Few distinct distances implies no heavy lines or circles
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This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework based on a single g ...
Unrefinement is a tool that allows to perform faster numerical simulations by controlling the level of precision in the specified area. We introduce an algorithm that creates a coarser geometry from an initial regular geometry, which is represented with re ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
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 ...
In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space Rd. We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...
Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
Nonparametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these issues in the de ...
This work extends the stress recovery for laminated composite solid plates, proposed in [1,2], to curved structures. Based on 3D Isogeometric Analysis (IGA) computations and equilibrium, this procedure uses a single element through the thickness in combina ...
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which r ...
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogenei ...