William Hinsberg, Joy Cheng, et al.
SPIE Advanced Lithography 2010
A solution strategy is proposed and implemented for taking advantage of the hierarchical structure of linear equation sets arising from the p‐type finite element method using a hierarchical basis function set. The algorithm dynamically branches to either direct or iterative solution methods. In. the iterative solution branch, the substructure of the finite element equation set is used to generate a lower order preconditioner for a preconditioned conjugate gradient (PCG) method. The convergence rate of the PCG algorithm is monitored to improve the heuristics used in the choice of the preconditioner. The robustness and efficiency of the method are demonstrated on a variety of three dimensional examples utilizing both hexahedral and tetrahedral mesh discretizations. This strategy has been implemented in a p‐version finite element code which has been used in an industrial environment for over two years to solve mechanical design problems. Copyright © 1992 John Wiley & Sons, Ltd
William Hinsberg, Joy Cheng, et al.
SPIE Advanced Lithography 2010
Imran Nasim, Melanie Weber
SCML 2024
Jaione Tirapu Azpiroz, Alan E. Rosenbluth, et al.
SPIE Photomask Technology + EUV Lithography 2009
Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering