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How to solve electric drift and diffusion PDE using `NDSolveValue`?

I am trying to learn how to use NDSolveValue with various boundary conditions. After going through several examples here, I thought I'd try it on what I thought ...
BeauGeste's user avatar
  • 2,877
1 vote
1 answer
84 views

EM Wave Equation: Insufficient initial conditions for NDSolve?

I am trying to model a EM wave propagation through a region of free space. However, Mathematica tells that there are insufficient initial conditions, even though I specify all values at ...
Dr__Soul's user avatar
1 vote
1 answer
98 views

Components of Faraday tensor

Maybe it's a very basic physics question but I'm confused and not sure if I should ask my question here. From this paper, I have the potential vector $$ A=A_t d t+A_\phi(d \phi-\omega d t) $$ where $$ ...
Dayzk's user avatar
  • 157
5 votes
1 answer
168 views

3D FEM Memory Problem with Hexahedral Elements & V14 & Apple Silicon

After using MM V12 for a long time on a MacBook Pro 2011, which just lost 8GB or RAM from 16GB, I am trying V14 on a MacMini M2pro with 32GB. I had previously coded a coupled 3D EM problem involving a ...
Greenasnz's user avatar
  • 381
1 vote
1 answer
101 views

Solving a 3+1D Wave Equation

I am having some problems with finding the solution to the magnetic field, B[x,y,z,t]. Is there anything I can change to my code to obtain a solution of B[x,y,z,t] with the initial conditions and ...
Tommy Wong's user avatar
2 votes
0 answers
128 views

Cavity resonator modeling with Wolfram Mathematica

I am attempting to determine eigenfrequencies and the corresponding electric field distribution in a rectangular cavity resonator with perfectly conducting walls. In the simplest case of a rectangular ...
Ian's user avatar
  • 41
5 votes
0 answers
142 views

What is resistivity function of a 3-bar electric switch?

I answered a question on Physics StackExchange - considered as homework - numerically. The question is: What is the resistance of three stacked identical blocks, the middle bar shifted by its half ...
Roland F's user avatar
  • 3,927
2 votes
1 answer
218 views

Machine overflow when defining boundary conditions

Recently I have been trying to code Maxwell's equations over a closed surface and have been facing some trouble defining the boundary conditions for the magnetic field. The equation for the normal of ...
Jole Stock's user avatar
3 votes
1 answer
185 views

Creating a plot for a summation function

I have this potential function which I believe is representative of a grounded cube in a 3D plane. I'm not entirely sure if this is it, but here is the general solution of the function: v(x,y,z) = G(...
Carson Joseph's user avatar
3 votes
2 answers
185 views

FEM Capacitor Not Converging with Parallel Plate Model

I am trying to model a 3D electrostatics finite element model of a capacitor to see if I can accurately model the behavior of a parallel plate capacitor before I alter the geometry of the electrodes ...
Dallon Penney's user avatar
11 votes
3 answers
838 views

Calculating the 3D magnetic vector field of a permanent magnet, with shape given by STL File

following my earlier question Link, I am trying to calculate the magnetic field of a permanent magnet. The shape of the magnet was generated with FreeCAD and is provided to Mathematica by an .STL file....
Tschibi's user avatar
  • 877
2 votes
1 answer
464 views

Properly Updating Particle Motion in 3D Electric Field Simulation

I have a code (very bottom of post) which plots a static electric field as it passed through some metal sheet with an aperture in it. I seek to observe the motion of some N charged particles (point ...
Zach's user avatar
  • 373
4 votes
1 answer
181 views

FEM solution of Helmholtz equation

I'm trying to solve the Helmholtz equation : https://en.wikipedia.org/wiki/Helmholtz_equation in a 3d space, in vacuum, using FEM. I expect the solution to be an function oscillating in the x ...
dnad's user avatar
  • 41
9 votes
1 answer
863 views

Calculating the 3D Vector field of a permanent magnet with FEM

trying to calculate the magnetic field of a permanent magnet using the finite element method I struggle setting up the equation system properly. In the end I want to be able to calculate the magnetic ...
Tschibi's user avatar
  • 877
7 votes
0 answers
270 views

System of coupled nonlinear pdes with FEM (magneto-hydrodynamic mass transfer)

EDIT 01 See end of post for an update. Original Question I'm trying to reproduce the magneto-hydrodynamic flow studied here using the nonlinear FEM functionality, and have been having trouble ...
George Varnavides's user avatar
0 votes
0 answers
195 views

