A locally based construction of analysis-suitable G1 multi-patch spline surfaces
Andrea Farahat, Mario Kapl, Aljaž Kosmač, Vito Vitrih
Abstract
Analysis-suitable G 1 (AS- G 1 ) multi-patch spline surfaces [7] are particular G 1 -smooth multi-patch spline surfaces, which ensure the construction of C 1 -smooth multi-patch spline spaces with optimal polynomial reproduction properties [20] . We present a local approach for the design of AS- G 1 multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS- G 1 multi-patch spline surface by approximating a given G 1 -smooth but non-AS- G 1 multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS- G 1 multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, with optimal rates of convergence over them.