A Robust Algebraic Multilevel Domain Decomposition Preconditioner for Sparse Symmetric Positive Definite Matrices

Domain decomposition (DD) methods are widely used as preconditioner techniques. Their effectiveness relies on the choice of a locally constructed coarse space. Thus far, this construction was mostly achieved using nonassembled matrices from discretized partial differential equations (PDEs). Therefore, DD were mainly successful when solving systems stemming PDEs. In paper, we present fully algebraic multilevel method where space can be and efficiently without any information besides coefficient matrix. The condition number preconditioned matrix bounded by user-prescribed number. Numerical experiments illustrate range problems arising different applications.