38 research outputs found
Superlinear convergence using block preconditioners for the real system formulation of complex Helmholtz equations
International audienceComplex-valued Helmholtz equations arise in various applications, and a lot of research has been devoted to finding efficient preconditioners for the iterative solution of their discretizations. In this paper we consider the Helmholtz equation rewritten in real-valued block form, and use a preconditioner in a special two-by-two block form. We show that the corresponding preconditioned Krylov iteration converges at a mesh-independent superlinear rate
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements
We consider the e�cient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an e�ective Schur complement approximation. Numerical results illustrate the competitiveness of this approach
IMplicit-EXplicit Formulations for Discontinuous Galerkin Non-Hydrostatic Atmospheric Models
This work presents IMplicit-EXplicit (IMEX) formulations for discontinuous
Galerkin (DG) discretizations of the compressible Euler equations governing
non-hydrostatic atmospheric flows. In particular, we show two different IMEX
formulations that not only treat the stiffness due to the governing dynamics
but also the domain discretization. We present these formulations for two
different equation sets typically employed in atmospheric modeling. For both
equation sets, efficient Schur complements are derived and the challenges and
remedies for deriving them are discussed. The performance of these IMEX
formulations of different orders are investigated on both 2D (box) and 3D
(sphere) test problems and shown to achieve their theoretical rates of
convergence and their efficiency with respect to both mesoscale and global
applications are presented