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Unanswered Questions

1,505 questions with no upvoted or accepted answers
12
votes
1answer
1k views

How to Run MPI-3.0 in shared memory mode like OpenMP

I am parallelizing code to numerically solve a 5 Dimensional population balance model. Currently I have a very good MPICH2 parallelized code in FORTRAN but as we increase parameter values the arrays ...
12
votes
0answers
2k views

Comparing Jacobi and Gauss-Seidel methods for nonlinear iterations

It is well known that for certain linear systems Jacobi and Gauss-Seidel iterative methods have the same convergence behavior, e.g. Stein-Rosenberg Theorem. I am wondering if similar results exist for ...
11
votes
1answer
238 views

For noisy or fine-structured data, are there better quadratures than the midpoint rule?

Only the first two sections of this long question are essential. The others are just for illustration. Background Advanced quadratures such as higher-degree composite Newton–Cotes, Gauß–Legendre, ...
11
votes
1answer
301 views

DG local equation, how to interpret mean-averaged test function

In the paper http://www.sciencedirect.com/science/article/pii/S0045782509003521, an HDG element-local equation is described on page 584 equation (4), with one of the equations taking the following ...
11
votes
0answers
2k views

Alternatives to hdf5

I've been using HDF5 for years, but as the size of the dataset grows I'm starting to experience the same problems listed here http://cyrille.rossant.net/moving-away-hdf5/ Can you point me to a ...
11
votes
0answers
296 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},...
11
votes
0answers
306 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 ...
10
votes
0answers
413 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 ...
9
votes
0answers
103 views

Are there shortcuts for numerically approximating systems of ordinary differential equations when autonomous?

Existing algorithms for solving ODEs handle functions $\frac{dy}{dt} = f(y, t)$, where $y \in \mathbb R^n$. But in many physical systems, the differential equation is autonomous, so $\frac{dy}{dt} = f(...
9
votes
0answers
131 views

Inverse problem in linear ODE

I have a linear ordinary differential equation (ODE) with a system matrix with constant coefficients: $$\dot{y}(t) = \mathcal{A}\; y(t), \quad y(0) = y_0$$ with $y(t) \in \mathbb{R}^{n \times 1}$ and $...
9
votes
0answers
108 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 ...
8
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0answers
92 views

How to find a good preconditioner to the system $(A^T A + \lambda I) x = A^T b$?

The system in the title has a damper factor $\lambda > 0$ and the matrix $A$ is sparse and rectangular, with a structure I can exploit to solve matrix vector products very fast. My current solver, ...
8
votes
1answer
63 views

Benchmark problems for eigenvalue reordering algorithms sought

Every real matrix $A$ can be reduce to real Schur form $T = U^T A U$ using an orthogonal similiary transform $U$. Here the matrix $T$ is quasi-triangular form with 1 by 1 or 2 by 2 blocks on the main ...
8
votes
0answers
387 views

Numerical implementation of the Dirichlet-to-Neumann map

I am solving the Dirichlet problem $$ \begin{cases} \Delta u = 0, \\ u|_{\partial D} = f, \end{cases} $$ in a $2d$ domain $D$ using the finite element method. What I want to get is the ...
8
votes
1answer
478 views

Time discretization of the variational formulation of the Navier-Stokes equation

I've asked this question on mathoverflow too. Let $T>0$ $I:=(0,T]$ $d\in\mathbb N$ $\Lambda\subseteq\mathbb R^d$ be nonempty and open, $$\mathcal V:=\left\{\phi\in C_c^\infty(\Lambda,\mathbb R^d):...

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