On the Multilevel Adaptive Iterative Method

The multilevel adaptive iterative method is a technique for solving the sparse matrix equations that typically arise from partial differential systems. Its core consists of a relaxation scheme and an active set strategy The active set is used to monitor where the iteration efficiently reduces the error. It is incrementally updated by exploiting the current solution and the matrix structure, and most arithmetic operations are restricted to it. The algorithm can be extended to a multilevel structure by additionally tracing the dependencies between unknowns on different levels. It improves the robustness and efficiency of classical multilevel methods; in particular, it is an almost ideal supplement to adaptive refinement techniques.