Some Aspects of Multigrid Methods on Non-Structured Meshes

To solve a given fine mesh problem, the design of a multigrid method requires the definition of coarse levels, associated coarse grid operators and inter-grid transfer operators. For non-structured simplified meshes, these definitions can rely on the use of non-nested triangulations. These definitions can also be founded on agglomeration/aggregation techniques in a purely algebraic manner. This paper analyzes these two options, shows the connections of the volume-agglomeration method with algebraic methods and proposes a new definition of prolongation operator suitable for the application of the volume-agglomeration method to elliptic problems.