MATHICSE Technical Report : Uncertainty Quantification by MLMC and Local Time-stepping For Wave Propagation
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An assembly refers to a collection of parts joined together to achieve a specific form and/or functionality. Assemblies make it possible to fabricate large and complex objects with several small and simple parts. Such parts can be assembled and disassemble ...
Multiscale or multiphysics partial differential equations are used to model a wide range of physical systems with various applications, e.g. from material and natural science to problems in biology or engineering. When the ratio between the smallest scale ...
An accurate solution of the wave equation at a fluid-solid interface requires a correct implementation of the boundary condition. Boundary conditions at acousto-elastic interface require continuity of the normal component of particle velocity and traction, ...
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 ...
We use the nodal discontinuous Galerkin method with a Lax-Friedrich flux to model the wave propagation in transversely isotropic and poroelastic media. The effect of dissipation due to global fluid flow causes a stiff relaxation term, which is incorporated ...
We present an exact mathematical framework for electromagnetic wave propagation in periodically time-modulated media, in which the permittivity is homogenous and modulated in a step-varying fashion. By using Hill’s equation theory, we show that this proble ...
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 ...
In this paper, we propose a monolithic algorithm for the numerical solution of the electromechanics model of the left ventricle in the human heart. Our coupled model integrates the monodomain equation with the Bueno-Orovio minimal model for electrophysiolo ...
In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...
The high electric field intensity achieved on the surface of sensors based on metasurfaces (metasensors) makes them an excellent alternative for sensing applications where the volume of the sample to be identified is tiny (for instance, thin-film sensing d ...