Application of unified DG analysis to preconditioning DG methods

Publisher Summary This chapter discusses the application of a unified analysis of several discontinuous Galerkin (DG) methods to accelerating the methods by a multigrid preconditioned. Primal forms of various DG methods are derived. Thus, efficient solution by these methods is possible by preconditioning the primal bilinear forms. All the methods presented are symmetric and consistent. The chapter presents the uniform multigrid preconditioners for each primal bilinear form. Smoothing iterations of the form are important ingredients of a multigrid algorithm. If one multiplicatively combines the local solves, one gets a Gauss-Seidel smoother in a standard fashion. The smoothers can be computed easily because primal bilinear form uses only local lifting operators. The chapter verifies the locality of the lifting operators by using decomposition methods.