Assessment of methods for the numerical solution of the fredholm integral eigenvalue problem

W. Betz, I. Papaioannou, D. Straub

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

The computational efficiency of random field representations with the Karhunen-Loève expansion relies on the numerical solution of a Fredholm integral eigenvalue problem. In this contribution, different methods for this task are compared. These include the finite element method (FEM), the finite cell method (FCM) and the Nyström method. For the FEM with linear basis functions, two different approaches to treat the covariance function in the integral eigenvalue problem are investigated: L2-projection and linear interpolation of the covariance function between the nodes of the finite element mesh. The FCM is a novel approach, originally presented in (Parvizian et al., Comput Mech, 41: 121-133, 2007) for the solution of elliptic boundary value problems. This method is based on an extension to the FEM but avoids mesh generation on domains of complex geometric shape. In the Nyström method, a numerical integration rule is applied to transform the integral eigenvalue problem to a matrix eigenvalue problem. It is shown that the expansion optimal linear estimation (EOLE) method proposed in (Li & Der Kiureghian, J Eng Mech-ASCE, 119(6): 1136-1154, 1993) constitutes a special case of the Nyström method. The behavior of all methods is investigated with respect to a two-dimensional example of a plate with a hole.

Original languageEnglish
Title of host publicationSafety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
Pages2031-2038
Number of pages8
StatePublished - 2013
Event11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 - New York, NY, United States
Duration: 16 Jun 201320 Jun 2013

Publication series

NameSafety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013

Conference

Conference11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
Country/TerritoryUnited States
CityNew York, NY
Period16/06/1320/06/13

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