Of America

We are concerned with the compatible gauge reformulation for H(div) equations and the design of fast solvers of the resulting linear algebraic systems as in [5]. We propose an algebraic reformulation of the discrete H(div) equations along with an algebraic multigrid (AMG) technique for the reformulated problem. The reformulation uses discrete Hodge decompositions on co-chains to replace the discrete H(div) equations by an equivalent 2 × 2 block linear system whose diagonal blocks are discrete Hodge Laplace operators acting on 2-cochains and 1cochains respectively. We illustrate the new technique, using the lowest order Raviart-Thomas elements on structured tetrahedral mesh in three dimension and present computational results.