Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media
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Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...
This thesis is devoted to the derivation of a posteriori error estimates for the numerical approximation of fluids flows separated by a free surface. Based on these estimates, error indicators are introduced and adaptive algorithms are proposed to solve th ...
Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...
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The Laboratory for Applied Mechanical Design (LAMD) designed, manufactured, and experimentally tested a novel recirculation fan for a 10 kWe solid oxide fuel cell (SOFC). The fan uses oil-free bearings, more specifically herringbone-grooved journal and spi ...
Soft adhesive pads attached to a rigid substrate show stick-slip behavior upon loading: they detach and reattach in a different location. This is accompanied by the lifting of the adhesive, the mechanical wave carrying this motion being known as a Schallam ...
In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, m ...
A family of effective equations for wave propagation in periodic media for arbitrary timescales O(epsilon-alpha), where epsilon MUCH LESS-THAN1 is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of ...
In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g., the Helmholtz equation. In this res ...
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