We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimize the sum of the first Dirichlet Laplace–Beltrami operator eigenvalues over a given number of partitions of a surface. We consider a method based on eigenfunction segregation and perform calculations using modern high performance computing techniques. We first test the accuracy of the method in the case of three partitions on the sphere then explore the problem for higher numbers of partitions and on other surfaces.
Cite this article
Charles M. Elliott, Thomas Ranner, A computational approach to an optimal partition problem on surfaces. Interfaces Free Bound. 17 (2015), no. 3, pp. 353–379DOI 10.4171/IFB/346