This year’s SIAM International Meshing Roundtable will feature three short courses, to be held on Tuesday 22nd February 2022.
Courses are taught by internationally known experts. Instructors typically include an overview of the state of the art of their topic, and highlight their own research, but also include the current work of others. It is intended to be a “course” in the traditional sense of enabling attendees to go forth and produce new results of their own, rather than simply use existing knowledge.
This year we have three courses, which will be held on February 22, 2022. Each of the course details is outlined below.
Spectral Element Methods and What They Need From Their Mesh Generator
Prof. David Kopriva (Florida State University)
Spectral element methods are high order approximations with the geometric flexibility of finite element methods. Introduced in 1985, the methods are predominantly used to approximate time dependent compressible and incompressible flows, but are also well-suited to compute wave propagation problems in electromagnetics and acoustics accurately. The attraction is high order, even exponential, convergence, with low phase and dissipation errors, all the while being geometrically flexible. The class of methods is matured to the point that commercial and open source solvers suitable for the solution of industrial scale problems are available. The fundamental feature of the methods is the use of high order polynomial approximations to the solutions and the geometry, with orders ranging from four to twenty. Finding suitable mesh generators that support elements with such orders has been problematic, forcing many practitioners to write their own. This short course will survey spectral element methods to help understand the relationship between the mesh and the method, with the hope to spur innovation in the development of high order mesh generators.
Discrete minimal surfaces for generating 3D fillet structures
Prof. Konrad Polthier (Freie Universität Berlin)
Modelling volumetric shapes with surface meshes is a core problem in 3d-manufacturing. In this presentation we combine two centrals aspects, the topological structure of 3d-volumes and the geometric filling with surface meshes based on discrete minimal surfaces.
Model reconstruction for boundary-fit isogeometric analysis
Prof. Kendrick Shepherd (Brigham Young University)
This short course motivates and discusses a boundary-fitted isogeometric spline model reconstruction framework for converting trimmed and faceted models into analysis-suitable splines. The course begins by reviewing isogeometric analysis, including model representation in computer-aided design (CAD) software, trimming, isogeometric analysis techniques on trimmed CAD models, and motivation for boundary-fit model reconstruction. After this, the problem of generating a boundary-fit, trim-free CAD spline model is recharacterized as computing a special metric on a surface. Next, state-of-the-art computational tools incorporating Ricci flow and metric optimization are presented that compute feature-aware curvilinear quadrilateral meshes. The efficacy of the work is demonstrated on the US Army’s DEVCOM Generic Hull vehicle and on the body-in-white of a 1996 Dodge Neon. Finally, the course discusses methods to integrate these techniques with commercial software using Rhinoceros 3D and LS-DYNA. The improved accuracy and efficiency of these isogeometric analyses compared to traditional finite element counterparts is shown.
Contact details
For any question concerning short course submissions please contact the short course chair:
- David Xianfeng Gu, Short Course Chair
Stonybrook University. email: gu@cs.stonybrook.edu
