# Questions tagged [wave-propagation]

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### Analytical Equation of the gaussian 1D wave equation with periodic Boundary condition

I am trying to validate the 1D analytical wave equation with a numerical solution with periodic boundary conditions. I have implemented the periodic boundary condition for the numerically calculated ...
• 121
1 vote
62 views

### Solving $u_{tt} = u_{xx}$ with spectral methods and homogeneous Dirichlet/Neumann BC

Suppose we want to approximate a function $u(x,t)$ with $(x,t)\in[-1,1]\times[0,4]$ that satisfies the wave equation $u_{tt}=u_{xx}$ in the inside and BC $u(-1,t)=u_x(1,t)=0$ with initial value given ...
• 11
1 vote
227 views

### (Regular) Coulomb wave function

I'm looking for a way to implement the regular Coulomb wave function in python. This function is a solution to \begin{align} \frac{\text{d}^2\,u}{\text{d}z^2}+\left(1-\frac{2\eta}{z}-\frac{\ell(\ell+1)...
• 110
42 views

### Unstable FDTD for axisymmetrical wave propagation

I am writing a 2.5D axisymmetric FDTD solver for Maxwell equations. It operates on three fields on staggered grids ($E_r$, $E_z$, $B_\varphi$). As a test problem, I am considering a cylindrical ...
68 views

### Looking for non-trivial examples of solutions to 3D wave equations?

We have developed a (new) numerical scheme to solve the classical wave equation in 3 dimensions and we aim to publish the results. We can read in the aim and scope of the journal of computational and ...
• 151
77 views

### Interpolation of 1D solution from an original grid to a new grid

I have a solution of a 1D wave on a grid (tangent hyperbolic variation) and now I want to interpolate the obtained solution to a new grid with the same number of points as the previous grid but the ...
• 121
55 views

### How to define a stretched coordinate perfectly matched layer (PML) parameters for maximum absorbtion?

I have written a MATLAB code for solving Maxwell's equations (electromagnetic wave propagation) in 3D with perfectly matched layer (PML) boundaries. I am using a stretched coordinate PML, but I see ...
332 views

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### What is the meaning of the Helmholtz wave equation?

I am trying to build understanding on the Helmholtz wave equation $\Delta p + k^2 p = 0$, where $p$ is the deviation from ambient pressure and $k$ the wave number, in order to use it in numerical ...
• 115
180 views

### Methodology Suggestion for Wave-propagation Problem using Finite Elements

I want to simulate the propagation of a sinusoidal plane wave in a rectangular domain using Finite Elements Method. First, the wave should propagate through a fluid medium, then it will encounter a ...
• 115
1 vote
107 views

### Partial differential equation FEM application

I have a PDE which looks like Helmholtz wave equation on one dimensional domain. $$\dfrac{d^2u(x)}{dx^2}+\pi^2u(x)=f(x)$$ where $-\infty <x<\infty$ Also, $f(x)= 1$ for $-0.25<x<0.25$, I ...
28 views

### Circumferencial waves on a cylinder/sphere

I was wondering how we can introduce $e^{ik.x}$ terms associated with circumferencially propagating waves? In this case $\hat{e}_\theta$ is the direction of wave propagation. However, I was not able ...
1 vote
88 views

### Simulating pressure waves at an impedance boundary

I am trying to simulate pressure waves crossing a boundary from one medium to another (e.g., water to air) in Matlab. The code that I have got so far, which is largely taken from Wikipedia on Partial ...
• 19
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### If not MATLAB, what software/programming language should I use to simulate/animate wave functions in various potentials + more? (example given)

I want to integrate programming into my learning in math and science in a very specific way. I want to create visualizations and simulations of concepts I am learning. When I learn a numerical method ...
661 views

### Numerical solution of zero-potential time-dependent Schrödinger equation in 1D

I want to solve numerically the one-dimensional time-dependent Schrödinger equation $$i \psi_t(x,t)=-\frac{\hbar}{2m} \psi''(x,t)$$ My issue is that I don't have the physical background to understand ...
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• 2,461
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### Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)

I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
578 views

• 568
1 vote
103 views

### Perfectly matched layer simulation with two vibrating sources

I'm doing PML simulation, and while I was looking for correct geometry for my layers of propagation, I got a question. My device has two vibration sources, and this vibration will propagate through ...
• 319
1 vote