Multigrid Methods for a Biharmonic Problem with Boundary Conditions of the Cahn-Hilliard Type
ثبت نشده
چکیده
We present multigrid methods for a biharmonic problem with boundary conditions of the Cahn-Hilliard type. These multigrid methods are based on discretizations obtained by a quadratic C interior penalty method. Since the finite element space is a standard space for second order problems, multigrid solves for second order problems can be used naturally in the smoothing steps. We will present theoretical results and numerical results, including GPU implementation of the multigrid algorithms.
منابع مشابه
UN CO RR EC TE D PR O O F 1 Multigrid Methods for the Biharmonic Problem with 2 Cahn - Hilliard Boundary Conditions 3
1 Department of Mathematics and Center for Computation & Technology, Louisiana State 5 University, Baton Rouge, LA 70803, USA. [email protected] 6 2 Department of Mathematics and Center for Computation & Technology, Louisiana State 7 University, Baton Rouge, LA 70803, USA. [email protected] 8 3 Department of Mathematics and Center for Computation & Technology, Louisiana State 9 University, B...
متن کاملUN CO RR EC TE D PR O O F 1 A Two - Level Additive Schwarz Preconditioner for C 0 2 Interior Penalty Methods for Cahn - Hilliard Equations 3
We study a two-level additive Schwarz preconditioner for C0 interior penalty 7 methods for a biharmonic problem with essential and natural boundary conditions with Cahn8 Hilliard type. We show that the condition number of the preconditioned system is bounded 9 by C(1+(H3/δ 3)), where H is the typical diameter of a subdomain, δ measures the overlap 10 among the subdomains, and the positive const...
متن کاملC IPG Method for Biharmonic Eigenvalue Problems
We investigate the C interior penalty Galerkin (C IPG) method for biharmonic eigenvalue problems with the boundary conditions of the clamped plate, the simply supported plate and the Cahn-Hilliard type. We prove the convergence of the method and present numerical results to illustrate its performance. We also compare the C IPG method with the Argyris C finite element method, the Ciarlet-Raviart...
متن کاملA boundary control problem for the viscous Cahn–Hilliard equation with dynamic boundary conditions
A boundary control problem for the viscous Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.
متن کاملOn the Cahn–Hilliard equation with dynamic boundary conditions and a dominating boundary potential
The Cahn–Hilliard and viscous Cahn–Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved.
متن کامل