
PARAOPT: A parareal algorithm for optimality systems
The time parallel solution of optimality systems arising in PDE constrai...
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A discussion on the approximate solutions of first order systems of nonlinear ordinary equations
We develop a one step matrix method in order to obtain approximate solut...
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Multilevel ActiveSet TrustRegion (MASTR) Method for Bound Constrained Minimization
We introduce a novel variant of the recursive multilevel trustregion (R...
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Large scale simulation of pressure induced phasefield fracture propagation using Utopia
Nonlinear phase field models are increasingly used for the simulation o...
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An Experimental Comparison of Trust Region and Level Sets
Highorder (nonlinear) functionals have become very popular in segmenta...
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Linear versus Nonlinear Acquisition of StepFunctions
We address in this paper the following two closely related problems: 1...
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NewtonKrylovBDDC deluxe solvers for nonsymmetric fully implicit time discretizations of the Bidomain model
A novel theoretical convergence rate estimate for a Balancing Domain Dec...
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On the Globalization of ASPIN Employing TrustRegion Control Strategies – Convergence Analysis and Numerical Examples
The parallel solution of large scale nonlinear programming problems, which arise for example from the discretization of nonlinear partial differential equations, is a highly demanding task. Here, a novel solution strategy is presented, which is inherently parallel and globally convergent. Each global nonlinear iteration step consists of asynchronous solutions of local nonlinear programming problems followed by a global recombination step. The recombination step, which is the solution of a quadratic programming problem, is designed in a way such that it ensures global convergence. As it turns out, the new strategy can be considered as a globalized additively preconditioned inexact Newton (ASPIN) method. However, in our approach the influence of ASPIN's nonlinear preconditioner on the gradient is controlled in order to ensure a sufficient decrease condition. Two different control strategies are described and analyzed. Convergence to firstorder critical points of our nonlinear solution strategy is shown under standard trustregion assumptions. The strategy is investigated along difficult minimization problems arising from nonlinear elasticity in 3D solved on a massively parallel computer with several thousand cores.
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