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5
votes
1answer
308 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 ...
3
votes
3answers
449 views

What are the current obstacles to reaching exascale computing?

I have heard that one of the current goals in scientific computing is to surpass the exascale level by 2018 or so... After having passed the petascale a few years ago, one would think that the ...
10
votes
3answers
767 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
1k 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
1answer
837 views

Replacing Mathematica's QuasiMonteCarlo integration in C++

I have a Mathematica program which performs some integrals in 3 or 4 dimensions using the QuasiMonteCarlo method. The problem is, it takes an annoyingly long time ...
19
votes
6answers
1k views

What is the best way to do reproducible research if you need proprietary libraries?

Reproducible research in computation aims to make the code needed to generate the results in a computational paper available to other researchers so that they can run this code to reproduce the ...
7
votes
4answers
580 views

When analyzing a parallel algorithm, how do you take communication costs into account?

My question is related in spirit to "Is algorithmic analysis by flop counting obsolete?". Counting the number of computational operations in an algorithm is commonly used as a first-order model to ...
6
votes
2answers
2k views

Which libraries have good implementations of Basis splines?

I'm looking to use the finite element method with B-splines as my function basis. Which C/C++ libraries have good B-spline support? Specifically, I'm looking for an implementation of a stable ...
3
votes
0answers
108 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 ...
10
votes
3answers
383 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?...
12
votes
4answers
865 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 ...
4
votes
3answers
287 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 ...
11
votes
6answers
5k views

Finite differences on domains with irregular boundaries

Can anybody help me to find the books on numerical solutions(finite difference and Crank–Nicolson methods) of Poisson and diffusion equations including examples on irregular geometry, such as a domain ...
15
votes
1answer
4k 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 ...
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 ...
40
votes
8answers
1k views

How to link code to publications

Scholarly papers in scientific computing (and many other fields, nowadays) typically involve some amount of code or even whole software packages that were written specifically for that paper or were ...
32
votes
11answers
2k views

Venues for publishing papers that emphasize software

Software is a fundamental part of computational science, and is increasingly recognized as an essential part of the scientific record. Given the value of using existing and well-tested code, it seems ...
6
votes
2answers
315 views

What guidelines should I use when choosing a scalable linear solver?

There are many different linear solvers, some which work best for diagonally dominant matrices, some for symmetric, some for positive definite ones, some for banded matrices, etc... There are direct ...
3
votes
1answer
519 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 ...
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 ...
7
votes
4answers
247 views

Testing for stability of a simulated dynamical system

Background and question I often work with simulations of dynamical systems and I usually track a single parameter $x$, such as the number of agents (for agents based models) or the error rate (for ...
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 ...
9
votes
3answers
823 views

Iterative methods for indefinite systems without block structure

Indefinite systems of matrices appear for example in the discretization of saddle point problems by mixed finite elements. The system matrix can then be put in the form $$\begin{pmatrix} A & B^t \...
-2
votes
1answer
290 views

Multi-objective optimization problem - Euclidean space

I am looking for some clues for an optimization problem. My problem consists on arriving to a image by optimizing multiple layers with the pixel position probability. This is an overview of the ...
8
votes
2answers
1k views

Kolmogorov–Smirnov test for multivariate data

I have a set of files consisting of randomly selected points from a dataset, each file belonging to a particular class. Each row in these files contains the coordinates in n-space of the point. I'd ...
11
votes
5answers
696 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 ...
6
votes
3answers
1k views

Krylov Subspace Methods for Dense Systems

I am currently researching on the viability of using KS methods for solving large dense systems. What I wish to prove (or disprove) is that methods like CG, BiCG and QMR are as good (if not better) ...
11
votes
1answer
280 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....
54
votes
5answers
27k views

How do I take the FFT of unevenly spaced data?

