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

TL;DR

This paper introduces a new biorthogonal spline basis for isogeometric mortar methods that offers local support and optimal approximation, improving finite deformation elasticity simulations.

Contribution

It presents a novel univariate and multivariate construction of biorthogonal splines with optimal properties for isogeometric analysis.

Findings

Numerical results confirm optimal approximation with large deformations.

The basis has local support and inherits properties from univariate to multivariate cases.

The method enhances mortar techniques in elasticity problems.

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.