Questions tagged [wave-propagation]
The wave-propagation tag has no usage guidance.
85
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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,...
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1
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1
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Mass Lumping in case of Dirichlet boundary conditions
I'm currently trying to implement a FEM to solve a type of wave equation with homogeneous Dirichlet boundary conditions by using standard $\mathcal{P}_1$ triangle elements and an explicit scheme for ...
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2
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What would be a simple approach to validate a wave propagation code?
I have a linear elastic wave propagation code and an elastoplastic wave propagation code based on FEniCS.
For now, I keep the 2D mesh (100, 100) fineness unit square and give a source wave of $\sin(...
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How to add a Ricker Wavelet (Mexican Hat) to a 2D/ 3D fem mesh?
I have a 2D square mesh and a 3D beam shaped mesh and I want to propagate a seismic wave in them. I am trying to simulate them using Open source FEM codes (fenics). I have left the top surface to be ...
- 347
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Weak form for elastoplastic wave propagation
I am trying to simulate elastoplastic seismic wave propagation using Fenics Solid Mechanics Application.
The app. provides some quasi-static demos to show elastoplastic behaviour in a cube/ beam/ ...
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Unwanted Oscillation in FDM simulation of elastic wave equation
I am using staggered grid FDTD for solving elastic wave equation. A description of which can be found at (geodynamics.usc.edu/~becker/teaching/557/reading/Virieux1987.pdf). I have generated a ...
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Finite difference scheme for Webster equation
Webster equation is a popular generalization of 1D wave equation used for ducts of variable cross-section $S \equiv S(x)$. Assuming harmonicity in time, the spatial equation for propagation of ...
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My discretization of a wave equation in first-order form does not give correct solutions. What should I do?
I haven't much experience with conservation laws, shocks, etc. After reformulating my wave equation to 1st order system (velocity-stress):
$$
\frac{\partial v}{\partial t} + A \frac{\partial v}{\...
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Runge Kutta for wave equation
Recently I work on mechanical shocks (e.g. impact) in FE (fenics). I've already put together simple timesteppers (Euler, Crank-Nicolson). I use higher order basis, so I think of higher order time ...
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Velocity-Stress formulation of Elastodynamics/Wave Equation for beginner
I'm used to displacement forumlation of elastic wave equation:
$$
\nabla \cdot \sigma (u) + F = \rho \ddot{ u }
$$
where $u$ is the primary variable. Recenty I started experimenting with DG and in ...
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Solving a simple Schroedinger equation with Fast Fourier Transforms
While trying to solve a stochastic Gross-Piaevskii equation I have found a problem that can be tracked down to something buggy occuring in the simplest Schrodinger equation possible:
$\partial_t \psi ...
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How to calculate dispersion relation from a Finite Difference (FD) wave simulation
I have a python code that calculates the solution of the inhomogeneous acoustic wave equation for a 2D medium with any velocity and source configuration. It was implemented using Finite Differences ...
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Resolving a stiff hyperbolic problem with Neumann boundary conditions
I am trying to numerically resolve the equation for an Euler-Bernoulli beam that is inextensible, unshearable, and subject to planar deformations:
$$\rho I(s) \frac{\partial^2 \theta}{\partial t^2}(s,...
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Analytical Solution to the acoustic / scalar (Inhomogeneous) wave equation with source term
The acoustic wave equation in 2D is
$$\frac{\partial^2}{\partial t^2}p(x,z,t) = c(x,z)^2\left[\frac{\partial^2}{\partial x^2}p(x,z,t) + \frac{\partial^2}{\partial z^2}p(x,z,t)\right] + s(x,z,t) \...
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Time discretization of wave equation
I am trying to model the seismic wave equation and have therefore been reading about discretization schemes and their stability. I recently came across an insightful paper on 'Galerkin FEM methods for ...
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Wave Equation PDE [closed]
I'm trying to solve the following PDE wave equation using method of lines:
Wave Equation: u_tt = u_xx
with initial condition: u(0,x) = sin*pi,u_t(0,x)=0, 0 < x < 1
boundary condition: u(t,0) = ...
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Need suggestions on how to implement this time stepping for wave equation [closed]
I have the following system of equations obtained by implementing Sympletic Euler time scheme to wave equation. I want to model this in Fenics. Here 'u' is the displacement and 'p' is corresponding ...
