Regularly striped preconditioner for implicit clothing simulation

Abstract

This paper investigates the question of whether the Jacobi preconditioner can be made to run faster by including a few additional outlying diagonals, for the case of mesh-based implicit clothing simulation. For the given N x N block system matrix A, we investigate two regularly striped (RS) preconditioners: (1) 3-RS which has two symmetric outlying diagonals with offset N/2 from the main diagonal and (2) 5-RS which has four symmetric outlying diagonals with offsets N/3 and 2N/3 from the main diagonal. This paper finds that both 3- and 5-RS preconditioners are consistently superior to the Jacobi preconditioner in the performance. Based on the loop iteration count and time measurement, we finally recommend 5-RS rather than 3-RS.