Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity

Abstract

A new construction of biorthogonal splines for isogeometric mortar methods is proposed. The biorthogonal basis has a local support and, at the same time, optimal approximation properties, which yield optimal results with mortar methods. We first present the univariate construction, which has an inherent crosspoint modification. The multivariate construction is then based on a tensor product for weighted integrals, whereby the important properties are inherited from the univariate case. Numerical results including large deformations confirm the optimality of the newly constructed biorthogonal basis.

arXiv commentbiorthogonal basis, finite deformation, isogeometric analysis, mortar methods, multi-patch geometries

References in corpus (7)

• Isogeometric analysis: an overview and computer implementation aspects
• Nitsche's method for two and three dimensional NURBS patch coupling
• Isogeometric mortar methods
• Multipatch Discontinuous Galerkin Isogeometric Analysis
• Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry
• Discontinuous Galerkin Isogeometric Analysis on Non-matching Segmentation: Error Estimates and Efficient Solvers
• A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis

Cited by in corpus (8)

• Towards higher-order accurate mass lumping in explicit isogeometric analysis for structural dynamics
• Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models
• A comparison of smooth basis constructions for isogeometric analysis
• Algebraic multigrid methods for saddle point systems arising from mortar contact formulations
• Scalable computational kernels for mortar finite element methods
• A hybrid isogeometric approach on multi-patches with applications to Kirchhoff plates and eigenvalue problems
• Easy and Efficient preconditioning of the Isogeometric Mass Matrix
• A dual lumping procedure for static condensation in mixed NURBS-based isogeometric elements with optimal convergence rates for arbitrary open knot vectors