11 votes
Accepted

Visualising Maxwell's equations using MATLAB

Here I have an example: ...
user avatar
  • 7,902
6 votes
Accepted

Finite difference methods in cylindrical and spherical co-ordinate systems

There are basically two methods: You can disrectize the angular part via grid points, or you can discretize it via basis expansion. I will focus on spherical symmetry here, the cylindrical case is ...
5 votes
Accepted

How to solve a Poisson equation using the finite difference method when there is an object inside a domain?

If you have simple, grid-aligned interior objects or accuracy is not crucial then stick with the method you have described. If you need to accurately represent arbitrary boundary shapes then you're ...
user avatar
5 votes
Accepted

I need to scale variables to solve a 2D PDE. What are the physical considerations of scaling?

I've found that if I reduce the radial domain to $8 \leq r \leq 20$, the condition number drops to ~10,000. This makes me think I need to scale my problem. I'm not sure how to do this, however, and I ...
user avatar
5 votes

Calculation of the EFIE integral

A classic paper for evaluation of the integrals commonly present in computational electromagnetics (EM) is: D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, ...
user avatar
  • 8,287
5 votes

Minimum number of elements (mesh size) for electromagnetic simulation

The Maxwell system is a wave equation at heart, so your ansatz (the space where you seek solutions, the combination of your mesh and basis functions) must be able to faithfully represent waves. The ...
user avatar
  • 4,286
5 votes
Accepted

How to create a good preconditioner for a system of linear equations that is created with FEM applied on the time harming Maxwell eqution?

As a preamble, I would not expect that splitting $E$ into real/imaginary parts is very profitable. Normally, block 2x2 systems are motivated because one block of unknowns is "easier" to ...
user avatar
  • 4,286
4 votes

Which type of meshing is more suited for simulation of electromagnetic metamaterial unit cells?

As for any other domain, your mesh needs to be fine enough to resolve the features you have. This means that the mesh has to be finer than the geometric details of your unit cell, and it needs to be ...
user avatar
4 votes
Accepted

Is it necessary to use Poisson - Boltzmann equation if I only need to build electrostatic potential from a PQR file?

So Is it neccesary to use Poisson - Boltzmann equation if I only need to build electrostatic potential from a PQR file? No. You can use Poisson. Since you know the positions of each point charge, ...
user avatar
  • 207
4 votes
Accepted

Finite Difference Beam Propagation Method problem

When you call Lapack's zgtsv, it doesn't just solve a tridiagonal system $Ax=b$. What it does first is perform an LU factorization (zgttrf) $A = LU$, where $L,U$ are lower- and upper-tridiagonal ...
user avatar
  • 11.4k
4 votes

Simulate electric fields due to surface charges in simple circuits using python

ANSYS Maxwell is a Finite Element solver for Electromagnetism. So, I assume that you are looking for a Finite Element package that has a Python interface (or is written in Python). There are some ...
user avatar
  • 7,902
4 votes
Accepted

How to force potential boundary conditions in the Yee scheme for solving Maxwell's equations?

Interesting question. I would expect the Yee scheme to be indifferent to static (bias) fields induced by constant potentials. In the electrostatic case, if you have a constant electric potential $\...
user avatar
  • 4,286
4 votes
Accepted

Integral of the Poisson Kernel

The tangent has periodic singularities, poles where it jumps from $+\infty$ to $-\infty$. At these points the inverse tangent will jump from $+\frac\pi2$ to $-\frac\pi2$. This is of course not ...
user avatar
  • 3,511
3 votes
Accepted

Questions about implementing an electromagnetism/photonics solver package

Your questions suggest that you are new to implementing solvers for PDEs, and that you are not familiar with the usual data structures and algorithms used in this field. It would probably be very ...
user avatar
3 votes
Accepted

