A Class Of AMG Algorithms For Criss-Cross Partitions And Three-dimensional Partitions With Equal Structure On Each Lay

This paper consists of two chapters. In the first chapter, we first make an orthogonal decomposition for the linear finite space on structured regular Criss-Cross partitions under the energy inner. Using two scale analysis for the orthogonal subspace, we obtain a restriction operator and corresponding AMG algorithms. We also prove that the decling rate of the error is independent of the size of the problems on standard Criss-Cross partitions. As a generalization to the algorithms, we construct AMG algorithms for solving finite equations on piece perforative unstructured Criss-Cross partitions. Numerical tests show that the algorithms are efficient and robust for solving elliptical equations.In the second chapter, on the basis of two-dimensional AMG algorithms, we construct two kinds of AMG algorithms on the partitions with equal algebraic structure on each lay. One is used for PDE with uniform coefficients, another is used for anisotropic PDE. The numerical results show the efficience and robustness of the AMG algorithms .