HIGHER-ORDER MULTILEVEL SOLVERS FOR THE EHL LINE AND POINT-CONTACT PROBLEM

This paper addresses the development of efficient numerical solvers fo r EHL problems from a rather fundamental point of view. A work-accurac y exchange criterion is derived, that can be interpreted as setting a limit to the price paid in terms of computing time for a solution of a given accuracy. The criterion can serve as a guideline when reviewing or selecting a numerical solver and a discretization. Earlier develop ed multilevel solvers for the EHL line and circular contact problem ar e tested against this criterion. This test shows that, to satisfy the criterion a second-order accurate solver is needed for the point conta ct problem whereas the solver developed earlier used a first-order dis cretization. This situation arises more often in numerical analysis, i .e., a higher order discretization is desired when a lower order solve r already exists. It is explained how in such a case the multigrid met hodology provides an easy and straightforward way to obtain the desire d higher order of approximation. This higher order is obtained at almo st negligible extra work and without loss of stability. The approach w as tested out by raising an existing first order multilevel solver for the EHL line contact problem to second order. Subsequently, it was us ed to obtain a second-order solver for the EHL circular contact proble m. Results for both the line and circular contact problem are presente d.