The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...
Optical manipulation at the micro- nano-scale is a fascinating topic due to its inherent non-invasive properties and multifaceted applications in various fields such as biology, sensing, micro-fluidics, and micro- nano-robotics. This thesis involves intens ...
We propose an innovative design for an integrated, low-loss on-chip terahertz (THz) field detector based on hybrid silicon-organic slot waveguides and THz antennas. We perform a numerical study of the dependency of electro-optic interaction on geometrical ...
The pursuit of high-speed and on-chip optical communication systems has promoted extensive exploration of all-optical control of light-matter interactions via nonlinear optical processes. Here, we have numerically investigated the ultrafast dynamic switchi ...
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 ...
Isogeometric analysis (IGA) was introduced to integrate methods for analysis and computer-aided design (CAD) into a unified process. High-quality parameterization of a physical domain plays a crucial role in IGA. However, obtaining high-quality parameteriz ...
Numerical solution of the involved governing equations confirm that the commonly used two orthogonal sets of gain- and loss-probes in BOTDA, differently affect the evolution of the pump state-of- polarization, thereby potentially compromising the minimizat ...
The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...
The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differe ...
