Computational Science Stack Exchange
Computational Science Stack Exchange

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1500 questions
17
votes
2 answers

Which version of Fortran should I learn?

I'm a Mechanical Engineering student interested in the field of aerospace engineering where, I'm told, Fortran is still commonly used. Which version of Fortran should I invest my time to learn?
user26358
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17
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5 answers

Parallel optimization algorithms for a problem with very expensive objective function

I am optimizing a function of 10-20 variables. The bad news is that each function evaluation is expensive, approx 30 min of serial computation. The good news is that I have a cluster with a few dozen computational nodes at my disposal. Thus the…
Michael
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17
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4 answers

Profiling CFD code with Callgrind

I'm using Valgrind + Callgrind to profile a solver I have written. As the Valgrind user manual states, I've compiled my code with the debugging options for the compiler: "Without debugging info, the best Valgrind tools will be able to do is guess…
tmaric
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17
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8 answers

Is there any open-source or easy-to-access software that can simplify algebraic expressions like $x^{2}+2x+3, x=\sqrt{2}t-1$?

I always calculate things by hand, but now my comrades are getting nasty and making a lot of repetitive exercises involving just plugging things in like the expression above. I am particularly interested in open-source software such as Python or R…
user664
17
votes
2 answers

Options for solving ODE systems on GPUs?

I would like to farm out solving systems of ODEs onto GPUs, in a 'trivially parallelisable' setting. For example, doing a sensitivity analysis with 512 different parameter sets. Ideally I want to do ODE solving with a smart adaptive timestep solver…
mirams
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17
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1 answer

When is Newton-Krylov not an appropriate solver?

Recently I have been comparing different non-linear solvers from scipy and was particularly impressed with the Newton-Krylov example in the Scipy Cookbook in which they solve a second order differential equation equation with non-linear reaction…
boyfarrell
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17
votes
4 answers

What are some applications which require interval arithmetic?

I have a very basic notion about interval arithmetic (IA), but it seems to be a very interesting branch of computational science both theoretically and practically. It is clear that the obvious applications are verified computing and ill-posed…
faleichik
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16
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1 answer

Complexity of MD simulations

I'm new to molecular dynamics (MD) simulations. What is the complexity of a molecular dynamics simulation in terms of simulation time? In other words, if I want increase the simulated time from 10 nanoseconds to 20 nanoseconds, what can I expect in…
Daniel Standage
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16
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4 answers

How do I calculate the numerical difference between two fields stored in two different VTK files with the same structure?

Suppose I have two VTK files, both in structured grid format. The structured grids are the same (they have the same list of points, in the same order), and there is a field, call it "Phi", in each VTK file. I want to create a third VTK file, again…
Geoff Oxberry
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16
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2 answers

Is it possible to solve nonlinear PDEs without using Newton-Raphson iteration?

I am trying to understand some results and would appreciate some general comments on tackling nonlinear problems. Fisher's equation (a nonlinear reaction-diffusion PDE), $$ u_t = du_{xx} + \beta u (1 - u) = F(u) $$ in discretised…
boyfarrell
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16
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5 answers

Minimizing the Sum of Absolute Deviation ($ {L}_{1} $ Distance)

I have a data set $x_{1}, x_{2}, \ldots, x_{k}$ and want to find the parameter $m$ such that it minimizes the sum $$\sum_{i=1}^{k}\big|m-x_i\big|.$$ that is $$\min_{m}\sum_{i=1}^{k}\big|m-x_i\big|.$$
mayenew
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16
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2 answers

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 to run the original program. This factor of five…
MRocklin
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16
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2 answers

What are the advantages/disadvantages of interior point methods over simplex method for linear optimization?

As I understand it, since a solution to a linear program always occurs at a vertex of its polyhedral feasible set (if a solution exists and the optimal objective function value is bounded from below, assuming a minimization problem), how can a…
Paul
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16
votes
7 answers

Scripted Mesh Generation Software

I'm looking for a mesh generation software that is free and open source, provides a sane scripting interface for domain specification, works for complex geometries, can generate 2D and 3D meshes, What options do I have?
Nico Schlömer
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1 answer

Pressure as a Lagrange Multiplier

In the incompressible Navier-Stokes equations, \begin{align*} \rho\left(\mathbf{u}_t + (\mathbf{u} \cdot \nabla)\mathbf{u}\right) &= - \nabla p + \mu\Delta\mathbf{u} + \mathbf{f}\\ \nabla\cdot\mathbf{u} &= 0 \end{align*} the pressure term is often…
Ben
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