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2
votes
1answer
1k views

How to measure the overall performance of a PETSc program using the -log_summary flag?

When I run a PETSc example in parallel with the flag "-log_summary", the first two tables of information look something like this: ...
6
votes
4answers
279 views

Approximately “solving” a linear system of equations without a feasible solution

A linear system of equations has the form $Ax = b$, where a matrix $A$ and a vector $b$ are given, and I wish to find a solution vector $x$. Suppose that the system $Ax = b$ has no feasible solution. ...
15
votes
1answer
464 views

How effective is the 'tendrils of knowledge' approach to Comp. Sci?

I was reading this on Math SE. The basic question is : Assume that someone wishes to study something advanced; one way to do this would be to start off from basics and build up. But the "bigger ...
3
votes
1answer
1k views

Problems running a PETSc example in parallel

After configuring and building PETSc, I have successfully been able to run several examples. In particular, I am working with this example. I have been able to run the program using the following ...
7
votes
4answers
2k views

precision vs matrix condition number

I have an application in which I am computing a quantity which is approximated by an average over $M$ points. In theory, the average converges to the correct quantity when $M$ is infinite. In practice,...
4
votes
1answer
544 views

What is the probabilistic model behind sudoku grids?

I'm talking about the vanilla sudoku game, with 9x9 grids equally split into 9 regions. I've tried a few approaches to estimate the probability that a specific number is in a specific location, but I ...
10
votes
1answer
6k views

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 ...
8
votes
1answer
2k views

How to efficiently determine the intersection of a vertical cutting plane with a mesh

I have a list of vertical cut planes, and I have a polygonal mesh ( it's a 2D+0.5D mesh, something like a 2D mesh with an extra dimension, $z$ attached to each point). One can assume that the mesh ...
8
votes
2answers
828 views

Which Sparse Matrix Solver Libraries can I run on Android?

The title says most of it. I'm looking for a lightweight and easy-to-use library that I can use for Android (NDK) projects. For dense stuff I like using Eigen but I haven't found many comprehensive (...
3
votes
1answer
97 views

What is the naming convention used in ScaLAPACK?

I see that there are many files in the ScaLAPACK library without any immediately obvious naming convention... I'm sure that if the first letter is "p", it means parallel. But I'm not sure how to make ...
2
votes
2answers
984 views

Lanczos solver implementations in MATLAB/C++ give different results

I have transferred my MATLAB Lanczos solver for symmetric eigenvalue solvers to C++ with the help of Intel MKL and MTL4 libraries. I have some wrapper templates for MKL routines. However during the ...
1
vote
0answers
81 views

Constraint solving over modular domains

I have a set of constraints over modular domains e.g. $\exists a \in A_i : x \equiv a \pmod{n_i}$ for all $i=0,\ldots,k$ The question is, does such an $x$ exist? I've been pointed to method of ...
2
votes
0answers
169 views

How to print out a network in peersim? [closed]

Peersim is a peer-to-peer network simulator. I'm simply trying to get the program to print out the network (an edge list is fine). Presumably this is possible, since there is an in-built ...
2
votes
1answer
112 views

Low performance on sge cluster

I'm having an issue with my project. When I run the code of Monte-Carlo simulation, on the local server (the machine in my office) it runs on a rate of roughly 100000 steps per 24 hours. When I run it ...
9
votes
1answer
1k views

Schrodinger equation with periodic boundary conditions

I have a couple of questions regarding the following: I am trying to solve the Schrodinger equation in 1D using the crank nicolson discretization followed by inverting the resulting tridiagonal ...
4
votes
1answer
2k views

How to run a PETSc example?

I just installed the PETSc library. This is what I did from the home directory ~ ...
8
votes
3answers
2k views

Solving a non-symmetric non-diagonally dominant sparse system the best way

I faintly recall from my early "numerics" lectures that iterative linear solvers for $Ax=b$ often require that when $A$ is decomposed as $$A=D + M$$ where D is a diagonal matrix and $M$ has zero ...
8
votes
1answer
205 views

Finding the fixed point of an operator

What numerical methods are available for finding the fixed point of an operator $A$ that is acting on functions $f : [a,b] \rightarrow [a,b]$? I am looking for the function $f$ for which $Af = f$. ...
5
votes
2answers
467 views

How to parallelize a banded direct solver?

