## Eigenmodes of isospectral drums |

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25 eigenvalues accuracy Adaptive mesh refinement Afflne Scaling Method Aiping Liao algorithm approximation basis functions boundary conditions boundary dCl BUSER Coleman and Wei computing the eigenvalues corner of dCl Descloux and Tolley differences and mode domain decomposition method drums agree drums of Figure due to Descloux efficient eigenfunctions EIGENMODES eigenpair eigenvalue estimates elliptic operators expansion finite differences finite element idea finite element methods G WW Global Optimization GWW drums GWW isospectral drums hear the shape interface interior angle iteration Kudrolli 17 Laplacian linear machine precision Martorell 18 Math MATLAB matrix Method for Nonlinearly method of particular microwave experiments Minimization mode matching method pair of isospectral parameter particular solutions planar regions PLTMG polygonal isospectral problem proof of isospectrality reentrant corners singularity spectra Sridhar and Kudrolli standard numerical subdivisions subfunction Uj superconvergent Theory Center Tolley 9 Tolley were able transplantation proof triangle Trust Region values Wei Yuan Yuying