Concept

Parametrization (geometry)

Related publications (35)

A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries

We present a Petrov-Galerkin reduced basis (RB) approximation for the parameterized Stokes equation. Our method, which relies on a reduced solution space and a parameter-dependent test space, is shown to be stable (in the sense of Babuska) and algebraicall ...

Elsevier2015

Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils

Andrea Manzoni

We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB a ...

Elsevier2015

An improvement on geometrical parameterizations by transfinite maps

Gianluigi Rozza, Laura Iapichino, Christoph Jäggli

We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon–Hall transfinite interpolation approach. It is defined globally over the reference domain. ...

Elsevier France-Editions Scientifiques Medicales Elsevier2014

Reduced basis method for the Stokes equations in decomposable parametrized domains using greedy optimization

Alfio Quarteroni, Gianluigi Rozza, Laura Iapichino

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

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Martins Bruveris, Martin Bauer

This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics th ...

Springer Verlag2014

Singularity Free Parametrization of Human Limbs

Ronan Boulic, Eray Molla

In this paper we propose the Middle-Axis-Rotation (MAR) parametrization of human limbs that addresses the ill-conditioned cases of analytical Inverse Kinematics (IK) algorithms. The MAR parametrization is singularity-free in the reach space of the human li ...

ACM Press2013

Free form deformation techniques applied to 3D shape optimization problems

Alfio Quarteroni, Gianluigi Rozza, Anwar Koshakji

The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametr ...

2013

Hecke modifications, wonderful compactifications and moduli of principal bundles

Michael Lennox Wong

In this paper we obtain parametrizations of the moduli space of principal bundles over a compact Riemann surface using spaces of Hecke modifications in several cases. We begin with a discussion of Hecke modifications for principal bundles and give construc ...

Scuola Normale Superiore2013

Incommensurate crystallography without additional dimensions

Philippe Kocian

It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve com ...

Wiley-Blackwell2013

Model reduction techniques for fast blood flow simulation in parametrized geometries

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni

In this paper we propose a new model reduction technique aimed at real-time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low-dimensional shape parametrization of the compu ...

2012

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