The Mathematica Journal
Volume 9, Issue 3

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T R O T T ' S C O R N E R
The Sound of an Unusual Drum
Michael Trott

The eigenvalue spectrum of the Laplace operator (and its negative) is of fundamental importance in mathematics and physics. In this column, the lowest eigenvalues of a fractal 2D drum are calculated using a finite element discretization. The corresponding eigenfunctions and their gradients are visualized. The cumulative number of the first 1000 eigenvalues is calculated and compared with Weyl's asymptotic formula.

*Notebook


*PDF


*HTML

*Introduction

*Construction of the Drum

*Solving the Eigenvalue Problem

*Visualization of the Eigenfunctions

*The Weyl Law

*References

Michael Trott
Special Functions Developer
Wolfram Research, Inc.
mtrott@wolfram.com


     
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