27 votes
Accepted

Conserving Energy in Physics Simulation with imperfect Numerical Solver

There are a few ways to conserve energy during ODE integration. Method 1: Symplectic Integration The cheapest way that is to use a symplectic integrator. A symplectic integrator solves the ODE on a ...
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13 votes
Accepted

What are the differences between CFD simulations and realistic ocean/atmosphere model simulations?

Atmosphere and ocean have highly-stratified flows in which the Coriolis force is a major source of dynamics. Maintaining geostrophic balance is extremely important and many numerical schemes are ...
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  • 25.3k
12 votes

What guidelines should I follow for simulation software projects?

I maintain (and am the main coder of) a simulation software that has been developed for ~8 years and is used by few hundreds people. It all started as a side project during my PhD, and it clearly ...
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  • 657
12 votes
Accepted

What guidelines should I follow for simulation software projects?

"developers lack the skills". Maybe. I think it's much more likely that the developers lack the incentives. Making solid code is difficult and expensive and, in academia, comes with minimal-to-...
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  • 3,131
11 votes
Accepted

Removing non-determinism from molecular dynamics code

Both the standard cluster and custom supercomputer (Anton) versions of molecular dynamics at D. E. Shaw Research are both deterministic and parallel invariant. That is, a test run on a single core ...
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10 votes
Accepted

How do I simulate an open end?

The problem you describe, how to prescribe non-reflecting or absorbing boundary conditions when solving partial differential equations (PDE) has been extensively studied. For complex (e.g. nonlinear) ...
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  • 5,744
10 votes

Why not use the convolution theorem for explicit timestepping?

This is a linear PDE, and so while this technique works here, it would not work for any nonlinear PDE. Often times when people are solving these equations it is to get experience with common solution ...
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  • 1,902
9 votes

Methods for solving $x'=Ax+b$ for small, sparse, singular $A$

Any general-purpose ODE solver should be able to handle this linear coupled system of ODE very easily, for example: scipy.integrate.ode CVODE from the Sundials solver suite; it appears to have Python ...
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  • 11.4k
8 votes

Optimization techniques for expensive multi-variable functions

One commonly used approach is the "Response Surface Method" in which you sample the feasible region, running the full simulation at the sample points, then use regression techniques to fit a surrogate ...
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8 votes
Accepted

What kind of a researcher am I?

Up until a couple of decades ago, science was based on two large pillars. Those were theory and actual physical experiments. It is an exciting time to see a third pillar arise with numerical ...
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  • 2,111
7 votes

Maximizing unknown noisy function

There are several Bayesian optimization techniques you could try. Easiest are based on Gaussian process: Harold J. Kushner. A new method of locating the maximum of an arbitrary multipeak curve in the ...
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  • 870
7 votes

Physics Simulation in C++

I think you are missing a very important and crucial step that lies exactly between the physics and simulation: the mathematical model. In order to model any physics, one has to formulate the ...
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  • 8,452
6 votes
Accepted

Which processor should I consider buying for a desktop built for scientific computing?

Disclaimer: most of this is purely opinion. In the $600 range for a whole computer, I'm not sure that processor matters all that much, as long as the architecture is x86. If you want to run ...
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6 votes
Accepted

Should a colorbar have constant values throughout a simulation?

The selection of colormap should be based on your dataset and audience, e.g., you do not want to use a colormap that have some cultural background for a group of people. Also, if your images are going ...
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  • 8,091
6 votes
Accepted

Solve implicit ODE numerically in orbit simulation

(1) Using the previous value of $\ddot{r}_j$ is like adding an error term to the r.h.s. of your equation of magnitude $\mathit{const}\times(\ddot{r}_j(t+\delta t) - \ddot{r}_j(t))$, meaning your ...
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  • 11.4k
6 votes

Good desktop PC for molecular dynamics simulations

There is a recently published paper addressing the question of what is the optimal combination of hardware on which to run GROMACS: Kutzner, C., Páll, S., Fechner, M., Esztermann, A., de Groot, B. L.,...
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6 votes

How to simulate over 1 billion particles?

A first step, if you "have never been up in computing", is to read the literature and see what others are doing and have done. The second step is that you will likely learn that what you want to do ...
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6 votes
Accepted

Artificial Intelligence, Modeling and Simulation

So bottom line is I don't see any comprehensive work on the use of AI in M&S as a whole, let's say having models that can learn how to produce new improved models using the existing models. There'...
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5 votes

Can other running processes harm the performance of my simulation?

If you just want the computational results and aren't running benchmarking tests then this isn't a serious problem. If you're trying to benchmark the performance of the code and get repeatable run ...
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5 votes
Accepted

Mean-squared displacement in Monte Carlo studies

This is possible (see [1]) but uncommon, as it requires Monte Carlo moves that alter the current conformations by a very small perturbation. In that setting of "small" Metropolis MC moves, it is ...
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5 votes

Mean-squared displacement in Monte Carlo studies

It is in some cases possible to map the dynamics obtained in MC simulations to other (more realistic) dynamics, especially for the case of dense colloidal suspensions. The following two papers talk ...
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  • 657
5 votes
Accepted

Simulation-based Optimization vs PDE-constrained Optimization

Both approaches apply to the same problem (numerical minimization of functionals which involve the solution of a PDE, although both extend to a larger class of problems). The difficulty is that for ...
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5 votes

What scientific problems can be simulated that couldn’t be simulated 10 years ago?

This report on exascale computing from the DOE might be useful: https://science.energy.gov/~/media/ascr/ascac/pdf/reports/Exascale_subcommittee_report.pdf
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5 votes
Accepted

Can one publish a new model and simulation without physical experiments?

The short answer is: it depends. Some journals have a requirement or a guideline to have experimental results that corroborate the numerical simulations. For example, IEEE Transactions on Microwave ...
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  • 8,452
5 votes

What's the relationship of machine learning and mechanical simulation?

Your question is a bit broad, I think. Lacking concreteness, I would give a high-level overview. Terms that you can search for are in italics. Machine learning is a huge field, that includes many ...
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5 votes

Why not use the convolution theorem for explicit timestepping?

For the linear, constant coefficient advection equation on a torus, one can simply use the exact solution. So there are no "popular" numerical methods for this problem.
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4 votes

What scale problem can be simulated on an PC using Smooth Particle Hydrodynamics?

This depends a great deal on the type of CFD problem and the methods being used. But as a rough start using a lightweight geometric multigrid for the pressure solve and explicit time stepping for ...
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  • 25.3k
4 votes
Accepted

What scale problem can be simulated on an PC using Smooth Particle Hydrodynamics?

All models are wrong, but some models are useful - George E. P. Box Let's establish one important fact: Simulation Models are not exact replicas of reality. We use models to understand only a small ...
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  • 11.8k
4 votes
Accepted

Sorting eigenvalues by the dominant contribution

You'd like to sort eigenvalues/eigenvectors in a way that is continuous as you move through momentum. This highly constrains the sorting - for most k-points, you must sort the eigenvalues to be a ...
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4 votes

Which processor should I consider buying for a desktop built for scientific computing?

(Turning a previous comment into an answer, because I want to say a bit more.) One thing you should keep in mind is that your time is significantly more valuable than any hardware (at least in the ...
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