Multilevel Solution of Integral and Integro-differential Equations in Contact Mechanics and Lubrication

Since their introduction multilevel techniques have influenced many fields in science. Wherever large scale computations are needed, e.g. fundamental research, applied research and design and development of technical equipment, they have reduced computational cost and/or created the ability to solve increasingly complex and extensive problems. In this paper we present an example from the field of tribology, i.e. the science and technology of interacting surfaces in relative motion, or, to use a more popular definition, the science of friction, lubrication and wear. In particular we will describe the essential steps leading to an efficient multilevel solver for the simulation of lubricated concentrated contacts. However, the techniques described in this paper are neither restricted to this problem, nor are they restricted to the field of contact mechanics and lubrication. In fact, they can be of interest for any problem described by Fredholm integral and integro-differential equations.