13:45
Zuiderduinzaal: Keynote: Thomas Richter, Universität Magdeburg, Germany
13:45
45 mins
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Modeling and Simulation of Temporal Multiscale Problems
Thomas Richter
Abstract: The coupling of different temporal scales is common in many application problems. One classic example is the weathering of mechanical structures like bridges, a process that takes decades that it is, however, affected by short term influences such as traffic, wind or stretching by daily and yearly temperature alteration. The problem is two-way coupled as material change could cause a shift of resonance regimes with a drastic influence on the fast scale. Another example is the growth of atherosclerotic plaques in blood vessels, a bio/chemical mechanism that causes material transformation and growth within the vessel wall in a time-span of months, but that is strongly affected by the mechanical forces arising from the pulsating blood flow in a fluid-solid interaction system. Narrowing of the blood vessel by growth will in term also affect the fast scale by changing the overall flow pattern.
These slow-scale / fast-scale problems have in common that they are two-way coupled processes and that we are usually interested in the slowly evolving scale only. A resolved simulation of all scales is not feasible. A year comprises 30 million heart cycles, a corresponding resolved fluid-solid simulation is out of bounds.
Based a replacement of the fast-scale by isolated local problems which are periodic in time, we describe and analyse temporal multiscale schemes for the efficient simulation of the slow-scale variable. For simplified classes of equations, we will show convergence of the resulting multiscale method with regard to all discretization and modelling parameters.
An important numerical ingredient is the fast approximation of the local periodic-in-time solutions of the fast scale that are required in every step of the multiscale scheme. We will present acceleration schemes for a direct-to-periodic-state solution. Numerical examples will substantiate the theoretical results.
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