Non-stationary two-stage relaxation based on the principle of aggregation multi-grid

Proceedings of the 18th Panhellenic Conference on Informatics

2014

Multigrid methods are considered amongst the most efficient methods for the solution of large sparse linear systems derived from the discretization of Partial Differential Equations (PDEs). In order to accelerate multigrid convergence a new class of Generic Approximate Inverses utilized, in conjunction with the Richardson's method, as smoothers. The Generic Approximate Inverses in conjunction with approximate inverse sparsity patterns, based on powers of sparsified matrices, are computed from the Incomplete LU factorization of the coefficient matrices. The proposed schemes are used to solve large linear systems derived from the discretization of a PDE with the Mehrstellen scheme which leads to solutions with fourth order accuracy by increasing slightly the computation effort. Moreover, the proposed schemes are used to solve boundary value problems in three dimensions. Furthermore, numerical results are presented for the proposed schemes to outline the applicability and effectiveness of the parametric design of the Approximate Inverse.

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Section: Drop Elements Ofmentioning

confidence: 99%

Section: Drop Elements Ofmentioning

confidence: 99%

“…The equation (22) denotes a two stage non-stationary approximate inverse smoother. Further information and convergence analysis of the DOUR algorithm were given in [19].…”

Section: Drop Elements Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Geometric multigrid methods based on Generic Approximate Sparse Inverses

Proceedings of the 18th Panhellenic Conference on Informatics

2014

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“…In order to accelerate the convergence of the Multigrid method, the Dynamic Over/Under Relaxation (DOUR) scheme is used (cf. [24]) in conjunction with the Generic Approximate Sparse Inverse (GenAspI) matrix (cf. [25]).…”

Section: Introductionmentioning

confidence: 99%

ParallelN-Body Simulation Based on the PM and P3M Methods Using Multigrid Schemes in conjunction with Generic Approximate Sparse Inverses

Kyziropoulos

Mathematical Problems in Engineering

2015

During the last decades, Multigrid methods have been extensively used for solving large sparse linear systems. Considering their efficiency and the convergence behavior, Multigrid methods are used in many scientific fields as solvers or preconditioners. Herewith, we propose two hybrid parallel algorithms forN-Body simulations using the Particle Mesh method and the Particle Particle Particle Mesh method, respectively, based on the V-Cycle Multigrid method in conjunction with Generic Approximate Sparse Inverses. TheN-Body problem resides in a three-dimensional torus space, and the bodies are subject only to gravitational forces. In each time step of the above methods, a large sparse linear system is solved to compute the gravity potential at each nodal point in order to interpolate the solution to each body. Then the Velocity Verlet method is used to compute the new position and velocity from the acceleration of each respective body. Moreover, a parallel Multigrid algorithm, with a truncated approach in the levels computed in parallel, is proposed for solving large linear systems. Furthermore, parallel results are provided indicating the efficiency of the proposed MultigridN-Body scheme. Theoretical estimates for the complexity of the proposed simulation schemes are provided.

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Parallel multigrid algorithms based on generic approximate sparse inverses: an SMP approach

2013

J Supercomput