This year’s SIAM International Meshing Roundtable will feature three short courses, to be held on Monday 6 March 2023.
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 6 March, 2023. Each of the course details is outlined below.
The level set method in connection with meshing
Charles Dapogny (Laboratoire Jean Kuntzmann)
Abstract: Since its introduction in the context of curvature-driven interface motion, the level set method has been one choice strategy for describing the time evolution of a domain. Crucially, this paradigm hinges on a change of perspectives: a shape is seen as the negative subdomain of an auxiliary ``level set’’ function defined on a larger, fixed computational domain. The time evolution of a shape along a given velocity field then translates in terms of a partial differential equation for an associated level set function, which can be conveniently solved on a fixed mesh.
This mini-course is devoted to the recent applications of the level set method has found multiple applications in connection with mesh processing. In a first part, we shall present the basic ingredients of the level set method, and notably the mathematics of implicitly-defined domains and surfaces, the numerical construction of level set functions as signed distance functions, and the tracking of the motion of a domain in the framework of the level set method. In a second time, we discuss several applications of this method which are more specifically connected with meshing, in particular,
- The reconstruction of a valid computational mesh from an input messy, invalid surface triangulation;
- The tracking of the evolution of a mesh of a domain undergoing arbitrarily large motions, including changes in its topology.
Biography: Charles Dapogny is a junior CNRS researcher, affiliated with Laboratoire Jean Kuntzmann (Grenoble, France). His research interests revolve around shape optimization (notably under its numerical aspects) and the asymptotic analysis of partial differential equations.
A metric-driven approach for the generation of anisotropic adapted meshes: theory & practice
Simona Perotto (Politecnico di Milano)
Abstract: The crucial role played by adapted meshes in computational modeling is recognized by the availability of specific modules devoted both to isotropic and anisotropic mesh adaptation in the majority of the current commercial software. Anisotropic adapted grids turn out to be an optimal choice to balance solution accuracy and computational efficiency, when dealing with the numerical modeling of phenomena characterized by highly directional features. Indeed, anisotropic meshes allow sharply detecting such directionalities by properly tuning the size, the shape, and the orientation of the mesh elements, in contrast to an isotropic adapted grid which adjusts the element size only. Anisotropic adapted meshes can be obtained by resorting to heuristic information (e.g., a numerical approximation of the Hessian of the solution) or to theoretical tools coinciding, in general, with estimators of the discretization error.
This short course focuses on the anisotropic setting proposed by L. Formaggia and S. Perotto in Numer. Math., 89 (2001), with the aim of:
- introducing the main theoretical results supporting the proposal of an anisotropic error estimator;
- furnishing two examples of anisotropic estimators for the discretization error associated with a finite element scheme;
- setting a computational strategy to commute an error estimator into a metric field in order to drive the mesh adaptation process;
- providing some examples of real-life problems modeled via a finite element scheme based on an anisotropically adapted mesh;
- highlighting the computational benefits led by the employment of anisotropic adapted meshes.
Biography: Simona Perotto is Associate Professor in Numerical Analysis at the Department of Mathematics of Politecnico di Milano, Italy. She got her Master Degree in Mathematics (University of Torino) and her Ph.D. in Computational Mathematics and Operations Research (University of Milano). Simona Perotto is member of the Management Committee of the Interdepartmental Laboratory MetaMAT-Lab (Politecnico di Milano); member of the Steering Committee of the Master in Mathematical and Physical Methods for Space Sciences and of the Master in Mathematical and Physical Methods for Aviation Sciences (University of Torino); delegate of the Department of Mathematics in the Management Committee of GEOLab (Politecnico di Milano); member of the Advisory Scientific Council of CIMNE.
Simona Perotto has a 20+ years experience in mesh generation and adaptation. Her main scientific interests cover anisotropic mesh adaptation; model reduction and model adaptation; modeling of free-surface flows and of solute transport in porous media; statistical-numerical analysis of high dimensional functional data; and, more recently, advanced techniques for the design of innovative cellular materials, as well as innovative methods and mathematical models applied to sustainability.
She is author and co-author of 75 scientific papers on international peer-reviewed journals, and of 38 contributions on books and proceedings. In particular, the paper in J. Sci. Comput., 60 (2014), 505- 536 has been listed among the most notable (out of 6) papers in 2014 for the class of Mathematics of Computing by the Association of Machine Computing.
Simona Perotto has supervised 72 Master Degree students, 7 PhD doctors (plus, 4 ongoing Ph.D. students), 33 students involved in industrial/academic internships, Erasmus projects, term contracts, research grants.
She has been PI and CoPi of several national and international projects (among these, a NSF and a H2020-MSCA project), and international fellowships.
Simona Perotto has been invited at more than 60 international conferences, 5 times as a Plenary speaker.
Finally, she is co-Founder, shareholder and President of the spin-off ADAPTA studio (Politecnico di Milano). In particular, in December 2019, Simona Perotto won the prize Switch2Product, Innovation Challenge, XI Edition, Politecnico di Milano, Deloitte, PoliHub and attended the acceleration program Switch2Product, Innovation Challenge, PoliHub, Innovation District & Startup Accelerator.
Introduction to mesh curving
Xevi Roca (Barcelona Supercomputer Center)
Abstract: In contrast to standard representations of curved geometry with straight-edged meshes, representations with curved meshes explicitly feature curvature. This explicit geometric feature is benefitial in applications that need to account for curvature, applications in fields such as computational mechanics and computational fluid dynamics.
For these applications, valid curved meshes are successfully generated with an indirect method called mesh curving. Mesh curving needs an initial straight-edged mesh and a boundary representation of the target geometric model. For the initial straight-edged elements, the method converts their linear representation to a high-order representation. Then, for these straight-edged high-order elements, mesh curving performs two key operations. First, to match the target boundary representation, it curves the boundary faces of the high-order mesh. Second, to accommodate the boundary curvature and preserve the mesh validity, mesh curving modifies the coordinates of all or part of the high-order elements. The result is a mesh composed of valid curved elements with a mesh boundary that matches the boundary of the target model.
In this course, attendees will learn the basics of mesh curving, how to automatically curve mesh boundaries and modify mesh coordinates, what are the new trends in mesh curving, and what are the main applications.
Biography: Xevi Roca leads the Geometry and Meshing group at the Barcelona Supercomputing Center (BSC), a group that he has created as an European Research Council Starting Grant fellow and a Ramon y Cajal fellow. He graduated in Applied Math at the Universitat Politècnica de Catalunya (UPC, 1999). He joined UPC to provide technical support to researchers at Laboratori de Calcul Numeric (LaCàN, 1999-2011). From 2004 to 2009, he combined the full-time technical duties with his research to obtain his PhD (UPC, 2009). From 2009 to 2011, he was a visiting scholar at the Massachusetts Institute of Technology (MIT) to later join the Aero-Astro Department as a postdoctoral associate (MIT, 2011-2015). He joined the BSC as a Marie Sklodowska-Curie fellow in 2015.
His research interests lie in the intersection of mesh generation, computational methods, and scientific computing, mainly motivated by aeronautical applications. He is now combining curved meshing with unstructured high-order methods to obtain a 4D space-time high-fidelity flow simulation capability of scientific and industrial interest. He has been fully involved with the International Meshing Roundtable as a contributor (since 2004), a member of the steering committee (2015-2018), and chair (2017-2018).
For any question concerning the short courses, please contact the chair:
- Franck Ledoux, Short Course Chair
CEA. email: email@example.com