Scattering by a Sound Soft Obstacle

We consider here the two-dimensional problem of scattering a time-harmonic incident field by a bounded sound soft obstacle D. Splitting up the total field into incident and scattered field, we have the following boundary value problem for the scattered field:

boundary value problem for sound soft object

The problem can be solved very efficiently by making a combined double- and single-layer potential ansatz,

combined double/single-layer potential ansatz
free field Green's function
denotes the free field Green's function for the Helmholtz equation in two dimensions. The resulting boundary integral equation can then be solved by a Nyström method which yields exponential convergence rates (cf. for details: Colton/Kress Inverse Acoustic and Electromagnetic Scattering Theory, Section 3.5, Springer-Verlag, 1998).

The images on the right-hand side show visualisations of the solution to this scattering problem for the case of a plane wave incident from the left. Each image shows the real part of the incident, scattered and total field computed with this method, respectively. Below you have the option of downloading an animation visualising the toatal field. Just click the button to start the animation.

Animated visualisation of the total field:

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Incident field:

Scattering from a sound soft obstacle, incident field

Scattered field:

Scattering from a sound soft obstacle, scattered field

Total field:

Scattering from a sound soft obstacle, total field

Page written and maintained by Tilo Arens
last change: 22 February 2001
Mathematical formulae by latex2html
Java animation applet by Markus Kraft and Tilo Arens