Parallel solution of modular ODEs with application to rolling bearing dynamics

In this paper, we study a model of rolling that yields a system of differential equations with a low degree of dependence between the different bodies and, hence, a Jacobian with a sparse structure. We utilize this specific topology in the integration of the ODEs with a stiff solver. Due to the weak coupling between the different machine elements in this rolling bearing model, the procedure for obtaining a solution can be performed efficiently on parallel computers. In this paper, we study the integrator CVODE, modified to enable a parallel integration of different subsystems; this entails function evaluations, the Jacobian computations and the solution of the linear systems of equations. The benefit of using parallel computers for this problem is verified by several test cases run on MIMD computers.