A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing. (English) Zbl 1216.65164
Summary: We present a data structure for parallel computing which is directly linked to geometric quantities of an underlying mesh and which is well adapted to the requirements of a general finite element realization. In addition, we define an abstract linear algebra model which supports multigrid methods extending our previous work [Comput. Vis. Sci. 1, No. 1, 27–40 (1997; Zbl 0970.65129)]. Finally, we apply the parallel multigrid preconditioner to several configurations in linear elasticity and we compute the condition number numerically for different smoothers, resulting in a quantitative evaluation of parallel multigrid performance.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Citations:
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