Restricted Additive Schwarz Method with Harmonic Overlap
نویسندگان
چکیده
In this paper, we introduce a new Schwarz preconditioner and with a new coarse space. We construct the preconditioner by grouping together, in one preconditioner, features from the additive overlapping Schwarz methods, from iterative substructuring methods and from a class of restricted additive Schwarz methods. The preconditioner is symmetric and considered as a symmetrized version of restricted additive Schwarz preconditioners. We also enhance the preconditioner with a new coarse space which is simple, easily parallelizable, has smaller stencil, and has one degree of freedom per substructure and can be used in problems with unstructured meshes. We study the spectral bounds for the method and discuss the several advantages of this preconditioners. Numerical results theory will be provided.
منابع مشابه
A Restricted Additive Schwarz Preconditioner with Harmonic Overlap for Symmetric Positive Definite Linear Systems ; CU-CS-920-01
متن کامل
RASHO: A Restricted Additive Schwarz Preconditioner with Harmonic Overlap
A restricted additive Schwarz (RAS) preconditioning technique was introduced recently for solving general nonsymmetric sparse linear systems [1, 3, 4, 7, 8, 9, 11]. The RAS preconditioner improves the classical additive Schwarz preconditioner (AS), [10], in the sense that it reduces the number of iterations of the iterative method, such as GMRES, and also reduces the communication cost per iter...
متن کاملIs Additive Schwarz with Harmonic Extension Just Lions’ Method in Disguise?
The Additive Schwarz Method with Harmonic Extension (ASH) was introduced by Cai and Sarkis (1999) as an efficient variant of the additive Schwarz method that converges faster and requires less communication. We show how ASH, which is defined at the matrix level, can be reformulated as an iteration that bears a close resemblance to the parallel Schwarz method at the continuous level, provided th...
متن کاملRestricted Additive Schwarz Preconditioners with Harmonic Overlap for Symmetric Positive Definite Linear Systems
A restricted additive Schwarz (RAS) preconditioning technique was introduced recently for solving general nonsymmetric sparse linear systems. In this paper, we provide one-level and two-level extensions of RAS for symmetric positive definite problems using the so-called harmonic overlaps (RASHO). Both RAS and RASHO outperform their counterparts of the classical additive Schwarz variants (AS). T...
متن کاملOptimized Additive Schwarz with Harmonic Extension as a Discretization of the Continuous Parallel Schwarz Method
The additive Schwarz method with harmonic extension (ASH) was introduced by Cai and Sarkis (1999) as an efficient variant of the additive Schwarz method that converges faster and requires less communication. We show that ASH can also be used with optimized transmission conditions to obtain faster convergence. We show that when the decomposition into subdomains contains no cross points, optimize...
متن کامل