Magnetostatics analysis of Switched Reluctance Motor in Mathematica

Accidentally stumbled upon magnetostatic calculation in Mathematica. https://www.wolfram.com/language/12/nonlinear-finite-elements/magnetostatics.html?product=mathematica I would like to ask a ...
ayr's user avatar
  • 2,434
2 votes
1 answer
425 views

FEM: Getting Resulting Electric Force on each body from electric field

Based on this excellent answer FEM: Electric Field between two arbitrary defined shapes I can compute the electric field ef between two conducting objects. $$ F = ...
james's user avatar
  • 3,093
8 votes
1 answer
468 views

FEM Simulation: Meshing Two Arbitrary Objects in an "Air" Mesh

Based on this excellent answer to my previous question: FEM: Electric Field between two arbitrary defined shapes I wanted to try out other shapes: ...
james's user avatar
  • 3,093
10 votes
1 answer
2k views

FEM: Electric Field between two arbitrary defined shapes

I was wondering how to do the following: I would like to compute the electrostatic field between two shapes using the FEM method. ...
james's user avatar
  • 3,093
0 votes
0 answers
150 views

Ways to decrease computational time?

I have created a 2D axisymmetric simulation of the motion of charged particles in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with ...
kjcole's user avatar
  • 353
1 vote
1 answer
442 views

How to create an animation of charged particles' motion in an electric field?

I am trying to create an animation of 3 particles' motion in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with a grounded plate ...
kjcole's user avatar
  • 353
5 votes
1 answer
888 views

Electric field produced by a capacitor consisting of two parallel plates of different lengths

I need to visualize the electrostatic field produced by a capacitor consisting of two parallel 1D plates of different lengths, as shown in the following figure (sorry for the crude drawing), in which ...
Enter's user avatar
  • 1,229
16 votes
1 answer
2k views

Solving Maxwell's Equations in Mathematica

For the sake of demonstration (for my students) and practice, I wanted to numerically calculate the electric and magnetic field (3D) for a sphere of uniform density moving slightly to the right and ...
Andre Reis Guimaraes's user avatar
8 votes
4 answers
1k views

Setting Up Boundary Conditions for Magnetostatic PDE

Bug introduced in 11.2.0 and fixed in 11.3.0 The system is a hollow cylinder (thin solenoid) with a current density $\text{J}$ and I'm looking to solve the magnetic potential ($\text{A}$) inside the ...
Young's user avatar
  • 7,515
3 votes
2 answers
1k views

Electric field calculation from Laplace's equation

I have a solution of Laplace's equation which shows electric potential. I would like to get some data on electric field strength, that is to say a negative gradient of the potential. Here is the code: ...
space bobcat's user avatar
11 votes
1 answer
885 views

Solution of electromagnetic wave in frequency domain seems strange

Bug introduced in 10, fixed in 11.1. I want to solve the electromagnetic wave equation in frequency domain. A known solution, a plane wave Exp[ I k0 x] is used to ...
quantum's user avatar
  • 111
7 votes
1 answer
861 views

Solve 3D Electric Field Using FEA

The objective is to solve the 3D electric fields for the geometry below and generate the continuous function eField3D[x_,y_,z_]. The method I was planning on using ...
Young's user avatar
  • 7,515
21 votes
2 answers
2k views

How to access FEM shape functions?

A couple of days ago I asked here about surface meshes and plotting on surfaces. Now I have another question: How can I access the surface or boundary element shape functions? I would like to ...
AxelF's user avatar
  • 977
13 votes
3 answers
2k views

How to create a surface mesh embedded in 3D?

I am working on a problem where I want to optimize current densities on 2D surfaces embedded in 3D to generate magnetic fields. The current density on a surface can be written as a scalar function ...
AxelF's user avatar
  • 977
15 votes
1 answer
2k views

Frequency domain Maxwell equations with PML boundary conditions

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
Quit007's user avatar
  • 1,255
5 votes
0 answers
2k views

FDTD Electromagnetic Simulations with Mathematica

Mathematica has some Finite Element capabilities (as explained here). Do you think mathematica is a realistic/sensible option for electromagnetic simulations? (aka making a movie of electric fields ...
Tom's user avatar
  • 3,416
15 votes
1 answer
638 views

How to specify PDE Boundary condition on a B-spline?

Context I would like to solve a PDE on a boundary which is parametrized as a BSpline. I am trying to solve the force-free Grad-Shafranov equation on a boundary ...
chris's user avatar
  • 23.1k