Hierarchically refined isogeometric analysis of trimmed shells
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We propose an Isogeometric approach for smoothing on surfaces, namely estimating a function starting from noisy and discrete measurements. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are geometrical represe ...
The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite elemen ...
Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...
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 ...
The aim of the project is double: to understand the flexibility of the Isogeometric Analysis tools through the solution of some PDEs problems; to test the improvement in the computational time given by a partial loops vectorization at compile-time of the L ...
This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error ...
We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...
We develop rigorous alternating direction optimization methods for a prototype constrained convex optimization template, which has broad applications in computational sciences. We build upon our earlier work on the model-based gap reduction (MGR) technique ...
In this article, we extend this approximation theory developed in (Bazilevs et al., Math Models Methods Appl Sci 16 (2006), 1031-1090) and (Beirão da Veiga et al., Comput Methods Appl Mech Eng 209-212 (2012), 1-11) to the case when the computational domain ...
We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...