Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.
Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineer ...
This paper deals with the mathematical model that describes the function of the human heart. More specifically, it addresses the equations that express the electromechanical process, that is the mechanical deformation (contraction and relaxation) of the he ...
We consider the Dynamical Low Rank (DLR) approximation of random parabolic equations and propose a class of fully discrete numerical schemes. Similarly to the continuous DLR approximation, our schemes are shown to satisfy a discrete variational formulation ...
Many engineering fields rely on frequency-domain dynamical systems for the mathematical modeling of physical (electrical/mechanical/etc.) structures. With the growing need for more accurate and reliable results, the computational burden incurred by frequen ...
This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...
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 ...
In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...
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 ...
We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...
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 propose and numerically assess three segregated ( partitioned) algorithms for the numerical solution of the coupled electromechanics problem for the left human ventricle. We split the coupled problem into its core mathematical models and we proceed to t ...
