Performance comparison of interpolation operators of multigrid methods based on distance weight and area (volume) intersection approaches Part I: Finite volume discretization

The construction of efficient interpolation/restriction operators is a key component for the successful implementation of multigrid (MG) methods. Although numerous interpolation operators for MG methods have been developed, a performance comparison of the methods has been rarely reported. In this study, an interpolation operator based on distance weight was newly proposed, and the performance of the method was compared with that of an interpolation operator by area (volume) intersection for the finite volume discretization of an elliptic equation. Results showed that interpolation by distance weight was more efficient than by area (volume) interaction mainly because of the smaller number of MG cycles to convergence. Moreover, the CPU time of MG methods based on the present distance interpolation was linearly proportional to the number of unknowns for 2D and 3D problems.