The Fast Fourier Transform algorithm computes a Fourier decomposition under the assumption that its input points are equally spaced in the time domain, $t_k = kT$. What if they're not? Is there ...
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 ...
2
votes
3answers
912 views

List of data munging libraries

I am trying to put together a complete list of all of the tools that computational scientists have found useful when trying to munge data, i.e. take data in one format, extract the useful bits, and ...
10
votes
1answer
215 views

Quadrature rules, methodologies, and references

There is at least one quite comprehensive encyclopaedia of quadrature rules that doesn't seem to have been updated in quite a while and has restricted access. This source refers to several classical ...
6
votes
3answers
634 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 (...
15
votes
2answers
4k views

Stopping criteria for iterative linear solvers applied to nearly singular systems

Consider $Ax=b$ with $A$ nearly singular which means there is an eigenvalue $\lambda_0$ of $A$ that is very small. The usual stop criterion of an iterative method is based on the residual $r_n:=b-Ax_n$...
6
votes
0answers
407 views

How to do FEM in sector elements?

Suppose we have an element in the polar coordinate as $0\leq r\leq 1$, $0\leq\theta\leq \alpha$. What are the correct basis functions in this element? For this kind of mesh, there are a lot of ...
6
votes
3answers
1k views

3d Ising model simulation - what critical exponents should I be looking for and how do I find them?

For the final project in my computational physics class, I've built and will be presenting results for monte carlo simulations of phase transition in the three dimensional ising model. Using the ...
3
votes
1answer
389 views

Testing a simple polygon for monotonicity in linear time question

I'm looking for the algorithm of Preparata and Supowit for testing a simple polygon for monotonicity in linear time. I've found it referenced in many textbooks but I can't find the algorithm itself. ...
2
votes
2answers
454 views

Is there a Moore's law for floating-point precision, and what would it imply?

Moore's law states that the number of transistors on an integrated circuit grow exponentially, roughly doubling at a period of 20 months. This affects the amount of memory available and the speed of ...
10
votes
2answers
1k views

Are 8 Gauss points required for second order hexahedral finite elements?

Is it possible to get second order accuracy for hexahedral finite elements with fewer than 8 Gauss points without introducing unphysical modes? A single central Gauss point introduces an unphysical ...
16
votes
5answers
5k 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 ...
5
votes
3answers
976 views

Implementing Euler's method for initial value ODEs

In my physics class, I had to calculate the trajectory of a projectile that was fired (very fast) with $v_0$ in an angle off a planet (radius $R$, mass $M$) from the surface. The projectile would ...
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 ...
10
votes
2answers
339 views

Where can I find a good reference for the stability properties of several methods of solving parabolic PDEs?

Right now I have a code that uses the Crank-Nicholson algorithm, but I think that I would like to move to a higher-order algorithm for timestepping. I know that the Crank-Nicholson algorithm is stable ...
21
votes
8answers
3k views

Software package for constrained optimization?

I am looking to solve a constrained optimization problem where I know the bounds on some of the variables (specifically a boxed constraint). $$ \arg \min_u f(u,x) $$ subject to $$ c(u,x) = 0 $$ $$ ...
15
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.
8
votes
7answers
6k views

Limitations of Density Functional Theory as a computational method?

This question arises from the need I have to prepare a lesson on the limitations of Density Functional Theory as a computational approach. I would like to know not only the limitations, but also ...
18
votes
2answers
5k views

Unstructured quad mesh-generation?

What is the best (scalability and efficiency) algorithms for generating unstructured quad meshes in 2D? Where can I find a good unstructured quad mesh-generator? (open-source preferred)
25
votes
5answers
639 views

Is there software that can autogenerate numerically-accurate floating point C routines from symbolic formulae?

Given a real function of real variables, is there software available that can automatically generate numerically-accurate code to calculate the function over all inputs on a machine equipped with IEEE ...
4
votes
2answers
193 views

Looking for a mathematical proof of stability in floating point arithmetic of CG - any reference?

I am looking for a reference - paper, book, discussion, anything that has a mathematical proof for stability of the conjugate gradient method in floating point arithmetic. Something similar for ...

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