Questions tagged [wave-propagation]

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Can this finite difference dispersion be eliminated somehow?

I am trying to solve the wave equation $$ {\partial ^2u(t,x) \over \partial x^2} = {\partial ^2u(t,x) \over \partial t^2} \tag1 $$ with the following boundary and initial conditions: $$ {\partial u \...
Nikola Ristic's user avatar
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1 answer
139 views

Solving the wave equation for a circular membrane in polar cordinates

As you see this mode is not right, unless for what i understand And the initial conditions were ...
Manuel Borra's user avatar
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0 answers
81 views

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 ...
Avii's user avatar
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1 vote
1 answer
372 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)...
mmikkelsen's user avatar
3 votes
0 answers
69 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 ...
NotaChoice's user avatar
2 votes
1 answer
85 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 ...
Avii's user avatar
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2 votes
1 answer
417 views

Numerical solution of 2D wave equation using Fourier transform and finite differences

This is the $2$-dimensional wave equation $$ u_{tt} = u_{xx} + u_{yy} $$ with initial condition $u(x,y,0)=f(x,y)$ and $u_{t}(x,y,0) = 0$. The inverse Fourier transform used is $$ u(x,y,t) = \iint \hat{...
Redsbefall's user avatar
0 votes
0 answers
51 views

Can you describe the Galerkin numerical method to solve the wave equation?

How would you describe the Galerkin method to solving the 3D wave equation $$u_{tt}= c^2\Delta u$$ to someone who wants to implement it immediately? More precisely, we want to solve the Cauchy problem ...
NotaChoice's user avatar
1 vote
1 answer
68 views

stability of a numercial scheme for a hyperbolic system?

This is related to my question here https://math.stackexchange.com/questions/4447383/lax-wendroff-scheme-stability-analysis-for-a-linear-system-of-conservation-laws . Consider the numerical scheme ...
NotaChoice's user avatar
0 votes
0 answers
61 views

schrodinger eq time propagation with dissipation using split step operator

I am looking in ways to include energy dissipation while propagating a coherent wavepacket in a 1d TDSE. for example I use the split step method: exp[Δt(D+V)]≈exp[ΔtV/2]exp[ΔtD]exp[ΔtV/2], and ...
yourds's user avatar
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Open boundary condition for 1d wave equation with variable wave speed using finite differences

I have implemented a finite difference solver for the 1d wave equation with variable wave speed: $$ u_{tt} = c(x)u_{xx}, \hspace{10mm}c(x) = \dfrac{6 -x^2}{2} \hspace{5mm} $$ on $-2 \leq x \leq 2, t &...
Adam Lau's user avatar
2 votes
1 answer
272 views

Beam propogation method for a waveguide. How to get single mode?

I am simulating a waveguide using diffractio python library (https://diffractio.readthedocs.io/en/latest/readme.html). The idea is to create a single mode waveguide using wave propogation method. ...
wosker4yan's user avatar
0 votes
0 answers
48 views

How do I identify negative group speeds?

This question is a continuation of one of my other questions. I've been trying to show that collocated (non-staggered) grids can suffer from negative group speeds in the linearized shallow water ...
theWrongAlice's user avatar
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1 answer
133 views

A simple wave for the linear shallow water equations

I'm looking for a simple, right-traveling wave for the linear shallow water equations (1D). My question: what are the initial conditions (velocity $U_0(x)$ and/or average water height, average ...
theWrongAlice's user avatar
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0 answers
227 views

FEM port Boundary definition for electromagnetics and wave guides

We are currently in the process of implementing ports in our EM FEM simulation SW. We have come across the definition of boundary conditions for the ports, and we do not understand the equation for ...
bbch's user avatar
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2 votes
0 answers
139 views

Divergence on wave equation simulation

I'm currenly working on my own PDE solver for non-linear simulations in python. I've done succesfully simulations for KdV and Fisher's equation, but now I'm playing with second order derivatives in ...
Rafael Riveros Ávila's user avatar
1 vote
0 answers
56 views

Results blow up when number of intervals is increases (Yee algorithm FDTD, dielectric sphere)

I have been trying to write a program that analyses EM wave scattering by a dielectric sphere for a project. The reference is Sadiku's book Numerical Methods in electromagnetics Edition 3. Now the ...
Hridey's user avatar
  • 41
0 votes
1 answer
91 views

Acoustic Simulation, how are boundaries handled?

