Computer visions for the eigenvalue problems of embedded surfaces and plane domains (Q2919588)

The present paper focuses on the numerical computation and the computer graphics of the eigenvalues and eigenfunctions for the eigenvalue problems of the Laplacian on compact embedded surfaces.NEWLINENEWLINE The first part is an introduction into the nature.NEWLINENEWLINE The second part presents the finite element method for the case of eigenvalues problems defined on a bounded domain \(\Omega\subset{\mathbb R}^{n}\) with piecewise smooth boundary \(\partial\Omega\).NEWLINENEWLINE The third part concerns the numerical results of eigenfunctions. One shows the computer graphics for the eigenvalue problems of the Laplacian on compact embedded surfaces: unit sphere, the embedded torus and the dumbells, comparing the exact eigenvalues with the numerical results.NEWLINENEWLINE The fourth section presents the variation of the eigenvalues by deforming either the distance between the centers or the radii, giving also the numerical results.NEWLINENEWLINE Some main observations are within the fifth section.