Towards an efficient numerical simulation of complex 3D knee joint motion

Sander, Oliver; Klapproth, Corinna; Youett, Jonathan; Kornhuber, Ralf; Deuflhard, Peter

doi:10.1007/s00791-014-0227-6

Cited by 6 publications

(6 citation statements)

References 43 publications

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“…Such problems arise, e.g., in the numerical simulation of subsurface flow problems or contact problems in mechanics with uncertain constitutive equations, specifically elastic moduli or friction coefficients (see, e.g., [35,36,38] and the references cited therein). Key characteristics of elliptic variational inequalities with stochastic coefficients are low spatial regularity of the permeability, small spatial correlation lengths (this implies slow convergence of Karhúnen-Loève expansions), and the possible nonstationarity of realistic stochastic models, particularly from computational geosciences.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities

Kornhuber

Schwab²,

Wolf³

2014

SIAM J. Numer. Anal.

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Abstract. Multi-Level Monte-Carlo Finite Element (MLMC-FE) methods for the solution of stochastic elliptic variational inequalities are introduced, analyzed, and numerically investigated. Under suitable assumptions on the random diffusion coefficient, the random forcing function, and the deterministic obstacle, we prove existence and uniqueness of solutions of "mean-square" and "pathwise" formulations. Suitable regularity results for deterministic, elliptic obstacle problems lead to uniform pathwise error bounds, providing optimal-order error estimates of the statistical error and upper bounds for the corresponding computational cost for classical Monte-Carlo and novel MLMC-FE methods. Utilizing suitable multigrid solvers for the occurring sample problems, in two space dimensions MLMC-FE methods then provide numerical approximations of the expectation of the random solution with the same order of efficiency as for a corresponding deterministic problem, up to logarithmic terms. Our theoretical findings are illustrated by numerical experiments.

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Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities

Kornhuber

Schwab²,

Wolf³

2014

SIAM J. Numer. Anal.

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“…Rigid body models, however, have limitations: bones are assumed to be rigid and tissues are spatially lumped. In contrast, finite element (FE) models can be used to accurately capture both the geometry and material properties of a variety of tissues making it possible to predict injury [106].…”

Section: Figurementioning

confidence: 99%

Dynamic Human Body Models in Vehicle Safety: An Overview

Fahse¹,

Kempter²,

Maier³

et al. 2023

Preprint

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Significant trends in the vehicle industry are autonomous driving, micromobility, electrification and the increased use of shared mobility solutions. These new vehicle automation and mobility classes lead to a larger number of occupant positions, interiors and load directions. As safety systems interact with and protect occupants, it is essential to place the human, with its variability and vulnerability, at the center of the design and operation of these systems. Digital human body models (HBMs) can help meet these requirements and are therefore increasingly being integrated into the development of new vehicle models. This contribution provides an overview of current HBMs and their applications in vehicle safety in different driving modes.The authors briefly introduce the underlying mathematical methods and present a selection of HBMs to the reader. An overview table with guideline values for simulation times, common applications and available variants of the models is provided.To provide insight into the broad application of HBMs, the authors present three case studies in the field of vehicle safety: (i) in-crash finite element simulations and injuries of riders on a motorcycle; (ii) scenario-based assessment of the active precrash behavior of occupants with the Madymo multibody HBM; (iii) prediction of human behavior in a take-over scenario using the EMMA model.

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“…The pelvis is kept in place with homogenous Dirichlet boundary conditions everywhere but for the contact boundary. The quasi-static contact is determined with a monotone multigrid contact solver described in [2]. For this purpose an interface between the Dune-FuFem module and the Kaskade7 1 FE-toolbox was created.…”

Section: Mechanical Joint Modelmentioning

confidence: 99%

“…The algebraic solution of the contact problem is computed with a non-linear multigrid method, namely the truncated non-smooth Newton-multigrid method (TNNMG). For more details, we refer the reader to [2].…”

Section: Mechanical Joint Modelmentioning

confidence: 99%