficient implementations in libraries like MKL but I am not able to ...
- 241
12
votes
0
answers
4k
views
Optimized open source BLAS / LAPACK package
I was wondering what is a more optimized open source BLAS/LAPACK package with respect to modern multi-core processors (Haswell and beyond). Is there any distribution that can attain performance close ...
- 121
12
votes
0
answers
139
views
Are there any standardized file formats for point group character tables?
Character tables are an important tool for symmetry analysis in many computational chemistry software packages. Are there any standardized file formats for point group character tables?
This may seem ...
- 221
11
votes
0
answers
348
views
Numerical integration using interval arithmetic, nowadays
Is there now a package for rigorous numerical integration that uses interval arithmetic and has access to a well-developed library of special functions?
By "well-developed", I mean something that, at ...
- 279
10
votes
0
answers
875
views
Implementing std::nextafter: Should denormals-are-zero mode affect it? If so, how?
This might be the wrong stackexchange site for this question. math.SE, cs.SE, programmers.SE, and of course stackoverflow are all possibilities. I'm hoping to reach an audience that might actually ...
- 310
10
votes
0
answers
240
views
Time advance in Adaptive Mesh Refinement method
I am working on solving complex system of 2D PDEs governing the behaviour of plasma in a gas lamp during discharge. Recent tests have shown that because of steep gradients in temperature field and ...
- 131
9
votes
0
answers
168
views
What's the most computationally efficient implementation of Kalman Filter
I know there are many formulations of the Kalman Filter. A few I can name are:
Classical Covariance Form
Informational Filter Form
Square-Root Form or Factor Form
But somehow it's hard for me to ...
- 425
9
votes
0
answers
234
views
Imbalance of variables in Mixing Newton's method and Linear solver for a Non-linear system
Problem
Solving a non-linear system of equations.
The number of variables is the same as the number of equations.
When I fix a set of variables (say $\vec{y}$) and keep another set free (say $\vec{...
- 163
9
votes
0
answers
142
views
Review of modern homotopy methods and practical techniques
I'm hoping someone can recommend recent literature concerning homotopy methods for solving systems of nonlinear equations. Already by the time of Layne Watson's 1986 paper there were a lot of methods,...
- 297
9
votes
0
answers
537
views
Updating matrix diagonal with Woodbury matrix identity and maintaining numerical accuracy
I have a dense matrix A and its corresponding inverse $A^{-1}$. The Woodbury matrix identity states:
$$ (A + UCV)^{-1} = A^{-1} - A^{-1}U(C^{-1} + VA^{-1}U)^{-1}VA^{-1} $$
I wish to perform small ...
- 1,320
9
votes
0
answers
438
views
Simple turbulence model appropriate for buoyancy-driven cavity like problem
Which turbulence model is suitable for resolving incompressible buoyancy-driven flow of a fluid within an cylindrical ampoule?
I prefer turbulence model which is sufficiently simple so that fully ...
- 927
9
votes
0
answers
451
views
What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?
I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in ...
9
votes
0
answers
167
views
Fast algorithms to solve Markov Decision Processes
In my master thesis I used an Algorithm called Approximative Dynamic Programming [1] to solve equations of the form
$$
\max_{\pi}\mathbb{E}^{\pi}\left\{\sum_{t=0}^{T}\gamma^tC_t^{\pi}(S_t,A_t^{\pi}(...
- 191