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Buffa, Annalisa; Harbrecht, Helmut; Kunoth, Angela; Sangalli, Giancarlo

BPX-preconditioning for isogeometric analysis. (English) Zbl 1286.65151

Comput. Methods Appl. Mech. Eng. 265, 63-70 (2013).
Summary: We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or NURBS mapping which we assume to be regular. The numerical solution of the PDE is computed by means of tensor product B-splines mapped onto the physical domain. We construct additive multilevel preconditioners and show that they are asymptotically optimal, i.e., the spectral condition number of the resulting preconditioned stiffness matrix is independent of \(h\). Together with a nested iteration scheme, this enables an iterative solution scheme of optimal linear complexity. The theoretical results are substantiated by numerical examples in two and three space dimensions.

Cited in 1 Review
Cited in 38 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
65D17 Computer-aided design (modeling of curves and surfaces)
35Jxx Elliptic equations and elliptic systems

Keywords:

isogeometric analysis; elliptic PDE; B-splines; multilevel preconditioning; BPX-preconditioner; uniformly bounded condition number

Software:

IETI
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References:

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