Isospectral drum simulations using FreeFem++

Abstract This research presents a program implemented in the software FreeFem++ to calculate approximate numerical solutions by the finite element method in twoisospectral regions. The original discovery of these domains was made by Gordon, Webb and Wolpert in 1992. The main objective of this work is to examinethe relative differences in corresponding eigenvalues. This paper is a pioneer in demonstrating numerical simulations performed on the well-known problem “Can you hear the shape of a drum?” produced by Mark Kac. Mathematics Subject Classification (2000) 35J86 · 58J53 · 65N30 · 65K05