Advanced finite element techniques in reactor theory

The solution to the Helmholtz equation, encountered in nuclear reactor theory, is obtained with the finite element technique, employing linear and quadratic Lagrange and cubic Hermite interpolation polynomials, and compared with the classical finite difference result. Transforming the Helmholtz equation into a weak form, the application of the finite element method is possible. Comparing the eigenvalues obtained using different numerical schemes with analytic results, the cubic Hermite finite element technique yields the most accurate results and highest order of convergence for identical mesh spacing. Optimization of the computer programs may demonstrate considerable savings in computer time using the cubic Hermite finite element technique. The behavior of the solution for each of the various numerical methods is investigated as material discontinuities become more pronounced