Abstract or Additional Information
Fast, scalable solution of very large problems in scientific computing can be performed effectively with algebraic multigrid. However, most existing multigrid algorithms target only the H1 space and are tailored to bilinear forms involving the gradient operator. In this talk we discuss the development of element-based algebraic multigrid methods for the whole de Rham sequence of H1, H(curl), H(div) and L2 spaces. We motivate the discussion by first developing the ideas of multigrid in a way that highlights what properties we need to consider when applying it to different operators, then we discuss the properties of the de Rham sequence that will be important on coarser multigrid levels, and finally we discuss the interplay of these issues when developing multigrid for the de Rham complex.