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Reduced basis approximation and error bounds for potential flows in parametrized geometries

Related publications (34)

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An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

2023

An a posteriori error estimator for isogeometric analysis on trimmed geometries

Annalisa Buffa, Rafael Vazquez Hernandez, Ondine Gabrielle Chanon

Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer-aided design, which generates meshes that are unfitted with the described physical object. T ...

2022

Isogeometric Analysis for High Order Geometric Partial Differential Equations with Applications

Andrea Bartezzaghi

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 ...

EPFL2017

A posteriori error estimations for elliptic partial differential equations with small uncertainties

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this article, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a pa ...

2016

MATHICSE Technical Report : Automatic reduction of PDEs defined on domains with variable shape

Andrea Manzoni, Federico Negri

In this work we propose a new, general and computationally cheap way to tackle parametrized PDEs defined on domains with variable shape when relying on the reduced basis method. We easily describe a domain by boundary parametrizations, and obtain domain de ...

MATHICSE2016

This thesis is concerned with the development, analysis and implementation of efficient reduced order models (ROMs) for the simulation and optimization of parametrized partial differential equations (PDEs). Indeed, since the high-fidelity approximation of ...

EPFL2015

Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

Andrea Manzoni, Federico Negri

In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely ...

Elsevier2015

MATHICSE Technical Report : Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

Andrea Manzoni, Federico Negri

MATHICSE2015

Isogeometric Analysis (IGA) is a computational methodology for the numerical approximation of Partial Differential Equations (PDEs). IGA is based on the isogeometric concept, for which the same basis functions, usually Non-Uniform Rational B-Splines (NURBS ...

2015

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Flow simulations in pipelined channels and several kinds of parametrized configurations have a growing interest in many life sciences and industrial applications. Applications may be found in the analysis of the blood flow in specific compartments of the c ...

Springer2014