Optimizing the number of multigrid cycles in the full multigrid algorithm
Copyright policy )Optimizing the number of multigrid cycles in the full multigrid algorithm
AbstractMultigrid (MG) methods are among the most efficient and widespread methods for solving large linear systems of equations that arise, for example, from the discretization of partial differential equations. In this paper we introduce a new approach for optimizing the computational cost of the full MG method to achieve a given accuracy by determining the number of MG cycles on each level. To achieve this, a very efficient and flexible Branch and Bound algorithm is developed. The implementation in the parallel finite element solver Hierarchical Hybrid Grids leads to a significant reduction in CPU time. Copyright © 2010 John Wiley & Sons, Ltd.
Multigrid methods; domain decomposition for boundary value problems involving PDEs, convergence, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Error bounds for boundary value problems involving PDEs, Integer programming, error bounds, Laplace equation, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Complexity and performance of numerical algorithms, full multigrid, cycle optimization, branch and bound algorithm, finite element, Polyhedral combinatorics, branch-and-bound, branch-and-cut, nonlinear integer programming problem
Multigrid methods; domain decomposition for boundary value problems involving PDEs, convergence, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Error bounds for boundary value problems involving PDEs, Integer programming, error bounds, Laplace equation, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Complexity and performance of numerical algorithms, full multigrid, cycle optimization, branch and bound algorithm, finite element, Polyhedral combinatorics, branch-and-bound, branch-and-cut, nonlinear integer programming problem
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