Linear elasticity

Wrap-up

Julia Kowalski

Chair of Methods for Model-Based Development in Computational Engineering

2024-05-10

A seismic survey to investigate the subsurface


How to simulate?

The simplest numerical solution of the wave equation

\[\frac{\partial^2}{\partial t^2} \mathbf w = c \, \frac{\partial^2}{\partial x^2} \mathbf w\]

is done by means of finite difference approximations

Simulation of a 1d wave propagation at wave speed 1

Figure 1: Space-time plot at wave speed 1

Simulation of a 1d wave propagation at wave speed 0.5

Figure 2: Space-time plot at wave speed 0.5

Animated simulation of a 1d wave propagation

Figure 3: Wave animation of wave with speed 1

Animated simulation of two 1d superposed waves

Figure 4: Wave animation at superposed waves with wave speed \((1, 0.5)\)

Animated simulation of 1d single and superposed waves