Unanswered Questions
2,597 questions with no upvoted or accepted answers
14
votes
0
answers
504
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},...
- 51
14
votes
0
answers
439
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 ...
- 16.4k
13
votes
0
answers
707
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 ...
- 8,602
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 ...
- 442
12
votes
0
answers
137
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 ...
- 365
10
votes
0
answers
333
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 ...
- 8,602
10
votes
0
answers
849
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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
229
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 ...
- 8,370
9
votes
0
answers
229
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{...
CommunityBot
- 1
9
votes
0
answers
138
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
293
views
Wanted: sequences of linear systems for recycling Krylov solver analysis
In the solution of sequences of linear systems
$$A_ix_i=b_i\quad\text{for}\quad i=1,2,\dots$$
with Krylov subspace methods, data can be recycled from already solved linear systems in order to speed up ...
- 231
9
votes
0
answers
517
views
Updating matrix diagonal with Woodbury matrix identity and maintaining numerical accuracy
I have a dense matrix A and its corresponding inverse $A^{-1}$. The Woodbury matrix identity states:
$$ (A + UCV)^{-1} = A^{-1} - A^{-1}U(C^{-1} + VA^{-1}U)^{-1}VA^{-1} $$
I wish to perform small ...
- 12.2k
9
votes
0
answers
430
views
Simple turbulence model appropriate for buoyancy-driven cavity like problem
Which turbulence model is suitable for resolving incompressible buoyancy-driven flow of a fluid within an cylindrical ampoule?
I prefer turbulence model which is sufficiently simple so that fully ...
- 927
9
votes
0
answers
446
views
What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?
I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in ...
- 6,931
9
votes
0
answers
163
views
Fast algorithms to solve Markov Decision Processes
In my master thesis I used an Algorithm called Approximative Dynamic Programming [1] to solve equations of the form
$$
\max_{\pi}\mathbb{E}^{\pi}\left\{\sum_{t=0}^{T}\gamma^tC_t^{\pi}(S_t,A_t^{\pi}(...
- 191