Non-overlapping domain decomposition solution schemes for structural mechanics isogeometric analysis

Abstract

Isogeometric analysis (IGA) is a novel computer aided engineering technique that addresses diverse problems in computational mechanics [1–4], all under the exact geometric representation. Apart from the exact geometric representation, the high continuity of IGA shape functions enhances the accuracy and robustness of the method. However, the price to pay is that the resulting matrices are denser, with increased bandwidth and overlapping which make the solution of large-scale problems more computationally intensive. As a result, effective solution techniques are still considered an open issue for further research. In this paper, an innovative family of solution schemes based on domain decomposition methods (DDM) is proposed, that significantly reduces the computational cost. Specifically, the solution of the global system is performed with the preconditioned conjugate gradient algorithm (PCG) whose preconditioning step is evaluated with a dual DDM where special care is taken to avoid the overlapped subdomains which are inherent in decomposed IGA formulation due to the increased continuity of the shape functions.