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 are having two short course tracks, each with two classes. One track is traditional “core” meshing topics, and the other is topics that we believe would “enrich” the perspective of meshing researchers beyond what they are most familiar with. The goal of the core topics is to bring attention to the state of the art, so that attendees would be positioned to contribute directly to that topic. The goal of the enrichment topics is to make attendees aware of exciting knowledge from nearby fields that could bring a new set of tools, math, and perspectives to meshing research. Both tracks are suitable for both new and experienced meshing researchers.
The IMR short courses will be held Monday, October 14, 2019. Courses are taught by internationally known experts in the field of Mesh Generation. Instructors will address practical issues in the design and implementation of both structured and unstructured mesh generation codes.
Core Track Instructors Enrichment Track Instructors
The Core session includes courses ideal for students just entering the field who may need a foundation for research.
|Dr. Marcel Campen
Osnabrück University, Germany
Title: Semi-Structured Quadrangulation using Vector Field and Grid Mapping Techniques
Biography: Prof. Dr. Marcel Campen is head of the Graphics & Geometric Computing group at Osnabrück University, Germany. He received his PhD from RWTH Aachen University in 2015, and performed postdoctoral research at the Courant Institute at New York University till 2017. His work commonly deals with aspects of robustness in the context of geometric data processing, with a particular focus on the computational generation and optimization of semi-structured surface and volume meshes.
Besides multiple best paper awards, Marcel Campen has received the Eurographics Best PhD Thesis Award in 2016. In 2018 he was elected Junior Fellow of the Eurographics Association. He has authored and co-authored state-of-the-art reports on directional fields and quadrilateral surface partitioning, and has organized multiple courses on these meshing-related topics at conferences like SIGGRAPH, SIGGRAPH Asia, and Eurographics.
Abstract: In various applications, meshes with quadrilateral elements are preferred over meshes with triangular elements due to their distinct characteristics. To facilitate the (semi-)automatic generation of such meshes for either planar domains or curved surfaces, a variety of algorithmic approaches have been proposed.
Over the past decade particular progress has been made in one particular, relatively novel category of quadrilateral meshing algorithms. These make use of vector fields (or more generally cross and frame fields) as well as quantized global parametrizations (or more specifically integer grid maps) of the domain to be meshed. When constructed properly, these objects from differential geometry impose semi-regular or block-structured grid patterns via their streamlines and isolines, respectively, well-suited for quad mesh generation purposes.
We discuss the underlying basic concepts and ideas, key algorithms and recent developments, questions of existence, robustness, efficiency, and generalizability, as well as future challenges in this exciting field.
|Teseo Schneider, New York University, USA
Title: Back-Box Analysis: From Theory to Practice
Biography: Dr. Teseo Schneider is an assistant professor/faculty fellow in Computer Science at the Courant Institute of Mathematical Sciences in New York University. Teseo earned his PhD in Computer Science from the Università della Svizzera italiana (2017) with the thesis entitled "Theory and Applications of Bijective Barycentric Mappings". He earned a Postdoc.Mobility fellowship by Swiss National Science Foundation (SNSF) to pursue his research aiming to bridge physical simulations and geometry. His research interests are in finite element simulations, mathematics, discrete differential geometry, and geometry processing. Teseo is the main developer of Polyfem (https://polyfem.github.io/) a flexible and easy to use Finite Element Library.
Abstract: The numerical solution of partial differential equations (PDEs) is ubiquitous in engineering applications, for the simulation of elastic deformations, fluids, and other physical phenomena.
The finite element method (FEM) is the most commonly used discretization of PDEs due to its generality and rich selection of off-the-shelf commercial implementations. Ideally, a PDE solver should be a ``black box'': the user provides as input the domain boundary, boundary conditions, and the governing equations, and the code returns an evaluator that can compute the value of the solution at any point of the input domain. This is surprisingly far from being the case for all existing open-source or commercial software, despite the research efforts in this direction and the large academic and industrial interest.
To a large extent, this is due to treating meshing and FEM basis construction as two disjoint problems. The FEM basis construction may make a seemingly innocuous assumption (e.g., on the geometry of elements), that lead to exceedingly difficult requirements for meshing software.
This state of matters presents a fundamental problem for applications that require fully automatic, robust processing of large collections of meshes of varying sizes, an increasingly common situation as large collections of geometric data become available. Most importantly, this situation arises in the context of machine learning on geometric and physical data, when one can run large numbers of simulations to learn from, as well as problems of shape optimization, which require solving PDEs in the inner optimization loop on a constantly changing domain.
The first part of the course introduces the finite element method and recent advancements toward an integrated pipeline, considering meshing and element design as a single challenge, leading to a black-box pipeline that can solve simulations on 10 thousand in the wild meshes, without any parameter tuning.
The second part demonstrates the effectiveness the black-box pipeline through practical examples in structural mechanics using state-of-the-art, easy-to-use, open-source Python libraries.
