A5101888528- Advanced Numerical Analysis Techniques
- Polynomial and algebraic computation
- Advanced Numerical Methods in Computational Mathematics
- Numerical methods in engineering
- Iterative Methods for Nonlinear Equations
- Computational Geometry and Mesh Generation
- Electromagnetic Simulation and Numerical Methods
- Model Reduction and Neural Networks
- Geodetic Measurements and Engineering Structures
- Induction Heating and Inverter Technology
- Computer Graphics and Visualization Techniques
- Advanced machining processes and optimization
- Numerical methods for differential equations
- Radiative Heat Transfer Studies
- 3D Shape Modeling and Analysis
- Advanced Theoretical and Applied Studies in Material Sciences and Geometry
- Probabilistic and Robust Engineering Design
- Advanced Measurement and Metrology Techniques
- Reinforcement Learning in Robotics
- Electromagnetic Scattering and Analysis
- VLSI and FPGA Design Techniques
- Machine Learning and Algorithms
- Nonlinear Waves and Solitons
- Coal Combustion and Slurry Processing
- Fractional Differential Equations Solutions
Universidade de Santiago de Compostela
2007-2024
École Polytechnique Fédérale de Lausanne
2017-2023
Istituto di Matematica Applicata e Tecnologie Informatiche
2014-2023
University of Florence
2018
Centre for Automation and Robotics
2006
This review paper collects several results that form part of the theoretical foundation isogeometric methods. We analyse variational techniques for numerical resolution PDEs based on splines or NURBS and we provide optimal approximation error estimates in cases interest. The theory presented also includes T-splines, which are an extension allowing local refinement. In particular, focus our attention elliptic saddle point problems, define spline edge face elements. Our demonstrated by a rich...
The concept of isogeometric analysis (IGA) was first applied to the approximation Maxwell equations in [A. Buffa, G. Sangalli, and R. Vázquez, Comput. Methods Appl. Mech. Engrg., 199 (2010), pp. 1143–1152]. method is based on construction suitable B-spline spaces such that they verify a De Rham diagram. Its main advantages are geometry described exactly with few elements, computed solutions smoother than those provided by finite elements. In this paper we develop theoretical background...
T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable of arbitrary degree and prove fundamental properties: Linear independence the blending functions optimal approximation properties associated T-spline space. These corollaries our main result: A T-mesh is if only it dual-compatible. Indeed, dual compatibility a concept already defined used L. Beirão da Veiga et al. 5 Analysis-suitable dual-compatible which allows for...
The construction of suitable mesh configurations for spline models that provide local refinement capabilities is one the fundamental components analysis and development adaptive isogeometric methods. We investigate design implementation algorithms hierarchical B-spline spaces enable locally graded meshes. rules properly control interaction basis functions at different levels. This guarantees a bounded number nonvanishing (truncated) B-splines on any element. performances are validated with...
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 13 February 2019Accepted: 14 July 2020Published online: 30 September 2020Keywordsisogeometric analysis, trimming, unfitted finite element, element methods, stabilized methodsAMS Subject Headings65N12, 65N15, 65N30, 65N85Publication DataISSN (print): 0036-1429ISSN (online): 1095-7170Publisher: Society for Industrial and Applied MathematicsCODEN: sjnaam
Isogeometric analysis (IGA) is a novel discretization method, introduced by Hughes, which based on nonuniform rational B-splines (NURBS). Among other features, IGA uses directly the geometry description coming from computer-aided design software without approximation, and performed using shape functions of variable (possibly high) regularity. In this paper we propose new scheme continuous B-splines, adapting to solution Maxwell's equations. We present extensive numerical results show that...
In this article, we extend approximation theory developed in (Bazilevs et al., Math Models Methods Appl Sci 16 (2006), 1031–1090) and (Beirão da Veiga Comput Mech Eng 209–212 (2012), 1–11) to the case when computational domain is a collection of nonuniform rational B‐splines patches. © 2014 Wiley Periodicals, Inc. Numer Partial Differential Eq 31: 422–438, 2015
We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and present the study of its numerical properties. By following [10,12,11], optimal convergence rates AIGM can be proved when suitable approximation classes are considered. This is in line with theory methods developed for finite elements, recently well reviewed [43]. The important output our analysis definition admissibility meshes underlying splines design strategy these meshes. adaptivity...
When implementing high-order surface impedance boundary conditions in collocation element method (BEM) with constant or linear elements, difficulties arise due to the computation of curvature conductors and tangential derivatives unknowns. The use nonuniform rational B-splines overcomes above problems gives a better representation complex geometries. After comparing previously derived formulation that obtained by other authors following different approach, resulting integral equations are...
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for numerical solution order partial differential equations. However, tensor-product structure standard multivariate B-spline models not well suited representation complex geometries, and to maintain continuity on general domains special constructions multi-patch geometries must be used. In this paper, we focus adaptive isogeometric methods with hierarchical splines, extend construction [Formula: see...