Problem Controlled Grid Generation for the Numerical Solution of Partial Differential Equations,

摘要

Conventional finite element analysis of elliptic partial differential equations involves the establishment of a discretization grid on which an energy functional is defined and minimized. By including the positions of the grid nodes as unknowns in the energy functional, one can obtain the optimum placement of the nodes as well as the equation solution from the energy minimization. The potential of Chebyshev iterate acceleration in the inverse iteration eigensolution process has long been understood but not realized in practical applications. Its potential is readily realized in the sectioning algorithm by virtue of the fixed interval over which analysis is made.