File:Eigenmodes of GWW Isospectral Domains.png
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editDescriptionEigenmodes of GWW Isospectral Domains.png |
English: A plot of the eigenmode amplitudes of the Laplace operator (with Dirichlet boundary conditions) on two domains proposed by Gordon, Webb and Wolpert. Cyan areas have positive amplitude, Yellow areas have negative amplitude, and black areas have zero amplitude.
Note the eigenvalues are all equal, while the domains are not rigid-transformation equivalent. These were all calculated using a home-made Finite-Element solver in Python, which first makes a triangulation of the domains using a wrapper of the Triangle library, and then solves a discretized diagonalization problem based on the variational formulation of the Laplacian diagonalization problem, in the subspace of continuous piecewise linear functions (where the "pieces"\domains where the function is linear are simply the aforementioned triangles). The diagonalization itself uses Scipy's sparse implicitly restarted Lanczos method, and the array manipulations were done using numpy. |
Date | |
Source | Own work |
Author | Rotem Shalev |
The image itself is a merger and color inversion of two different plots (each of which were individually made with Python)
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current | 12:43, 5 November 2021 | 1,280 × 480 (415 KB) | Sonicrs (talk | contribs) | Uploaded own work with UploadWizard |
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