All Questions
Tagged with physics finite-element-method
57
questions
1
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0
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69
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Why is NDSolve ignoring two PDEs out of three ones I am solving?
I am solving the following coupled system of 3 PDEs modelling a 1D membrane coupled to a 1D fluid flow field underneath.
However, on putting them into NDSolveValue (and trying with FEM), it says the &...
- 165
2
votes
1
answer
114
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NDSolveValue is unable to provide a solution because of boundary conditions
I have the following Mathematica code for solving a partial differential equation, which I took from this paper (page 6, 10) for B = 0 (which has ...
- 2,433
3
votes
1
answer
158
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Dirac equation for a Coulomb potential in 2D with NDEigensystem
I want to numerically solve the ground state wave function of the hydrogen atom with the Coulomb potential using the NDEigensystem. Here is the code to get the ground state wave function from the ...
- 51
6
votes
2
answers
1k
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Numerically solving radial Schrödinger equation with Yukawa potential
I am trying to solve the radial Schrödinger equation using NDEigensystem but I am running into some issues. There are posts about doing this (see here for example), ...
- 343
2
votes
1
answer
222
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Numerical ground state wavefunction of Schrödinger equation with a Coulomb potential in 2D from NDEigensystem
I want to numerically solve the ground state wave function of the hydrogen atom with the Coulomb potential using the NDEigensystem. Here is the code to get the ground state wave function from the ...
- 51
3
votes
4
answers
196
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NDSolve over derivatives of Heaviside function
I am trying to numerically solve for the strain of a Maxwell material in response to a step stress. The governing equations are $$\dot{\sigma} + \sigma = \dot{\varepsilon}$$ and I want to find $\...
- 407
2
votes
1
answer
360
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Solving Schrödinger equation for Dirac comb potential (kicked rotor)
I need to solve the Schrödinger equation for a Dirac delta potential. I could not find the correct way to write the time-dependent potential and how to solve the time-dependent equation for it.
The ...
- 2,644
1
vote
1
answer
90
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Fitting Parameters to the Heat Equation [closed]
As part of my research, I have been trying to use a model of heat conduction through a 2D layer given an input steady-state Gaussian power profile and a heat loss term to the environment. All but one ...
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1
vote
1
answer
134
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Why does NDSolve solution not match physical intuition?
Related to a previous question I posted, I am trying to solve for the electric potential on a box which obeys Ohm's law:
\begin{equation}\nabla\cdot(\overset{\scriptscriptstyle\leftrightarrow}{\sigma}...
- 516
1
vote
2
answers
221
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Setting up a PDE for a time-independent Schrödinger equation
I am trying to solve a 2d Schrödinger equation with a non-separable potential because I want to calculate the probability of reflection for different angles of incidence of a plane wave.
Here I ...
- 21
5
votes
1
answer
322
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Solving Coupled nonlinear Differential Equations For Eigenvalue And Eigen functions
I tried to solve coupled nonlinear differential equations from this paper https://sci-hub.hkvisa.net/10.1016/j.jcp.2019.109058 to see eigenvalues and eigenfunctions in different dimensions. At first, ...
- 341
2
votes
2
answers
688
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How should I define the boundary conditions of free end and fixed end scenarios for 1D Wave Equation?
The 1D wave equation is $$\frac{\partial^2 u(x,t)}{\partial t^2} = c^2 \frac{\partial^2 u(x,t)}{\partial x^2}$$
where $c$ is the wave speed, $c^2=E/\rho$, $E$ is the Young's modulus and $\rho$ is the ...
- 95
3
votes
1
answer
327
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Solving 3D Nonlinear Integral Partial Differential Equation
I am trying to solve Equation number (1.2) numerically in MATHEMATICA. This equation is solved in the papers https://arxiv.org/pdf/2205.05193.pdf, https://arxiv.org/pdf/2202.13264.pdf, and https://...
- 341
5
votes
1
answer
347
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Monte Carlo Simulation of Charged Particles in Non-Uniform Electric Field
I have a code (provided below) which simulates the motion of an ensemble of charged particles which are subjected to a complex static electric field which passes through some aperture in a metallic ...
- 373
2
votes
1
answer
469
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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 ...
- 373