Questions tagged [computational-physics]

Computational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists.

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35
votes
6answers
5k views

Are there simple ways to numerically solve the time-dependent Schrödinger equation?

I would like to run some simple simulations of scattering of wavepackets off of simple potentials in one dimension. Are there simple ways to numerically solve the one-dimensional TDSE for a single ...
2
votes
0answers
165 views

Heisenberg Model python : Specific heat capacity for spin 2

I have the correct plot for specific heat capacity when I am using the formula which is $C_V$ = differentiation of entropy with respect to temperature. However, When I try to calculate $C_V$, by using ...
24
votes
5answers
6k views

What language should I use when teaching an undergraduate course in computer programming?

Going to teach students of undergraduate level a course titled Introduction to Computer Programming. I am confused a bit. In Computational Physics scientists use C/C++ or Python or Fortran,CUDA etc.......
6
votes
2answers
3k views

Calculating the log-determinant of a large sparse matrix

I need to calculate $\log(\det (\mathbf M_i))$ where the $\mathbf M_i$'s are large sparse matrices, which are real, symmetric and positive semi-definite. I hope to have between $10$ and $100$ of ...
3
votes
2answers
2k views

GPU-enabled Lattice Boltzmann solvers?

Is anybody aware of any GPU-enabled Lattice Boltzmann solvers (preferably on C++/OpenCL and open-source) that would be recommended? I have found Advanced Simulation Library, but it seems to be very ...
7
votes
2answers
2k views

Efficiently finding all (x,y,z) points within certain distance of point P

I am using Python, and I have a Pandas dataframe with hundreds of thousands, if not millions, of $(x,y,z)$ coordinates. I am looking to find an efficient method to index the original dataframe so that ...
3
votes
3answers
118 views

Numerically finding constants of motion

Given a set of ODE's $ \dot{z} = f(z) $ (or discrete time $ z_{t+1} = f(z_t) $), is there a way to numerically find constants of motion? For $ f(z_t) \approx M z_t $, diagonalizing the matrix $ M $ ...
3
votes
1answer
560 views

ground state from the Schroedinger equation with a central potential what happens to the origin

I have code that attempts to implement a solution to the Schrödinger equation where there is a central potential (more or less im thinking of hydrogen), in 1-D using the numerov method to construct ...
2
votes
3answers
511 views

Algorithm suggestion for PDE - example: heat equation

I want to solve the PDE equation numerically. For this, I started my study with something simple; heat equation $$ \frac{\partial u}{\partial t}=\frac{\partial^2 u}{\partial^2 x} $$ with the initial ...
1
vote
1answer
179 views

Runge-Kutta fourth order method. Integrating backwards

I am using a Runge-Kutta fourth order method to solve numerically the usual equation of motion of a background scalar field in curved spacetime with a quartic potential: $\phi^{''}=-3\left(1+\frac{H^{...
0
votes
1answer
2k views

Solving Time dependent Schrodinger equation using MATLAB ode45 [closed]

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ I try to implement solve the Schrodinger equation for time-dependent Hamiltonian in ODE ...
0
votes
1answer
125 views

Scattering of waves in a symmetrical potential (using python)

I'm looking at scattering of waves in a symmetrical potential as part of a research project. If a plane wave $e^{(ikr)}$ is incident on a spherically symmetric potential $V(r)$ the scattered wave is ...
5
votes
1answer
650 views

How is rigid bodies implemented in finite element codes

I am writing a finite element code for structural analysis, and I want to implement rigid bodies. How is this usually done? Say that I have a square mesh, with one half of the mesh being defined rigid ...
3
votes
1answer
643 views

How can I make velocity verlet algorithm more stable?

The answer to this question implies that reducing the time step would make it more stable. However I have tried reducing the time step but the system is still unstable(the total energy increases to a ...
2
votes
2answers
368 views

2d Euler manufactured solutions

Where can I find manufactured solutions for the 2d Euler equations, with the complete analytical terms, including the Jacobian of the source term ?
0
votes
1answer
253 views

Euler-Bernoulli beam element versus continuum beam element

I am using OpenSees to model a simply supported beam with a point load in the middle. The model is in consistent units. The beam is made up of bilinear quad elements. I have used 30 elements along the ...