Browsing by Author "Peterseim, Daniel"
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- ItemComputational Multiscale Methods(Zürich : EMS Publ. House, 2019) Peterseim, DanielMany physical processes in material sciences or geophysics are characterized by inherently complex interactions across a large range of non-separable scales in space and time. The resolution of all features on all scales in a computer simulation easily exceeds today's computing resources by multiple orders of magnitude. The observation and prediction of physical phenomena from multiscale models, hence, requires insightful numerical multiscale techniques to adaptively select relevant scales and effectively represent unresolved scales. This workshop enhanced the development of such methods and the mathematics behind them so that the reliable and efficient numerical simulation of some challenging multiscale problems eventually becomes feasible in high performance computing environments.
- ItemComputational Multiscale Methods(Zürich : EMS Publ. House, 2014) Engquist, Björn; Peterseim, DanielAlmost all processes in engineering and the sciences are characterised by the complicated relation of features on a large range of nonseparable spatial and time scales. The workshop concerned the computer-aided simulation of such processes, the underlying numerical algorithms and the mathematics behind them to foresee their performance in practical applications.
- ItemReconstruction of quasi-local numerical effective models from low-resolution measurements(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Caiazzo, Alfonso; Maier, Roland; Peterseim, DanielWe consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on low-resolution measurements. We rely on recent quasi-local numerical effective models that, in contrast to conventional homogenized models, are provably reliable beyond periodicity assumptions and scale separation. The goal of this work is to show that the identification of the matrix representation of these effective models is possible. Algorithmic aspects of the inversion procedure and its performance are illustrated in a series of numerical experiments.
- ItemSimulation of composite materials by a Network FEM with error control(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Eigel, Martin; Peterseim, DanielA novel Finite Element Method (FEM) for the computational simulation in particle reinforced composite materials with many inclusions is presented. It is based on a specially designed mesh consisting of triangles and channel-like connections between inclusions which form a network structure. The total number of elements and, hence, the number of degrees of freedom are proportional to the number of inclusions. The error of the method is independent of the possibly tiny distances of neighbouring inclusions. We present algorithmic details for the generation of the problem adapted mesh and derive an efficient residual a posteriori error estimator which enables to compute reliable upper and lower error bounds. Several numerical examples illustrate the performance of the method and the error estimator. In particular, it is demonstrated that the (common) assumption of a lattice structure of inclusions can easily lead to incorrect predictions about material properties.