报告1

报告人：Thomas Takacs

单位：University of Pavia (Italy)

标题：Isogeometric function spaces over parameter domains of arbitrary shape

时间：2015/8/18 14:00-15:00

地点：英国威廉希尔公司1楼教室

报告内容：In this talk we discuss two topics. First we study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces that have a tensor-product structure locally, but not globally. This includes configurations such as B-splines over multi-patch domains with extraordinary points, analysis-suitable unstructured T-splines, or more general constructions. Within this framework, we generalize the concept of dual-compatible B-splines (originally developed for structured T-splines). This allows us to prove the key properties that are needed for isogeometric analysis, such as linear independence and optimal approximation properties for h-refined meshes.

The second part of this talk will cover the construction of smooth isogeometric function spaces. Isogeometric analysis provides smooth shape functions on a tensor product domain. However, on a manifold-based geometry it is not trivial to construct C1 isogeometric spaces of optimal accuracy. Note that C1 smooth isogeometric functions on two-dimensional domains can be derived from G1 smooth constructions for surfaces. We show that constructions based on bilinear geometries are more or less the only ones, for which it is possible to obtain optimally accurate C1 spaces. Second, we present approaches based on weak continuity using a Nitsche type method. We numerically compare the accuracy of strong and weak methods.

报告人简介：I am currently working as a post-doctoral researcher at the University of Pavia (Italy). Previously, I have been working as a PhD student at the Johannes Kepler University Linz (Austria) under the supervision of Bert Jüttler. My research experience is mostly focused on Isogeometric Analysis and on the underlying function spaces. Topics of interest include the study of singularly parameterized domains, including regularity properties and approximation error estimates. Moreover, I developed exact formulas to evaluate derivatives of isogeometric functions, which can be used to construct function spaces of high smoothness over irregular (singular or multi-patch) domains. Current and ongoing research includes the study of error bounds and spectral approximation properties of B-spline function spaces; regularization methods for vector fields on manifolds; and the study of non-standard geometry representations, such as spline manifold spaces and multi-patch geometries, which I will present in my talk. My collaborators include Annabelle Collin, Guozhi Dong, Bert Jüttler, Giancarlo Sangalli, Otmar Scherzer, Stefan Takacs, and Rafael Vazquez.

报告2

报告人：Andrea Bressan

单位：Institute of applied geometry, JKU, Linz (Austria)

标题：LR-splines

时间：2015/8/18 15:00-16:00

报告内容：LR-splines where introduced by Tor Dokken, Tom Lyche and Kjell Fredrik Pettersen as an extension of tensor product B-splines that allows local refinement. The first part of the talk will introduce the LR-spline definition and theoretical framework. During the second part I will describe an explicit construction of LR-spline spaces that guarantees local linear independence while and provide locally linearly independent basis functions.

报告人简介：I studied in University of Pavia where I got my PhD degree under the supervision of Giancarlo Sangalli and Annalisa Buffa. Then I moved to Linz where I work as a postDoc for the Applied Geometry group directed by Bert Jüttler.

My research topics are: infsup-stability of isogeometric elements for the Stokes equation, LR-spline spaces, T-splines. At the moment I am working on extending the Stokes result from tensor product B-splines to hierarchical B-splines and on providing a reasonable subclass of LR-splines for applications.