The main feature of multigrid methods is a assimptotically linear behavior of the solution cost of systems of equations. In most cases, nested meshes are used, simplifying the restriction and prolongation operators present in multigrid strategies. The geometry complexity in engineering problems, mainly in three-dimensions, makes it difficult to generate nested meshes. For this purpose, algebraic multigrid methods or non-nested approximation spaces are used.
This work considers non-nested multigrid methods applied to two and three-dimensional elastic problems using the finite element method. The generation of non-nested meshes requires the use of automatic mesh generation procedures. The present work uses non-structured and the Delaunay mesh generation techniques. Another important aspect is related to the implementation of the transfering operators based here on quadtree and octree data structures.
The results are compared with direct and iterative conjugated gradient methods. For three-dimensional problems, it was obtained a linear average cost for the solution of the system of equations. Adaptive procedures are also considered by defining automatic strategies based on error estimators and multigrid estrategies. All procedures were implemented in C++.
Prof. Dr. Marco Lúcio Bittencourt e-mail: firstname.lastname@example.org Dept. of Mechanical Design - DPM/FEM Phone: +55 (19) 239-8384/8475 State University of Campinas Fax: +55 (19) 239-3722