Some Aspects of Multigrid Methods on Non-structured Meshes

SUMMARY To solve a given ne mesh problem, the design of a multigrid method requires the deenition of coarse levels, associated coarse grid operators and inter-grid transfer operators. For non-structured simplicial meshes, these deenitions can rely on the use of non-nested triangulations. Another possibility is to found these deenitions 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 deenition of prolongation operator suitable for the application of volume-agglomeration method to elliptic problems.