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In this thesis, we consider the numerical approximation of high order geometric Partial Differential Equations (PDEs). We first consider high order PDEs defined on surfaces in the 3D space that are represented by single-patch tensor product NURBS. Then, we ...
One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a control policy to max ...
Understanding the plasma dynamics in tokamaks is of fundamental importance to reliably predict the performances of future fusion devices. Because of the complex phenomena at play, state-of-the-art simulation codes are needed to investigate the plasma dynam ...
Solar energy has seen tremendous advances in the past years. For thin film photovoltaics, which use less of the expensive semiconductor materials, insufficient light absorption can be a limiting factor. It is hoped that by using diffractive optics to impro ...
We propose and analyze a novel Multi Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a s ...
In fusion plasmas, the strong magnetic field allows the fast gyro-motion to be systematically removed from the description of the dynamics, resulting in a considerable model simplification and gain of computational time. Nowadays, the gyrokinetic (GK) code ...
We consider the numerical approximation of lipid biomembranes, including red blood cells, described through the Canham-Helfrich model, according to which the shape minimizes the bending energy under area and volume constraints. Energy minimization is perfo ...
In this contribution, we introduce an efficient method for solving the optimal control problem for an unconstrained nonlinear switched system with an arbitrary cost function. We assume that the sequence of the switching modes are given but the switching ti ...
This paper presents a novel class of preconditioners for the iterative solution of the sequence of symmetric positive-definite linear systems arising from the numerical discretization of transient parabolic and selfadjoint partial differential equations. T ...
Mathematical models involving partial differential equations (PDE) arise in numerous applications ranging from Natural Sciences and Engineering to Economics. Random and stochastic PDE models become very powerful (and sometimes unavoidable) extensions of de ...
