A non-overlapping dual-primal domain decomposition solver for isogeometric collocation methods

Isogeometric collocation (IGA-C) simulation methods have been introduced as alternative to isogeometric Galerkin (IGA-G) formulations due to their potential in reducing the computational cost for the same accuracy. However, the implementation of efficient numerical schemes for solving large scale IGA-C formulations is more algorithmically and computationally demanding than the IGA-G simulations. In this context, the isogeometric analysis of complex geometric domains requires the representation of the domain as the union of multi-patch domains, which provides a natural decomposition for the application of non-overlapping domain decomposition methods (DDM). Although, this type of solution domain decomposition schemes have been applied for IGA-G simulations, their application to IGA-C problems is not straightforward, as it does not only requires algebraic modifications to handle the non-symmetric system matrices, but also a thorough numerical evaluation of the solution algorithms, given the limited mathematical framework available for these cases. In this work, a non-overlapping DDM has been implemented for solving IGA-C problems on multi-patch-domains. The proposed numerical scheme is based on the dual-primal DDM (P-FETI-DP), properly modified to address non-symmetric matrices, for accelerating as preconditioner the generalized minimal residual method (GMRES) for the solution of the resulting algebraic systems. In this context, an assessment of the computational efficiency and numerical scalability of the proposed domain decomposition solution scheme is performed on characteristics test problems.