IG-LSPIA: Least Squares Progressive Iterative Approximation for Isogeometric Collocation Method

The isogeometric collocation method (IGA-C), which is a promising branch of analysis (IGA), can be considered fitting the load function with combination numerical solution and its derivatives. In this study, we develop an iterative method, least-squares progressive-iterative approximation (IG-LSPIA), to solve problem in method. IG-LSPIA starts initial blending function, where control coefficients are combined B-spline basis functions their A new generated by constructing differences for points (DCP) (DCC), then adding DCC corresponding coefficients. procedure performed iteratively until stop criterion reached. We prove convergence show that computation complexity each iteration related only number unrelated Moreover, incremental algorithm designed; it alternates knot refinement desired precision achieved. After refinement, result last round iterations used generate iteration, thereby saving great computation. Experiments proposed stable efficient. three-dimensional case, total time saved twice compared traditional