Globally Convergent Multigrid Methods for Porous Medium Type Problems

Globally Convergent Multigrid Methods for Porous Medium Type Equations

Adaptive Monotone Multigrid Methods for some Non{Smooth Optimization Problems

We consider the fast solution of non{smooth optimization problems as resulting for example from the approximation of elliptic free boundary problems of obstacle or Stefan type. Combining well{known concepts of successive subspace correction methods with convex analysis, we derive a new class of multigrid methods which are globally convergent and have logarithmic bounds of the asymptotic converg...

Truncated Nonsmooth Newton Multigrid Methods for Simplex-Constrained Minimization Problems

We present a multigrid method for the minimization of strongly convex functionals defined on a finite product of simplices. Such problems result, for example, from the discretization of multi-component phase-field problems. Our algorithm is globally convergent, requires no regularization parameters, and achieves multigrid convergence rates. We present numerical results for the vector-valued All...

A Globally Convergent Filter–trust-region Method for Large Deformation Contact Problems

We present a globally convergent method for the solution of frictionless large deformation contact problems involving hyperelastic materials. For the discretisation we apply the dual mortar method which is known to be more stable than node-to-segment approaches. The resulting non-convex constrained minimisation problems are solved using a filter–trust-region scheme. This method combines several...

Monotone Multigrid Methods for Elliptic Variational Inequalities I

We derive fast solvers for discrete elliptic variational inequalities of the rst kind (obstacle problems) as resulting from the approximation of related continuous problems by piecewise linear nite elements. Using basic ideas of successive subspace correction, we modify well-known relaxation methods by extending the set of search directions. Extended underrelaxations are called monotone multigr...