THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

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Blow-up, partial regularity and turbulence in incompressible fluid dynamics

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Weak solutions arise naturally in the study of the Navier-Stokes and Euler equations both from an abstract regularity/blow-up perspective and from physical theories of turbulence. This thesis studies the structure and size of singular set of such weak solu ...

EPFL2022

Quadrature-free immersed isogeometric analysis

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This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...

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Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

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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 ...

2022

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

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Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

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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 ...

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CO2-Driven diffusiophoresis and water cleaning: similarity solutions for predicting the exclusion zone in a channel flow

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We investigate experimentally and theoretically diffusiophoretic separation of negatively charged particles in a rectangular channel flow, driven by CO2 dissolution from one side-wall. Since the negatively charged particles create an exclusion zone near th ...

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Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

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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 ...

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Non-smooth solutions in incompressible fluid dynamics

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This work is devoted to the study of the main models which describe the motion of incompressible fluids, namely the Navier-Stokes, together with their hypodissipative version, and the Euler equations. We will mainly focus on the analysis of non-smooth weak ...

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Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

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We present asymptotically sharp inequalities, containing a 2nd term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kroger inequalities in the limit as the eigenvalues tend ...

OXFORD UNIV PRESS2021

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Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

EPFL2022