DMS Applied Mathematics Seminar

Speaker: Jiguang Sun (Michigan Technological University)

Title: Finite Element Methods for Eigenvalue Problems

Abstract: The numerical solution of eigenvalue problems is of fundamental importance in many scientific and engineering applications, such as structural dynamics, quantum chemistry, electrical networks, magnetohydrodynamics, and control theory. Due to the flexibility in treating complex structures and rigorous theoretical justification, finite element methods, including conforming finite elements, non-conforming  finite  elements, mixed finite elements, discontinuous Galerkin methods, etc., have been popular for eigenvalue problems of partial differential equations. In this talk, we shall introduce finite element approximations for several typical problems, including the Dirichlet eigenvalue problem, the biharmonic eigenvalue problems, Maxwell's eigenvalue problem, and the new quad-curl eigenvalue problem. Furthermore, we shall discuss two non-selfadjoint eigenvalue problems: the transmission eigenvalue problem and the Steklov eigenvalue problem. To solve the resulting matrix eigenvalue problems, a new algebraic eigensolver is developed and some recent progresses are presented.