# All Questions

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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
823 views

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.
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 ...
5k views

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)