I don't have a background in numerical modeling so this question is rather broad. What I am interested in is modeling the propagation of an ultrasonic acoustic wave in 3d space. The basic 3d wave ...
FourierFlux's user avatar
6 votes
1 answer
1k views

Gauss-Lobatto quadrature and nodal points for FEM

By using the Legendre-Gauss-Lobatto (LGL) quadrature formula (QF) and LGL nodal points one achives a diagonal mass-matrix for finite element problems. (More specifically, the spectral element method.) ...
Dagon's user avatar
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0 answers
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Split of complex parts in weak form

I am working on a numerical model to simulate the acoustic and elastic wave propagation in frequency domain via the Finite Element Method. Basically, the problem is to solve the Helmholtz equation in ...
Lucas Vieira's user avatar
1 vote
2 answers
441 views

Solve wave equation with discontinuous coefficients numerically?

I would like to solve the following equation $$\frac{\partial^2 y}{\partial t^2} - c^2(x,t)\frac{\partial^2 y}{\partial x^2}=0,$$ for $y=y(x,t)$ numerically. The wave speed, $c(x,t)$, is of the form $$...
Peanutlex's user avatar
  • 219
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0 answers
402 views

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 ...
Lucas Vieira's user avatar
2 votes
1 answer
191 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 ...
Lucas Vieira's user avatar
1 vote
1 answer
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 ...
Aldrich Taylor's user avatar
0 votes
0 answers
29 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 ...
11235's user avatar
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1 vote
1 answer
95 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 ...
Jacob_K's user avatar
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-1 votes
1 answer
122 views

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 ...
Sean O'Gary's user avatar
4 votes
2 answers
776 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 ...
VoB's user avatar
  • 540
2 votes
1 answer
432 views

Modified Equation and Stability for Centred Finite Differences for Wave Equation

I am trying to use the modified equation to derive the stability condition for the finite difference approximation $$ \frac{u(x,t+\Delta t) - 2 u(x, t) + u(x, t -\Delta t)}{\Delta t^2} = c^2 \frac{...
Daniel's user avatar
  • 1,238
1 vote
1 answer
64 views

What is the right way to set up two random tensor fields which have an identical average diffusivity

I want to compare some properties of traveling waves through two randomly diffusive media. The traveling waves follow the fisher equation: $$\frac{du}{dt} = \nabla(\mathbf{D}_{\gamma} \nabla u) + u(1-...
MPIchael's user avatar
  • 2,627
2 votes
1 answer
619 views

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 ...
FeelsToWaltz's user avatar
5 votes
3 answers
631 views

Finite difference for 1D wave equation: why the spike initial data results in a noisy output?

I am using a second-order finite difference in space and time approximation for the 1D wave equation. No source but initial data: $I(x)=\mathrm{e}^{-400 (x-0.5)^2}$. Velocity $c=1$, $nx=501$, $nt=...
Herman Jaramillo's user avatar
4 votes
2 answers
471 views

Why is my simulation of a first-order wave equation not stable?

According to the equation $$ \frac{\partial y}{\partial t} = -a\frac{\partial y}{\partial x} $$ I simulated this in python. I used center differentiation, and I determined step size based on Von-...
user28053's user avatar
4 votes
0 answers
295 views

How can I solve the wave equation for a circular rod in cylindrical coordinates using finite differences?

I have a problem with the stability of finite difference method for the wave equation in cylindrical coordinates. the equation is: $$ \frac{\partial^2 \omega_n}{\partial r^2}+\frac{1}{r}\frac{\...
alireza's user avatar
  • 41
0 votes
1 answer
359 views

Introducing EigenModes from 2D FEM into 3D FEM

This particular FEM question concerns waveguides and FEM 3D simulation. To excite a waveguide with waveport (TE10 and so on), we typically have to solve for eigenvalues ($k$) of helmholtz equation ...
Aakusti's user avatar
  • 163
1 vote
0 answers
222 views

shallow water equation maccormack method

I am trying to make a code for 1D shallow water equation (nonlinear without source terms) using the MacCormack method for sinusoidal wave propagation. My issue is that the wave fluctuates and does not ...
babar's user avatar
  • 11
0 votes
1 answer
540 views

