Article ID Journal Published Year Pages File Type
6917750 Computer Methods in Applied Mechanics and Engineering 2013 17 Pages PDF
Abstract
We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a uniform mesh on a unit interval, the explicit representation of B-spline basis functions for a fixed mesh size h is given for p=2,3,4 and for C0- and Cp-1-continuity. The presented methods show h- and (almost) p-independent convergence rates. Supporting numerical results for convergence factor and iterations count for AMLI cycles (V-, linear W-, nonlinear W-) are provided. Numerical tests are performed, in two-dimensions on square domain and quarter annulus, and in three-dimensions on quarter thick ring.
Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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