{"id":30206,"date":"2020-08-21T12:54:27","date_gmt":"2020-08-21T12:54:27","guid":{"rendered":"http:\/\/tugraztestweb.asol.at\/gesamtverzeichnis\/unkategorisiert\/analysis-of-boundary-element-methods-for-laplacian-eigenvalue-problems-2\/"},"modified":"2020-08-21T14:55:27","modified_gmt":"2020-08-21T12:55:27","slug":"analysis-of-boundary-element-methods-for-laplacian-eigenvalue-problems-ebook","status":"publish","type":"product","link":"https:\/\/tugraztestweb.asol.at\/en\/gesamtverzeichnis\/bauingenieurwissenschaften\/analysis-of-boundary-element-methods-for-laplacian-eigenvalue-problems-ebook\/","title":{"rendered":"Analysis of Boundary Element Methods for Laplacian Eigenvalue Problems"},"content":{"rendered":"

Sorry, this entry is only available in Deutsch<\/a>.<\/p>

This book provides an analysis of the boundary element method for the
\nnumerical solution of Laplacian eigenvalue problems. The representation
\nof Laplacian eigenvalue problems in the form of boundary integral
\nequations leads to nonlinear eigenvalue problems for related boundary
\nintegral operators. The concept of holomorphic Fredholm operator
\nfunctions is used for the analysis of the boundary integral formulations
\n of Laplacian eigenvalue problems. A convergence and error analysis for
\nthe Galerkin approximation of eigenvalue problems for holomorphic
\ncoercive operator functions is established. These results are applied to
\n the Galerkin boundary element discretization of Laplacian eigenvalue
\nproblems. Different methods for the solution of algebraic nonlinear
\neigenvalue problems such as inverse iteration, Rayleigh functional
\niterations and Kummer\u2018s method are presented. For the latter method a
\nnumerical analysis for simple and multiple eigenvalues is given. In a
\nnumerical example, a boundary element and a finite element approximation
\n of a Laplacian eigenvalue problem are compared. The theoretical results
\n of the analysis of the boundary element method could be confirmed.<\/p>","protected":false},"excerpt":{"rendered":"

Sorry, this entry is only available in Deutsch<\/a>.<\/p>\n

This book provides an analysis of the boundary element method for the
\nnumerical solution of Laplacian eigenvalue problems. The representation
\nof Laplacian eigenvalue problems in the form of boundary integral
\nequations leads to nonlinear eigenvalue problems for related boundary
\nintegral operators. The concept of holomorphic Fredholm operator
\nfunctions is used for the analysis of the boundary integral formulations
\n of Laplacian eigenvalue problems. A convergence and error analysis for
\nthe Galerkin approximation of eigenvalue problems for holomorphic
\ncoercive operator functions is established. These results are applied to
\n the Galerkin boundary element discretization of Laplacian eigenvalue
\nproblems. Different methods for the solution of algebraic nonlinear
\neigenvalue problems such as inverse iteration, Rayleigh functional
\niterations and Kummer\u2018s method are presented. For the latter method a
\nnumerical analysis for simple and multiple eigenvalues is given. In a
\nnumerical example, a boundary element and a finite element approximation
\n of a Laplacian eigenvalue problem are compared. The theoretical results
\n of the analysis of the boundary element method could be confirmed.<\/p>\n","protected":false},"featured_media":39825,"comment_status":"open","ping_status":"closed","template":"","meta":[],"yoast_head":"\n\n\n\n\n\n\n\n\n\n\t\n\t\n\n\n\t\n