Trying to plot 1D wave equation for benchmarking

I am trying to plot a reference solution for the 1D wave equation using python. The above link states the following: For a rod fixed at the right end and free at the left end and subjected to a ...
user32882's user avatar
  • 251
1 vote
0 answers
30 views

Simulation of a lens, insufficient points

I am simulating the propagation of a light pulse using the equation $$\frac{\partial}{\partial z}A=\frac{1}{2\cdot k_0}\nabla^2_rA$$ with $$k_0=\frac{2\pi}{\lambda_0}$$ The propagation with a step ...
arc_lupus's user avatar
  • 543
1 vote
0 answers
53 views

How do we implement Parameter free generalised Moment limiter in 1D Case in Discontinuous Galerkin methods?

I am referring to this paper:- "A Parameter-Free Generalized Moment Limiter for High- Order Methods on Unstructured Grids " by Michael Yang and Z.J. Wang. http://dept.ku.edu/~cfdku/papers/AIAA-2009-...
Manish's user avatar
  • 163
7 votes
1 answer
647 views

Discrete wave simulation - absorbing boundaries?

I wrote a simple 2D wave simulation using the following equations: $$\frac{\partial^2 u}{\partial t^2}=c^2\nabla^2u$$ Where $\nabla^2$ is the discrete laplace operator using a Von Neumann neighborhood ...
Bloc97's user avatar
  • 171
0 votes
2 answers
1k views

Time step relationship with number of elements or material properties

When looking at the output file of my solver, I have been told that the time-step taken by the solver depends on parameters like the total number of elements and their relative size in my geometry, or ...
Blue_Elephant's user avatar
9 votes
1 answer
810 views

CFL condition in polar coordinates

In this question, I suggested that the Couran-Friedrichs-Lewy (CFL) condition for the wave equation in polar coordinates reads $$C = 2c\frac{\Delta t}{\Delta r \Delta \phi} \leq C_\max \enspace ,$$ ...
nicoguaro's user avatar
  • 8,370
1 vote
0 answers
69 views

Degree of freedom for elastic wave propagation problem

I am solving a elastodynamics (vector valued elastic wave) equation. I create the 2D mesh in Gmsh discretised into triangular elements of second order. Therefore, it is my understanding that the ...
CRG's user avatar
  • 347
0 votes
1 answer
102 views

Regarding solution vector of the wave equation

I am simulating the wave equation using FEM. For a 2D wave equation, when I visualise my output in Paraview, I see a separate solution in 'x' and 'y' direction for each node on the mesh. Therefore, if ...
CRG's user avatar
  • 347
0 votes
1 answer
144 views

Damping for Dynamic Problem using FEM

I came across this form of damping implemented in an elastodynamics problem. The stress tensor without the damping would look like: $ \sigma = 2 \mu \epsilon + (\lambda \, \text{tr} (\epsilon)) I $ ...
CRG's user avatar
  • 347
0 votes
1 answer
118 views

How to use non-dimensional form in open source codes instead of Units

I am using an open source FEM platform, which requires you to convert your equation system to non-dimensional form. So, there are no units specified for the parameters in the problem. If you use ...
CRG's user avatar
  • 347
1 vote
1 answer
4k views

Using backward vs central finite difference approximation

I am solving the simple 2nd-order wave equation: $$ \frac {\partial ^2 E}{\partial t^2} = c^2 \frac {\partial ^2 E}{\partial z^2} $$ Over a domain of (in SI units): $ z = [0,L=5]$m, $t = [0,t_{max} ...
Mathews24's user avatar
  • 578
1 vote
1 answer
106 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 ...
user65452's user avatar
  • 319
1 vote
0 answers
881 views

Seismic Wave modelling: Elastic Wave or Acoustic Wave?

I am modelling a seismic wave equation using FEM. In the few papers that I read, I understand the following: (Kindly correct me if you disagree) A shear (secondary wave - no change of volume) is more ...
CRG's user avatar
  • 347
3 votes
1 answer
321 views

Measure the convergence rate of a discretization of a wave equation

I'm currently trying to approximate the following type of wave equation (in weak formulation): Let $\Omega \subset \mathbb{R}^d$ ($d=2$) be some polygonal domain. We seek a function $u \in L^2\left(0,...
Simul's user avatar
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