Overlapping Additive Schwarz (OAS) preconditioners are here constructed for isogeometric collocation discretizations of the system of linear elasticity in both two and three space dimensions. Isogeometric collocation methods are recent variants of isogeometric analysis based on the numerical approximation of the strong form of partial differential equations at appropriate collocation points. Numerical results in two and three dimensions show that two-level OAS preconditioners are scalable in the number of subdomains N, quasi-optimal with respect to the mesh size h and optimal with respect to the spline polynomial degree p. Moreover, two-level OAS preconditioners are more robust than one-level OAS and non-preconditioned GMRES solvers when the material tends to the incompressible limit, as well as in the presence of strong deformation of the NURBS geometry.

重叠叠加式Schwarz（OAS）预处理器在此构造，用于在两个和三个空间尺寸中线性弹性系统的等几何搭配离散化。等几何搭配方法是等几何分析的最新变体，它基于在适当的搭配点处偏微分方程强形式的数值逼近。二维和三维的数值结果表明，两级OAS预处理器在子域N上可扩展，相对于网格大小h为准最优，而对于样条多项式p为最优。此外，当材料趋于不可压缩的极限以及存在NURBS几何形状的强烈变形时，两级OAS预处理器比一级OAS和非预处理GMRES求解器更强大。