Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity. (English) Zbl 1440.74451
Summary: 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.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65D07 | Numerical computation using splines |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 74B05 | Classical linear elasticity |
Keywords:
biorthogonal basis; finite deformation; isogeometric analysis; mortar methods; multi-patch geometriesReferences:
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