Implementation and performance evaluation of a hierarchical parallel solver for saddle point problems on a GPU cluster
Hiroto Tadano · Journal of Advanced Simulation in Science and Engineering · 2023
Recently, we have proposed an efficient method for solving saddle point problems using their block structure. Instead of solving an original problem directly, this method solves a linear system with multiple right-hand sides. Then it computes solution vectors of the original problem using a solution matrix of this linear system. Since solving a linear system with multiple right-hand sides is the most time-consuming part of our method, it is desirable to solve that as fast as possible. In this paper, a parallelization strategy of our method is proposed, and our method is implemented on a parallel computation environment. Moreover, to achieve further speed-up of our method, this paper also proposes an implementation strategy using GPUs. Numerical experiments illustrate the parallel performance of our method on a GPU cluster.