Christos K. Filelis-Papadopoulos¹, George A. Gravvanis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.3, pp. 233-253, 2013, DOI:10.3970/cmes.2013.090.232

Abstract During the last decades, multigrid methods have been extensively used in order to solve large scale linear systems derived from the discretization of partial differential equations using the finite difference method. Approximate Inverses in conjunction with Richardon’s iterative method could be used as smoothers in the multigrid method. Thus, a new class of smoothers based on approximate inverses could be derived. Effectiveness of explicit approximate inverses relies in the fact that they are close approximants to the inverse of the coefficient matrix and are fast to compute in parallel. Furthermore, the class of finite difference More >

P.H. Gaskell¹, Y.C. Lee², H.M. Thompson¹

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 77-112, 2010, DOI:10.3970/cmes.2010.062.077

Abstract The three-dimensional flow of a gravity-driven continuous thin liquid film on substrates containing micro-scale features is modelled using the long-wave lubrication approximation, encompassing cases when surface topography is either engulfed by the film or extends all the way though it. The discrete analogue of the time-dependent governing equations is solved accurately using a purpose designed multigrid strategy incorporating both automatic error-controlled adaptive time stepping and local mesh refinement/de-refinement. Central to the overall approach is a Newton globally convergent algorithm which greatly simplifies the inclusion of further physics via the solution of additional equations of the More >

R. Zakhama^1,2,3, M.M. Abdalla², H. Smaoui^1,3, Z. Gürdal²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.051.001

Abstract A multigrid accelerated cellular automata algorithm for two and three dimensional continuum topology optimization problems is presented. The topology optimization problem is regularized using the traditional SIMP approach. The analysis rules are derived from the principle of minimum total potential energy, and the design rules are derived based on continuous optimality criteria interpreted as local Kuhn-Tucker conditions. Three versions of the algorithm are implemented; a cellular automata based design algorithm, a baseline multigrid algorithm for analysis acceleration and a full multigrid integrated analysis and design algorithm. It is shown that the multigrid accelerated cellular automata More >

Y. Wada¹, T. Hayashi², M. Kikuchi³

The International Conference on Computational & Experimental Engineering and Sciences, Vol.8, No.4, pp. 127-132, 2008, DOI:10.3970/icces.2008.008.127

Abstract Due to more complex and severe design, more effective and faster finite element analyses are demanded. One of the most effective analysis ways is the combination of adaptive analysis and multigrid iterative solver, because an adaptive analysis requires several meshes with different node densities and multigrid solver utilizes such meshes to accelerate its computation. However, convergence of multigrid solver is largely affected by initial shape of each element. An effective mesh improvement method is proposed here. It is the combination of mesh coarsening and refinement. A good mesh can be obtained by the method to More >

Suely Oliveira², Fang Yang²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 113-120, 2007, DOI:10.3970/icces.2007.003.113

Abstract In this paper we describe and compare preconditioners for saddle-point systems obtained from meshfree discretizations, using the concepts of hierarchical (or H-)matrices. Previous work by the authors using this approach did not use H-matrix techniques throughout, as is done here. Comparison shows the method described here to be better than the author's previous method, an AMG method adapted to saddle point systems, and conventional iterative methods such as JOR. More >