Description
Finite Element Methods for Eigenvalue Problems
Chapman & Hall/CRC Monographs and Research Notes in Mathematics Series
Authors: Sun Jiguang, Zhou Aihui
Language: EnglishSubjects for Finite Element Methods for Eigenvalue Problems:
Keywords
Eigenvalue Problem; hilbert; Transmission Eigenvalue; space; Lagrange Elements; rayleigh; Transmission Eigenvalue Problem; quotient; Generalized Eigenvalue Problems; lipschitz; Unit Square; domain; Galerkin Orthogonality; generalized; Fourth Order Problem; sesquilinear; Friedrichs Inequality; form; Dirichlet Eigenvalue; algebraic; Algebraic Multiplicity; Mixed Fem; Geometric Multiplicity; Reference Triangle; Arnoldi Method; Triangular Mesh; Local Stiffness Matrix; Lipschitz Domain; Unit Ball; Rayleigh Quotient; Arnoldi Factorization; Posteriori Error Analysis; St 2nd 3rd 4th 5th; QR Method; Rayleigh Quotient Iteration
· 15.6x23.4 cm · Hardback
Description
/li>Contents
/li>Biography
/li>
This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.
Introduction of Eigenvalue Problems. Preliminaries. Finite Elements. The Laplacian Eigenvalue Problems. The Maxwell’s Eigenvalue Problems. The Bi-Harmonic and Quad-Curl Eigenvalue Problems. Eigenvalue Problems of Schrödinger Operator. The Transmission Eigenvalue Problems. Techniques for Matrix Eigenvalue Problems. Appendix.