Solve Laplace-Beltrami Equation on Geometrically Continuous Curves in Isogeometric Analysis

Abstract

<p indent=0mm>Research on isogeomatric analysis on a complex computational domain is one of the key problems. Normally a complex computational domain is composed by several simple patches with geometric continuity. Thus, it is necessary to discuss the relationship between the convergence of isogeometric analysis and geometric continuity. Solving Laplace-Beltrami equation on a geometrically continuous curve by analysis isogeometric analysis error theory is discussed. Based on this theoretic result, a method for choosing a spline space to obtain an optimal convergence rate in isogeometric solving is introduced and the numerical experiments are illustrated. Moreover, we validate the spline space, chosen by its approximate property, reaches the optimal convergence rate numerically. The results provide a theoretical basis for isogeometric analysis on complex computational domains.