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In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...
This paper deals with a new analytical model for microfluidic passive mixers. Two common approaches already exist for such a purpose. On the one hand, the resolution of the advection-diffusion-reaction equation (ADRE) is the first one and the closest to ph ...
In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...
Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...
The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...
Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured for ...
In this Master thesis we explore the convex integration method by S. Müller and V. Šverák and its applications to partial differential equations. In particular, we use it to build very irregular solutions to elliptic systems. We also apply this method to b ...
We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...
The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis metho ...
Many physical and chemical reactions are driven by nonadiabatic processes, which imply the breakdown of the celebrated Born-Oppenheimer approximation. To understand these processes, experimentalists employ spectroscopic techniques. However, the obtained re ...