Numerical Methods for Solution of Finite Element Systems

by Edward L. Wilson, Univ of California, United States,

Document Type: Proceeding Paper

Part of: Computer Utilization in Structural Engineering


A personal summary of solution methods for the static and dynamic analysis of finite element systems, which have been developed during the past 30 years, will be given. Numerical techniques for the solution of equations by direct or iteration methods, dynamic response analysis and the calculation of eigenvectors or load-dependent Ritz vectors will be discussed. The first automated finite element programs used iteration methods. With the transfer of banded and space matrices techniques from the field of numerical analysis the current generation of computer programs use frontal or profile methods for the factorization of the global stiffness matrix. The subspace iteration method provided one of the first general techniques to calculate the exact eigenvalues for very large systems. Recent research on the use of load dependent vectors have reduced the computational requirements significantly. Solution methods which have previously been rejected may prove to be effective on computers with multiple processors.

Subject Headings: Finite element method | Dynamic loads | Matrix (mathematics) | System analysis | Dynamic analysis | Computer analysis | Computer software | Structural response

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