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
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, ...
- 8,602
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 ...
- 4,822
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 ...
- 4,822
5
votes
Is my differential equation solving code wrong?
The cross product with $H$ acts like a complex unit in the plane that has $H$ as normal, especially if you select $H$ to be a unit vector. Components parallel to $H$ remain unchanged. What you should ...
- 5,519
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 ...
- 8,370
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 $\...
- 4,822
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 ...
- 5,519
4
votes
Euler's Method for fast moving particle trajectory
I tried to modify your code as little as possible and include the comments by @lightxbulb. I changed the indices in the time stepping loop and modified $F$ and $B$ so that they are being updated in ...
- 361
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 ...
- 8,370
3
votes
Accepted
Poincare map for Arnold-Beltrami-Childress Magnetic Field in Python
One first observation is that as $x,y,z$ are angles, one should take their values mod $2\pi$. Without that, the trajectory of the initial point $[0,0,0]$ exhibits this interesting pattern
...
- 5,519
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 ...
- 8,602
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 ...
- 4,822
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 ...
- 54.1k
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....
- 146
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....
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 ...
- 93
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 ...
- 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 ...
- 8,370
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 ...
- 54.1k
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 ...
- 211
3
votes
Simple reference problems for time harmonic Maxwell equations
That depends a lot on the specific numerical method in use, 2D/3D, and application.
Common reference problems are likely to have an analytical solution or be verifiable qualitatively by some ...
- 8,602
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 ...
- 4,822
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
$$
\dot x=v,~~~ m\dot v ...
- 5,519
3
votes
Accepted
Billiard reflection inside a triangular mesh
Funnily enough, determining the relationship between a point and a triangle is a big part of the work I'm doing right now on supersonic panel methods (check out https://github.com/usuaero/MachLine).
...
- 64
2
votes
Plot vector field in matlab
For plotting, it is easier in my opinion to not use meshgrid if you want to scale the arrows. You have a vector field $(E_X, E_Z)$ and you can simply normalize it like in the code below:
...
- 187
2
votes
Accepted
Why FEM electric analysis gives only access to current density?
They are saying the same thing, at a fundamental level - it's just that the implementation is a bit different. The first equation you noted is valid throughout the system because it solves for the ...
- 674
2
votes
Accepted
FEM or FD eigenvalue equation to get wave number instead of cutoff frequency
Assuming that you have scalar permitivity and permeability, you can relate your wavenumber with your angular frequency by
$$\omega = kc$$
where $c = 1/\sqrt{\epsilon_0 \mu_0}$ is the speed of the wave ...
- 8,370
2
votes
Data analysis of a magnetic hysteresis loop
First, you can replace the hysteresis plot with either smooth or piecewise-linear model presented in the article “An improved parametric model for hysteresis loop approximation” (R. V. Lapshin, Review ...
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