دانلود کتاب چالش های هندسی در تحلیل ایزوهندسی

The INdAM workshop “Geometric Challenges in Isogeometric Analysis” was held in Rome (Italy) from January 27 to 31, 2020. The workshop provided a discussion forum for researchers working in the area of isogeometric analysis and related fields, with a particular focus on the issues pertaining to the discretization of differential problems over complex geometries. The efficient and accurate description of complex geometries with tools that are appropriate for analysis (analysis-suitable) is one of the research fields of greatest interest for—but definitely not limited to—the isogeometric paradigm. Spaces of smooth (spline) functions on unstructured meshes, suitable for both geometric design and numerical simulation, are indispensable for isogeometric analysis to exploit its full potential for the treatment of complex real-life problems. Thematic survey talks were complemented with talks presenting recent and inno- vative results on themes central to the scope of the workshop. The addressed topics include • high-quality spline surfaces on complex and trimmed geometries, • construction and analysis of smooth spline spaces on unstructured meshes, • numerical aspects and benchmarking of isogeometric discretizations on unstruc- tured meshes, meshing strategies, and software. The present volume comprises a selection of fifteen contributions by several workshop participants and their collaborators. The construction of smooth spline surfaces of any topological genus and of high quality on complex and trimmed geometries is the topic of the papers, “Quadrilateral Orbifold Splines” by Beccari and Prautzsch, “Trimmed Spline Surfaces with Accu- rate Boundary Control” by Martin and Reif, and “Subdivision and G-Spline Hybrid Constructions for High-Quality Geometric and Analysis-Suitable Surfaces” by Peters and Karˇciauskas. The two papers, “B-Symmetric Univariate Splines and Euler Numbers” by Boafo- Adade et al., and “Simplex-Splines on the Clough-Tocher Split with Arbitrary Smoothness” by Lyche et al., deal with structural properties of specific spline spaces. In particular, B-spline-like bases and Marsden-like identities are proposed for the Clough-Tocher split of any smoothness.