Publications related to Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

Shape Optimization of an Hydrofoil by Isogeometric Analysis

We use Isogeometric Analysis as a framework for NURBS-based shape optimization of hydrofoils. We present geometrical representations by NURBS and some of their properties to design an hydrofoil. Then, we consider an irrotational flow around an hydrofoil an ...

2014

Isogeometric Analysis for the Elastic Wave Equation

Christoph Jäggli

In everyday life of an engineer, CAD (Computer Aided Design) and FE (Finite Element) programs play an important role. The two different structures, CAD and FE programs, use different mathematical functions. In CAD programs, so called NURBS find their appli ...

2013

Anisotropic Error Estimates And Space Adaptivity For A Semidiscrete Finite Element Approximation Of The Transient Transport Equation

Marco Picasso

A stabilized semidiscrete finite element discretization of the transient transport equation is studied in the framework of anisotropic meshes. A priori and a posteriori error estimates are derived, the involved constants being independent of the mesh aspec ...

Siam Publications2013

Mesh generation and numerical analysis of a Galerkin method for highly conductive prefractal layers

Annalisa Buffa

In this paper we provide a piecewise linear Galerkin approximation of a second order transmission problem across a highly conductive prefractal layer of von Koch type. We firstly generate an appropriate mesh adapted to the geometric shape of the interface ...

2013

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

Adelmo Cristiano Innocenza Malossi

The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned so ...

EPFL2012

Isogeometric discrete differential forms in three dimensions

Annalisa Buffa, Rafael Vazquez Hernandez

The concept of isogeometric analysis (IGA) was first applied to the approximation of Maxwell equations in [A. Buffa, G. Sangalli, and R. Vázquez, Comput. Methods Appl. Mech. Engrg., 199 (2010), pp. 1143-1152]. The method is based on the construction of sui ...

2011

Some estimates for h-p-k-refinement in isogeometric analysis

Annalisa Buffa

In this paper, we propose a theoretical study of the approximation properties of NURBS spaces, which are used in Isogeometric Analysis. We obtain error estimates that are explicit in terms of the mesh-size h, the degree p and the global regularity, measure ...

2011

Multilevel Schwarz methods for elliptic partial differential equations

Alfio Quarteroni, Giovanni Migliorati

We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method. In our analysis we deal with unstruc ...

Elsevier2011

Adaptive finite elements with large aspect ratio for electroosmotic and pressure-driven microflows

Martinus Gijs, Marco Picasso, Virabouth Prachittham

A space–time adaptive method is presented for the numerical simulation of mass transport in electroosmotic and pressure-driven microflows in two space dimensions. The method uses finite elements with large aspect ratio, which allows the electroosmotic flow ...

Wiley-Blackwell2010

Finite-element preconditioning of G-NI spectral methods

Alfio Quarteroni

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −laplace(u) = f in the domain

\Omega = (-1, 1)^d

(d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of bothcondi ...

2009

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

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Shape Optimization of an Hydrofoil by Isogeometric Analysis

Isogeometric Analysis for the Elastic Wave Equation

Anisotropic Error Estimates And Space Adaptivity For A Semidiscrete Finite Element Approximation Of The Transient Transport Equation

Mesh generation and numerical analysis of a Galerkin method for highly conductive prefractal layers

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

Isogeometric discrete differential forms in three dimensions

Some estimates for h-p-k-refinement in isogeometric analysis

Multilevel Schwarz methods for elliptic partial differential equations

Adaptive finite elements with large aspect ratio for electroosmotic and pressure-driven microflows

Finite-element preconditioning of G-NI spectral methods

Some estimates for h-p-k-refinement in isogeometric analysis

Multilevel Schwarz methods for elliptic partial differential equations

Mesh generation and numerical analysis of a Galerkin method for highly conductive prefractal layers

Isogeometric Analysis for the Elastic Wave Equation

Adaptive finite elements with large aspect ratio for electroosmotic and pressure-driven microflows

Isogeometric discrete differential forms in three dimensions

Anisotropic Error Estimates And Space Adaptivity For A Semidiscrete Finite Element Approximation Of The Transient Transport Equation

Finite-element preconditioning of G-NI spectral methods

Shape Optimization of an Hydrofoil by Isogeometric Analysis

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System