Colloquium-Finite Element/Holomorphic Operator-Value Function Approach for Nonlinear Eigenvalue Problems

Time: Nov 19, Friday 1-2 PM

Location: Zoom

Prof. Jiguang Sun (Michigan Tech University)

Title: Finite Element/Holomorphic Operator-Value Function Approach for Nonlinear Eigenvalue Problems

Abstract: We propose a new approach combining the holomorphic operator value function and finite elements for some nonlinear eigenvalue problems. The eigenvalue problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. Finite element methods are used for discretization. The convergence of eigenvalues/eigenvectors is proved using the abstract approximation theory for holomorphic operator functions. Then the spectral indicator method is extended to compute the eigenvalues. The proposed approach is employed to compute the band structures of photonic crystals.