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Bounding the influence of domain parameterization and knot spacing on numerical stability in isogeometric analysis. (English) Zbl 1295.65116
Summary: Isogeometric Analysis (IGA) was introduced by T. J. R. Hughes et al. [Comput. Methods Appl. Mech. Eng. 194, No. 39–41, 4135–4195 (2005; Zbl 1151.74419)] as a new method to bridge the gap between the geometry description and numerical analysis. Similar to the finite element approach, the IGA concept to solve a partial differential equation leads to a (linear) system of equations. The condition number of the coefficient matrix is a crucial factor for the stability of the system. It depends strongly on the domain parameterization, which provides the isogeometric discretization. In this paper we derive a bound for the condition number of the stiffness matrix of the Poisson equation. In particular, we investigate the influence of the domain parameterization and the knot spacing on the stability of the numerical system. The factors appearing in our bound reflect the stability properties of a given domain parameterization.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D17 Computer-aided design (modeling of curves and surfaces)
Software:
ISOGAT; FEAPpv
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