I have a linear system whose matrix that is diagonally dominant, non-symmetric, but banded. Since the band-radius is 2 (producing only 5 variables per equation), a banded direct solver (gaussian ...
6
votes
1answer
316 views

What efficient algorithms are there to generate arbitrary dimensional meshes of simplices?

I know that delaunay triangulation can be extended into arbitrary dimensions by solving the convex hull problem in $(p+1)$ dimensions and projecting the lower hull into dimension $p$ to obtain a mesh ...
4
votes
3answers
294 views

How to fill a 2D set over a cartesian lattice with as few rectangles as possible?

Suppose I have a black and white image (composed of binary pixel values in a 2D cartesian array) that contains an irregular, nonconvex shape. Let's further suppose that the shape is one connected ...
15
votes
1answer
2k views

Can a Krylov subspace method be used as a smoother for multigrid?

As far as I am aware, multigrid solvers use iterative smoothers such as Jacobi, Gauss-Seidel, and SOR to dampen the error at various frequencies. Could a Krylov subspace method (like conjugate ...
11
votes
1answer
819 views

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 ...
6
votes
2answers
408 views

How can I reduce the communication bottleneck of a parallel explicit finite difference scheme?

Suppose i was trying to solve a parabolic PDE (heat equation) on a rectangular domain using an explicit finite difference scheme. I am storing my solution vector in a matrix form (because it closely ...
11
votes
1answer
2k views

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 ...
9
votes
7answers
931 views

Is there a standard rating system for scientific journal publications?

I have heard that some journals are rated more highly than others. Is this true? And if so, what are the criteria for judging the value of one peer reviewed journal over another? How do I find out ...
6
votes
3answers
640 views

Surface Mesh Library

I'm thinking a bit about the Front Tracking method used for simulation of Two phase flow with sharp interfaces. The literature tells me that the main issue is the surface mesh representation (...
2
votes
3answers
1k views

Computational Complexity of Image Segmentation algorithms

I have a question. I need to calculate the computational complexity of image segmentation algorithms. Can anyone please help me? For example, I have a screen-size picture with white background ...
4
votes
2answers
2k views

How do I compile a program that contains both MPI and OPENMP

I have a fortran 90 code that distributes blocks of computations (from a matrix) to multiple nodes in a cluster using MPI, but in each node, the for loops are executed in parallel using openmp. I ...
12
votes
3answers
2k views

finite volume method: unstructured mesh vs octree adaptation + cell cutting

I'm working with the OpenFOAM C++ Computational Continuum Mechanics library (it can deal with fluid-solid interaction, MHD flows...) which uses arbitrary unstructured meshes. This was driven by the ...
3
votes
2answers
1k views

Looking for a library or algorithms to perfom clipping 3D unstructured meshes by a set of surfaces

We have a 3D (volume) unstructured, possibly hybrid, degenerative irregular mesh data structure that we are capable of generating (mostly composed of hexahedra and general polyhedra, using a mix of ...
10
votes
3answers
778 views

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 ...
7
votes
2answers
2k views

Reference implementation of Nédélec-Elements

Does anybody know of an implementation of Nédélec elements that does not come along with a huge bulk of additional software? Is there a small library written in a language like Python, Matlab, or ...
12
votes
4answers
893 views

Scalability of Fast Fourier Transform (FFT)

To use the Fast Fourier Transform (FFT) on uniformly sampled data, e.g. in connection with PDE solvers, it is well known that the FFT is an $\mathcal{O}(n\log(n)$) algorithm. How well do the FFT scale ...
10
votes
3answers
395 views

Which is computed faster, $a^b$, $\log_a c$ or $\sqrt[b]{c}$?

