Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity
This work provides a practical solution for weak patch-coupling in isogeometric analysis, addressing a known bottleneck in computational mechanics.
The paper proposes a new construction of biorthogonal splines for isogeometric mortar methods that achieve local support and optimal approximation properties, yielding optimal results in finite deformation elasticity problems.
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.