Rolf Krause

Monotone Multigrid Methods on Nonmatching Grids for Nonlinear Multibody Contact Problems

Nonconforming domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We use a generalized mortar method based on dual Lagrange multipliers for the discretization of a nonlinear contact problem between linear elastic bodies. In the case of unilateral contact problems, pointwise constraints occur and monotone multigrid methods yield efficient iterative solvers. Here, we generalize these techniques to nonmatching triangulations, where the constraints are realized in terms of weak integral conditions. The basic new idea is the construction of a nested sequence of nonconforming constrained spaces. We use suitable basis transformations and a multiplicative correction. In contrast to other approaches, no outer iteration scheme is required. The resulting monotone method is of optimal complexity and can be implemented as a multigrid method. Numerical results illustrate the performance of our approach in two and three dimensions.

A massively parallel, multi-disciplinary Barnes-Hut tree code for extreme-scale N-body simulations

The efficient parallelization of fast multipole-based algorithms for the N-body problem is one of the most challenging topics in high performance scientific computing. The emergence of non-local, irregular communication patterns generated by these algorithms can easily create an insurmountable bottleneck on supercomputers with hundreds of thousands of cores. To overcome this obstacle we have developed an innovative parallelization strategy for Barnes–Hut tree codes on present and upcoming HPC multicore architectures. This scheme, based on a combined MPI–Pthreads approach, permits an efficient overlap of computation and data exchange. We highlight the capabilities of this method on the full IBM Blue Gene/P system JUGENE at Julich Supercomputing Centre and demonstrate scaling across 294,912 cores with up to 2,048,000,000 particles. Applying our implementation pepc to laser–plasma interaction and vortex particle methods close to the continuum limit, we demonstrate its potential for ground-breaking advances in large-scale particle simulations.

A Nonsmooth Multiscale Method for Solving Frictional Two-Body Contact Problems in 2D and 3D with Multigrid Efficiency

We present a nonsmooth multiscale method for the numerical solution of frictional contact problems in

Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour

2d

On the Convergence of Recursive Trust-Region Methods for Multiscale Nonlinear Optimization and Applications to Nonlinear Mechanics

and

A Multigrid Method Based on the Unconstrained Product Space for Mortar Finite Element Discretizations

3d

In vivo electromechanical assessment of heart failure patients with prolonged QRS duration

. The computational effort is comparable to that of solving linear problems. Our method does not require any regularization, neither of the nonpenetration condition nor of the friction law and can be applied to contact problems with Tresca friction as well as to contact problems with Coulomb friction. For the case of Tresca friction, the global convergence of the method is shown. For the more complicated case of Coulomb friction, we develop a nonsmooth multiscale method which can be directly applied to the corresponding variational quasi-inequality. No outer iteration is required. Moreover, our multiscale approach is general in the sense that it can be used in the context of geometric as well as algebraic multigrid methods. Nonconforming domain decomposition techniques (or mortar) methods are employed in order to enforce the transmission conditions at the interface between different bodies with nonmatching meshes. Numerical examples illustrate the high robustness and efficiency of our method.

An in-silico analysis of the effect of heart position and orientation on the ECG morphology and vectorcardiogram parameters in patients with heart failure and intraventricular conduction defects

Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.

The time-dependent biomechanical behaviour of the periodontal ligament—an in vitro experimental study in minipig mandibular two-rooted premolars

We prove new convergence results for a class of multiscale trust-region algorithms originally introduced by Gratton, Sartenaer, and Toint in [SIAM J. Optim., 19 (2008), pp. 414-444] to solve unconstrained minimization problems within the Euclidean space

A stencil-based implementation of Parareal in the C++ domain specific embedded language STELLA

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