Which is computed faster, $a^b$ or $\log_a c$ or $\sqrt[b]{c}$? $a$, $b$ and $c$ are positive reals with $b>1$. What kinds of algorithms will you use in the comparison? What are their complexities?...
3
votes
0answers
110 views

Up-/downdating methods for a series of normal equations

In an application I have to solve a series of positive definite linear systems of the form $A^TA x = A^Tb$ (i.e. normal equations). The next system is obtained from the previous one by adding and/or ...
15
votes
1answer
5k views

How to derive the Weak Formulation of a Partial Differential Equation for Finite Element Method?

I have taken a basic introduction to Finite Element Method, which did not emphasize a sophisticated understanding of a 'weak formulation'. I understand that with the galerkin method, we multiply both ...
11
votes
5answers
704 views

Is it preferable to concentrate on studying math or computation?

Concurrent to my research on Krylov Subspace Methods, I have the option of exploring mathematics behind HPC a step ahead or the theory of computation (hardware, OS, compilers etc.). Currently, I know ...
3
votes
1answer
524 views

Fitting a grid to an STM image

Suppose I have a scan from an STM image (very much like the things you see here). Suppose I have a simple square lattice with lattice parameter a. What I'd like to do is to numerically find the ...
12
votes
1answer
4k views

Efficient solution of mixed integer linear programs

Many important problems can be expressed as a mixed integer linear program. Unfortunately computing the optimal solution to this class of problems is NP-Complete. Luckily there are approximation ...
12
votes
2answers
687 views

When is automatic differentiation cheap?

Automatic differentiation allows us to numerically evaluate the derivative of a program on a particular input. There is a theorem that this computation can done at a cost less than five times the cost ...
8
votes
3answers
2k views

Scientific Programming on Mac using Objective-C/Cocoa for MATLAB Users

I want to get started on scientific programming on the Mac using Objective-C. I am very familiar with MATLAB which makes it easy to store complex-valued waveform data in vectors and generating plots. ...
18
votes
5answers
6k views

State of the Mac OS in Scientific Computing and HPC

Back towards the dawn of OS X, there seemed to be a great deal of hubbub, at least in the Mac world (I was nowhere near scientific computing at the time) about the Mac OS as a platform for scientific ...
16
votes
5answers
3k views

What is the advantage of multigrid over domain decomposition preconditioners, and vice versa?

This is mostly aimed for elliptic PDEs over convex domains, so that I can get a good overview of the two methods.
4
votes
0answers
134 views

Probabilistic algorithms for matrix approximation

Considering regular matrix approximation inequality || $A - QQ^TA $|| < e where we try to approximate matrix $A$ by a lower rank orthonormal matrix $Q$. I've read an article on probabilistic ...
8
votes
1answer
3k views

What is a good stop criterion when using an iterative method to find eigenvalues?

I read this answer, and realized I have been using the difference between sucessive iterates to define a stop criterion for an iterative method of finding eigenvalues/vectors. What are good stop ...
4
votes
2answers
1k views

Solution oscillations with a small timestep in backward Euler

I am using backward Euler in a FEM scheme for a convection-diffusion problem. On a given mesh, I can take arbitrarily large time steps, as expected. But if I decrease time step, at some point it will ...
11
votes
1answer
287 views

What are the possible numerical schemes for a diffusion equation with a nonlinear reaction term?

For some simple convex domain $\Omega$ in 2D, we have some $u(x)$ satisfying the following equation: $$ -\mathrm{div}(A\nabla u)+cu^n = f $$ with certain Dirichlet and/or Neumann boundary conditions....
5
votes
1answer
146 views

Looking for an understandable discussion of creating Maximum Entropy classifiers

Texts, articles, and papers on Maximum Entropy Classifiers tend to come in two varieties: the more popular "upper level", and the more technical. The popular variety are good at explaining the ...
27
votes
2answers
11k views

Why is my iterative linear solver not converging?

What can go wrong when using preconditoned Krylov methods from KSP (PETSc's linear solver package) to solve a sparse linear system such as those obtained by discretizing and linearizing partial ...

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