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How to physically understand time dependent boundary conditions?
I am a beginner in Computational science and FEM. I came across some PDEs which implement time dependent boundary conditions.
I am not able to visualize exactly a physical scenario of how that would ...
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1
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Finite difference scheme for 2D sound propagation
I am simulating the sound wave propagation in non-rectangular and asymetric spaces using finite-difference method. I presume linear acoustics equations to be enough (i.e. $\Box p = 0$, $\Box \vec{v} = ...
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Dirichlet BCs - alternative implementation methods
I am having problems with solving a hyperbolic wave problem with Dirichlet BCs. I have tried reducing the time step sizes, which does not affect the results, and notices increasing the number of nodes ...
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How can I solve wave equation for circular membrane in polar coordinates?
The original equation is
$$\frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \frac{\partial^2 u}{\partial r^2} + \frac{1}{r}\frac{\partial u}{\partial r} + \frac{1}{r^2}\frac{\partial^2 u}{\partial \...
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Absorbing boundary conditions for acoustics in Discontinuous Galerkin
Note: I'm trying to implement a Discontinuous Galerkin method, as kind of a way to learn about these things.
As of now, I've taken the acoustic wave equation $c^2 \nabla \cdot \nabla u(x,t) - \frac{\...
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Finding the frequencies of vibration of a circular and square drum
I want to find the frequencies of vibration of a circular and square drum. To do this, I need to solve a 2-dimensional wave equation (PDE) with boundary conditions. Every method that I have researched ...
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2D wave equation with Mur boundary condition - setting up the RHS and solving (time-steps)
I am trying to solve a 2D wave equation implicitly using FD with central approximations with the following boundary conditions
$$\begin{align}
&u=2\sin\left(\frac{2\pi}{5}t\right)\quad \text{at }...
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Eikonal Equation solver with different grid densities
The Fast Marching Method, Fast Iterative Method, and Fast Sweeping Method are three ways of solving the Eikonal Equation on a discrete grid, essentially just a wavefront spreading out from initial ...
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Absorbing BC's / PML on a graph
The wave equation,
$$\ddot{u} = c^2 \Delta u,$$
can be generalized to abstract graphs by using the negative graph Laplacian in place of the physical Laplacian.
Is there a graph-theoretic analog of ...
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Simulating a traveling sine wave
I'm trying to make an animation of a travelling sine wave (amplitude vs. position) would anyon here happen to know how to do so?
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Euler Equation Eigensystem with Gravity in the Energy Flux
I am modifying a conservative form of the Euler equations with gravity in the energy flux (see previous question: Energy Conservation in Conservation Laws with Source Terms) for use in a Riemann ...
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Energy Conservation in Conservation Laws with Source Terms
I'm wondering if anyone can help me understand energy conservation when using conservation law methods (i.e. Riemann solver, High-Resolution Wave-Propagation Methods) with the addition of source terms:...
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Sound Waves Simulation in 3D Environment
I want to do a simulation of sound waves including wave propagation, absorption, and reflection in 3D space.
I did some research and I found this question in stackoverflow but it talks about ...
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Numerically evaluate 1D inhomogeneous wave equation solution
I am trying to solve the following 1D inhomogeneous wave equation.
Forgive me if I a miss any rigorous mathematical concept.
$$ \frac{\partial^2 u}{\partial x^2} - \frac{1}{c^2}\frac{\partial^2 u}{\...
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Solving nonlinear wave equation in a dispersive infinite waveguide
I would like to solve a three-dimensional nonlinear wave equation in an infinite cylindrical waveguide numerically. Since the waveguide is dispersive, shocks are less likely to form. Both the ...
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Analytic solution 2D scalar wave equation in cylindrical coordinates numerical implementation
I am trying to compare my finite difference's solution of the scalar (or simple acoustic) wave equation with an analytic solution.
For that purpose I am using the following analytic solution ...
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1
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Time-dependent wavefunction numerical simulator
I want to develop a visual simulation of a propagating 2D wavefunction with an added attractive potential. Basically I have to numerically solve the time-dependent Schrodinger equation (PDE with x,y,t ...
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Energy conservation in the solution of the Helmholtz equation
This might be a silly question, but I know very little about the theoretical properties finite elements, so here goes. Suppose you were to solve the Helmholtz equation (let's say in 2D) with a ...
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