Simple and efficient acceleration of existing multigrid algorithms

A simple, robust, and efficient procedure to accelerate multigrid algorithms is discussed in detail. The approach used in this study is based on the BoostConv routine recently proposed by Citro et al. (“Efficient Stabilization and Acceleration of Numerical Simulation of Fluid Flows by Residual Recombination,” Journal of Computational Physics, Vol. 344, 2017, pp. 234–246). The present study starts from the idea that an existing multigrid code can be improved without any coding effort: a simple call to a black-box subroutine is enough to accelerate the iterative procedure. As a consequence, the proposed approach is well suited to be applied in real-life applications where the complexity of numerical codes is quite far from textbook standards. The application of BoostConv to a model problem is presented here. The algorithm is able to reduce the number of iterations required to get the target accuracy without increasing the computational time of the original code. As a consequence, BoostConv can be used on simple models, characterized by few degrees of freedom, or large numerical problems arising from the discretization of three-dimensional problems.