Comparative study of the boundary element technique and the finite element method in two dimensional eigenvalue problem

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:5672867

Baradari, F

In this work the applicability of a ''Boundary Element method'' for the numerical solution of the Liouville and Helmholtz eigenvalue problem for different two dimensional geometries including a typical reactor configuration was investigated. The method is based on the discretization of the unknown along the boundary and Green's function representation of the governing equation. To compare the capability of this method with the finite element method, a finite element code which uses quadratic quadrilateral isoparametric elements was developed. A boundary element code was also written. These codes were used to determine the fundamental eigenvalue for several two dimensional geometries--square, ''L'' shaped, circular, and a quarter of a typical reactor core. The results of both codes were compared with each other and with analytical solutions where available. To optimize the computer time for the code based on the boundary element method, a powerful search technique called Fibonacci search was used to determine the fundamental eigenvalues. During the course of this study, it was found that eliminating the imaginary part of the fundamental solution of the Helmholtz equation produced an instability in the result. The results show that, due to the use of the iteration procedure in the boundary element method to evaluate the determinant of the deduced matrix, more computer time is required for the boundary element solution than the finite element solution. However, the results obtained on the basis of the boundary element technique are more accurate than those from the finite element method.

• OSTI ID: 5672867
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
220100* -- Nuclear Reactor Technology-- Theory & Calculation
BOUNDARY-VALUE PROBLEMS
COMPARATIVE EVALUATIONS
COMPUTER CODES
EIGENVALUES
FINITE ELEMENT METHOD
GEOMETRY
MATHEMATICAL MODELS
MATHEMATICS
NUMERICAL SOLUTION
REACTOR COMPONENTS
REACTOR CORES