Is this a proper implementation of point charge dynamics with ODEs

It's an interesting question - how does a dipole actually move? It seems to me you're not entirely sure what to expect, so we need to get a solid test case where we understand what's actually going on....
user avatar
3 votes
Accepted

Edge and Nodal finite element methods in MATLAB for Magnetic induction tomography

The paper: I. Anjam, J. Valdman, "Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements", Applied Mathematics and Computation, 267, (2015), 252–263; states the following. http://www....
user avatar
3 votes

H(curl) conforming Nédélec-Elements to satisfy div(B)=0

One issue (and this is mentioned by Mur in the first paper you linked in the comments above) is the fact that, while these edge functions provide tangential field continuity across interfaces and zero ...
user avatar
3 votes

Good introduction to numerical methods for magnetohydrodynamics (MHD)

From what I understand, you'd like to see which numerical method best simulate the real physics relevant for a particular problem. MHD spans a wide scale of phenomena -- plasma physics (on length ...
user avatar
3 votes
Accepted

Magnetic field simulation and visualization on Mac OS X?

For this purpose you need to use a simulation software. One of the most common methods in Electromagnetics would be Finite element method, but you can also find Boundary Element Methods or Finite ...
user avatar
  • 7,902
3 votes
Accepted

PQR files make from pdb2pqr are different to GROMACS

The Van der Walls radius - last column in the output - is calculated from the force field. Probably pdb2pqr and editconf uses different force fields, hence different radius. I don't use pdb2pqr, but ...
user avatar
3 votes
Accepted

Introducing EigenModes from 2D FEM into 3D FEM

You're looking for waveguide port boundary conditions. I think the most accessible treatment is within Jin & Riley's Finite Element Analysis of Antennas and Arrays, Chapter 5. It's available on ...
user avatar
  • 4,286
3 votes
Accepted

Combine Hydrodynamics and Electromagnetics

Regarding simulation: There are several commercial solvers that might be helpful. A very popular FDTD Maxwell equation solvers for nanophotonics is Lumerical. It features opto-thermal and liquid ...
user avatar
  • 8,287
3 votes

Graphing electric potential of a ring of charge using MATLAB help

I received a solution to this question from MATLAB's community. Essentially, I need to specify which contour lines to plot using the 'levels' spot on the 'contour()' command. Levels allows you to ...
user avatar
  • 163
3 votes
Accepted

Graphing electric potential of a ring of charge using MATLAB help

You don't need symbolic variables to compute the approximated potential for your Riemann sums. You can just use meshgrid to evaluate the potential in each point of ...
user avatar
  • 7,902
3 votes
Accepted

Is there any method to incorporate minor changes into solved meshes to speed convergence in particle-in-cell solvers?

Every iterative solver -- Jacobi, SSOR, CG, etc -- starts with an initial approximation. One often just uses the zero vector, but there is nothing wrong with using the solution of the previous time ...
user avatar
3 votes

Minimum number of elements (mesh size) for electromagnetic simulation

It sounds like you are interested in a finite-element analysis, which is out of my area of expertise. But I can hopefully provide some insight from the perspective of finite-difference methods which ...
user avatar
  • 201
3 votes
Accepted

Finite element method for high-frequency electromagnetics

Using the typical expansion functions (1-forms/edge-elements for E, and 2-forms/facet-elements for B) the formulations are basically the same after spatial discretization and you'd expect more or less ...
user avatar
  • 4,286
3 votes

Using ODE to plot particle-motion with scipy.integrate.solve_ivp

Your particle is a rounded proton (mass m = 2e-27 kg instead of 1.672e-27 kg). The equation of motion is $$ \dot x=v,~~~ m\dot v ...
user avatar
  • 3,511
3 votes

Billiard reflection inside a triangular mesh

Funnily enough, determining the relationship between a point and a triangle is a big part of the work I'm doing right now on supersonic panel methods (check out https://github.com/usuaero/MachLine). ...
user avatar
  • 31

Only top scored, non community-wiki answers of a minimum length are eligible