2021/09/13 by Hussam Al Daas, Daas, Hussam Al, Pierre Jolivet +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Algebraic number #Applied mathematics #Bounded function #Coefficient matrix #Condition number #Discretization #Domain (mathematical analysis) #Domain decomposition methods #Eigenvalues and eigenvectors #Electromagnetic Scattering and Analysis #FOS: Mathematics #Finite element method #Linear system #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix decomposition #Numerical Analysis (math.NA) #Physics #Positive-definite matrix #Preconditioner #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2109.05908
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/09/13 · openalex publication_date 2021/09/13 · arxiv updated 2021/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 non-assembled matrices from discretized partial differential equations (PDEs). Therefore, DD methods were mainly successful when solving systems stemming from PDEs. In this paper, we present a fully algebraic multilevel DD method where the coarse space can be constructed locally and efficiently without any information besides the coefficient matrix. The condition number of the preconditioned matrix can be bounded by a user-prescribed number. Numerical experiments illustrate the effectiveness of the preconditioner on a range of problems arising from different applications.