Recent developments in the solution of models of rough contact have demonstrated the advantages of fast matrix multiplication methods in increasing the size of problem that can usefully be solved. However, to date, no attempt has been made to compare these methods with existing approaches. In this paper a survey of solution methods reveals that three main classes of solution method have been developed: active set methods with direct matrix solution; active set methods with iterative matrix solvers; iterative methods based on fast matrix multiplications. The best features of each class are assembled from the literature and combined to formulate a ‘‘best-possible’’ algorithm in each class. These algorithms are implemented and compared, with emphasis on their solution speed, accuracy and memory requirements. For smaller problems with fewer than 2000 grid points in contact, the direct matrix solution method proves to be most efficient, and is always the most accurate. However, the method is limited by memory requirements as the contact region increases. For large problems with more than 2000 grid points in contact, the multilevel multisummation approach requires less memory, and performs faster, but gives errors in predicted pressure and contact region of approximately 0.5%. The active set method with iterative matrix solver requires less memory than direct matrix solution, is more accurate than the multilevel multisummation approach, but is always slower than one of the other methods.