Enrichment Track Instructors
|Dr. Na Lei
Dalian University of Technology, China
Title: Mesh Generation Based on Computational Conformal Geometry
Biography: Dr. Na Lei is currently a professor of DUT-RU International School of Information Science and Engineering in Dalian University of Technology, director of Institute of Geometric Computing and Inteligent Media Technology, affiliated professor of Beijing Advanced Innovation Center for Imaging Technology, Mathematical Review reviewer of American Mathematical Society, member of Technical Committee on Computer Vision of China Computer Federation, member of Technical Committee on Geometric Design and Computation of China Society for Industrial and Applied Mathematics, member of Technical Committee on Computer Mathematics of Chinese Mathematical Society. Dr. Na Lei got her Ph. D. from Jilin University in 2002. Then she spent one year in Institute for Computational Engineering and Sciences of University of Texas at Austin, working with Dr. Bajaj as a JTO research fellow, and another year in Computer Science Department of the State University of New York at Stony Brook, working with Dr. David Xianfeng Gu as a visiting professor. She is a reviewer for many distinguished journals, such as IEEE Transactions on Visualization and Computer Graphics, Computer Aided Geometric Design, Computer-Aided Design, Graphical Models, The Visual Computer, Journal of Computational and Applied Mathematics, Computer vision and pattern recognition and so on. She was also a PC member for many important international conferences, such as International Joint Conference of Artificial Intelligence, Geometric Modeling and Processing, Asian Conference on Design and Digital Engineering and so on.
Dr. Na Lei’s research interest is to deal with the practical problem in engineering and medical fields by applying the theory and methods of modern differential geometry and topology.
Abstract: Generating meshes with regular structure plays a fundamental role in isogeometric analysis. Regular hexahedral mesh generation is called the holy grid problem in computational mechanics. Intensive research efforts have been spent on it for tens of years. Although there are many heuristic methods in practice, the theoretic foundation still remains widely open. Recently, we have established a theoretic framework for quadrilateral mesh generation based on conformal geometry. Basically, we have discovered the intrinsic relation between quad-meshes and meromorphic differentials on Riemann surfaces. This framework is simple, elegant but powerful. It can answer many fundamental problems, that no other methods could shed a light. For examples, it can show the existence of quad-meshes with special properties, estimate the dimension of quad-meshes with constraints, specify the geometric relations among the singular vertices of quad-meshes. More importantly, it gives a simple algorithm for high quality quad-mesh generation based on Riemann-Roch and Abel-Jacobi theorems. Furthermore, the quad-meshes based on Strebel differential can leads to hexahedral mesh generation for volumes.
|Dr. Suzanne Shontz
University of Kansas, USA
Title: Introduction to Moving Meshes
Biography: Suzanne Shontz is an Associate Professor of Electrical Engineering and Computer Science at the University of Kansas. She is also the Director of the Computational Bioengineering Track for the Bioengineering Graduate Program and is affiliated with the Information and Telecommunication Technology Center. Before joining the University of Kansas in 2014, Suzanne was on the faculty at Mississippi State and Pennsylvania State Universities. Previously, she was also a postdoc at the University of Minnesota and earned her Ph.D. from Cornell University in 2005. Suzanne’s research focuses centrally on parallel scientific computing, more specifically on the development of unstructured mesh and numerical optimization algorithms and their applications to computational medicine and aerospace engineering, among others. She has nearly 20 years of experience in unstructured mesh generation. Professor Shontz has received numerous awards for her research including the prestigious NSF Presidential Early CAREER Award (i.e., NSF PECASE Award) from President Obama for her research in computational- and data-enabled science and engineering and an NSF CAREER Award for her research on parallel dynamic meshing algorithms, theory, and software for simulation-assisted medical interventions. She has chaired or co-chaired several top conferences in computational science and engineering including the 2019 SIAM Computational Science and Engineering Conference and the 2019 International Meshing Roundtable.
Abstract: There are numerous scientific application problems for which either the domain of interest or the quantity being simulated moves as a function of time. For example, the heart beats while pumping blood throughout the human body. In this case, the mesh must be updated in order for it to accurately represent the cardiac geometry. This process of moving the mesh from a source domain to the target domain using interpolation or extrapolation is called mesh warping or mesh morphing.
Another application for which moving meshes are employed is that of crack propagation. When the crack initiates and then propagates throughout a material, the forces on various parts of the material change rapidly. In such a case, the mesh must be refined in places where the solution varies rapidly; it may be coarsened in areas where the solution is slowly varying. Moving mesh techniques are used to adapt the mesh according to this variation in the solution.
In this short course, we will first overview the basics of moving meshes. Next, we will cover several mesh warping algorithms followed by moving mesh algorithms employed for the purpose of adapting the mesh. Methods based on partial differential equations, numerical optimization, and geometry will be explored, as well as their underlying mathematics. Applications of moving meshes, such as those from medicine, computational fluid dynamics, and computer graphics will be explored. Finally, future research directions in moving meshes will be discussed.