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29 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 ...
Chris Rackauckas's user avatar
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 ...
lr1985's user avatar
  • 677
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-...
Richard's user avatar
  • 3,971
10 votes
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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) ...
Bill Greene's user avatar
  • 6,144
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 ...
EMP's user avatar
  • 2,089
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 ...
Brian Borchers's user avatar
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 ...
MPIchael's user avatar
  • 2,985
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 ...
Anton Menshov's user avatar
  • 8,672
6 votes
Accepted

MD Simulation: Reference for the Neighbor's List Method

I'd recommend "The Art of Molecular Dynamics Simulation" by D. C. Rapaport. The code samples are written in C. I'm not a huge fan of the programming style of the book, but at least it's not ...
lr1985's user avatar
  • 677
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 ...
Wolfgang Bangerth's user avatar
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'...
Chris Rackauckas's user avatar
6 votes

Starting configuration for Molecular Dynamics

Usually one needs to employ periodic boundary conditions (at least in the horizontal directions). Any atoms which fly outside of the box will be mapped to the opposite side. This also has to be ...
MPIchael's user avatar
  • 2,985
5 votes
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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 ...
Juan M. Bello-Rivas's user avatar
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 ...
lr1985's user avatar
  • 677
5 votes
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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 ...
Christian Clason's user avatar
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
EssentialAnonymity's user avatar
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 ...
Anton Menshov's user avatar
  • 8,672
5 votes
Accepted

N-body problem with differents solvers (RK2, RK4, Euler symplectic, Stormer-Verlet) : planets drift to infinity

All-over this is a nicely structured code. The main problems are related to the Runge-Kutta solvers, where the first-order system was not uniformly applied to the computation. What is obviously wrong ...
Lutz Lehmann's user avatar
  • 6,109
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.
David Ketcheson's user avatar
5 votes

What evidence exists to suggest that computational science produces more information than studying real phenomena as they are?

This is the nature of science, at least the more physical ones. You have a hypothesis about some object. You devise some experiment that would highlight this hypothesis the clearest, with the least ...
Lutz Lehmann's user avatar
  • 6,109
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 ...
deemaregee's user avatar
4 votes

What are the things I should keep in mind before doing an analysis of my gromacs simulation?

I think that this question is too generic for a complete answer, as the latter would depend entirely on what you are simulating and what observables you are interested in. The only things that come to ...
lr1985's user avatar
  • 677
4 votes

Is saying "math modeling and numerical simulation" wordy and redundant?

The obvious answer is "it depends". However, it's not helpful. I would certainly separate the work in mathematical modeling and actual numerical simulation. Sometimes it might be a bit tough to draw ...
Anton Menshov's user avatar
  • 8,672
4 votes
Accepted

Symplectic linear multistep method?

Yes, but you have to mean symplectic on a higher-dimensional phase space than your original problem that includes previous steps too. As I understand there are also some subtle stability issues too. ...
Daniel Shapero's user avatar
4 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 ...
Zoltan Csati's user avatar
4 votes

Using velocity verlet algorithm for nbody simulation results in planet leaving orbit

There are two sources for such an error, if the exact solution is known to stay bounded. Verlet becomes catastrophically incorrect in singular situations, that is, if two objects become close in a N-...
Lutz Lehmann's user avatar
  • 6,109
4 votes
Accepted

How to correct for collision in $N$-dimensional bounded motion of a particle?

The correction you are looking for is a projection $$ \newcommand{\norm}[1]{\left\lVert#1\right\rVert} \DeclareMathOperator*{\argmin}{arg\,min} P_{C} : \mathbb{R}^{d} \rightarrow C, \, \, \pmb{x} \...
Marko Lalovic's user avatar
4 votes

Projection (or fractional-step) methods Vs coupled method for incompressible Navier-Stokes

Let us consider the system of equations describing viscous incompressible flow in a unit cube $0\le x\le 1, 0\le y \le 1, 0 \le z \le 1$, and in time interval $0\le t \le 1$, we have \begin{equation}\...
Alex Trounev's user avatar
4 votes

Deformation matrix, Math hack for stability on large simulation steps?

The part about your 'stability' requirements seems impossible to answer without more detail. But if you just want to ensure that $\det F_{n+1} = 1$ at each step, then a quick fix is scaling your ...
Federico Poloni's user avatar
3 votes
Accepted

Finite-volume method applied to a particular advection equation

Your proposed discretisation appears to be consistent, but wouldn't normally be interpreted as a finite volume discretisation. Indeed, it looks a lot more like a finite difference method with a ...
origimbo's user avatar
  • 2,249

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