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• W2062932012 abstract "A class of algebraic multi-p methods for solving the p-version of the finite element equations is first presented and discussed. It is then shown howthese multi-p methods can be used as preconditioners for the conjugate gradient (CG) method. In particular, it is shown that given any preconditioner Mp to CG, a multi-p preconditioner Bp based on Mp can be constructed, which leads to a smaller condition number (and hence faster convergence). Numerical experiments on representative problems indicate that the condition numbers after multi-p preconditionings are, in fact, independent of p. The numerical results also show greater efficiency for the preconditioned conjugate gradient (PCG) method with the multi-p preconditioners in terms of number of iterations and CPU time when compared with two sophisticated linear equation solvers: (1) a direct frontal solver specially designed for the p-version of the finite element analysis; (2) a highly tuned PCG code in ITPACK2C, http://www.netlib.org.itpack/, 1994. Preliminary comparisons of the number of iterations are also made with ROCKITS [Solvers International, Inc., Boulder, CO, 1994], a new commercial code used for the p-version." @default.
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• W2062932012 date "1997-11-01" @default.
• W2062932012 modified "2023-09-24" @default.
• W2062932012 title "Multi-p Preconditioners" @default.
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• W2062932012 doi "https://doi.org/10.1137/s1064827595279368" @default.
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