On efficient solution of linear systems arising in \(hp\)-FEM. (English) Zbl 1157.65496
Kunisch, Karl (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007. Berlin: Springer (ISBN 978-3-540-69776-3/hbk). 199-206 (2008).
Summary: The author studies the static condensation of internal degrees of freedom which allows for efficient solution of linear algebraic systems arising in higher-order finite element methods. On each element, the static condensation eliminates the degrees of freedom corresponding to the internal (or bubble) basis functions. The elimination is local in elements and can be done in parallel. The resulting Schur complement system is considerably smaller and, moreover, it has less nonzero elements and better condition number in comparison with the original system. This paper focuses on the numerical performace of the static condensation and shows its CPU time efficiency.
For the entire collection see [Zbl 1145.65001].
For the entire collection see [Zbl 1145.65001].
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 65F10 | Iterative numerical methods for linear systems |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
