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An economical aggregation algorithm for algebraic multigrid (AMG). (English) Zbl 1290.65027

Summary: The aggregation-based algebraic multigrid (AMG) method is a widely studied technique of robustness for large-scale linear systems. Some previous aggregation algorithms, belonging to a part of aggregation-based AMG method, exhibit certain excellent properties. These aggregation methods, however, have to aggregate every grid points so that these methods lead expensive computation with grid points increasing. In the paper, a property that the aggregations hold particular structure associated with certain condition is discovered to damp the computation of aggregation algorithms. Meanwhile, this property is under the condition of the system matrix derived from the 9-point finite difference method (FDM) and the particular setting of grid numbers. Furthermore, the conclusions about multilevel, such as the setting rule of grid numbers and corresponding theoretical analysis, are obtained from the extension of two level issues. Computational experiments demonstrate that the CPU time of new aggregation algorithm which generates the same aggregations with previous aggregation algorithms, keeps on a low level evidently, even for the linear systems of millions grade.

MSC:

65F10 Iterative numerical methods for linear systems
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N06 Finite difference methods for boundary value problems involving PDEs
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