Lawrence Livermore National Laboratory, USA
Title: Large-scale Finite Element Applications on High-Order Meshes
Biography: Tzanio Kolev is a computational mathematician at the Center for Applied Scientific Computing of Lawrence Livermore National Laboratory (LLNL) where he works on efficient finite element discretizations and solvers for problems in compressible shock hydrodynamics, multi-material ALE, computational electromagnetics and other application areas. He joined LLNL in 2004 after earning a Ph.D. in Mathematics from Texas A&M University. Tzanio is the director of the Center for Efficient Exascale Discretizations (CEED) in the Exascale Computing Project and the project leader of several projects at LLNL, including MFEM, BLAST and ETHOS. Tzanio’s research interests include the development and analysis of finite element discretizations, high-order methods and applications, performance optimizations and scalability, discretization-enhanced multigrid solvers, and the design and implementation of large-scale scientific software. His work on AMS – the first provably scalable solver for electromagnetic diffusion problems, was selected as one of the top ten breakthroughs in computational science in a 2009 DOE-ASCR report.
Abstract: High-order simulation methods using general unstructured high-order meshes are a win-win proposition with respect to both mathematical accuracy and performance efficiency on upcoming HPC architectures. It has long been known that high-order methods provide increased accuracy at low cost for problems with large regions of smooth but non-trivial variation, such as vortices and boundary and mixing layers. Our work on Arbitrary Lagrangian Eulerian (ALE) hydrodynamics  shows that high-order finite elements on high-order meshes can also have mathematical benefits with respect to symmetry preservation, energy conservation, robustness in Lagrangian flow, and sub-zonal resolution for shock problems.
While high-order discretization methods have been developed and studied extensively in the past, the overall solution approaches have often used low-order computational meshes. One practical reason for this is that high-order meshes come with a unique set of challenges that have not been addressed by prior research on low-order (linear) meshes. For example, the Jacobians of high-order element mappings are highly varying polynomial functions that can not be treated as constants and require special considerations in the high-order case.
In this talk I will review the use of high-order polynomial spaces to define both the mapping and the reference basis functions in the Lagrange phase of ALE hydrodynamics and will discuss the application of the curvilinear technology to the “advection phase” of ALE, including a DG-advection approach for conservative and monotonic high-order finite element interpolation (remap). I will review in particular our recent work on robust and efficient algorithms for high-order mesh optimization, which is critical components of the ALE remap phase. This research builds on the Target-Matrix Optimization Paradigm (TMOP) and nonlinear variational minimization to develop new node-movement strategies for high-order mesh quality optimization and adaptation in both purely geometric settings, as well as in the context of a given physical simulation. In addition to ALE, this work targets moving mesh applications, smoothing in mesh generation, and applications where symmetry preservation or adaptation to physics is important (e.g., inertial confinement fusion and tokamak magnetohydrodynamics). The algorithms are freely available as part of the MFEM finite element library .
 "High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics", V. Dobrev and Tz. Kolev and R. Rieben, SIAM Journal on Scientific Computing, (34) 2012, pp.B606-B641.
 MFEM: Modular finite element library, https://mfem.org.
|Dr. David Bommes,
University of Bern, Switzerland
Title: Integer-Grid Maps for Quadrilateral and Hexahedral Mesh Generation
Title: Integer-Grid Maps for Quadrilateral and Hexahedral Mesh Generation
Biography: David Bommes is a full professor in the institute of computer science at University of Bern and head of the Computer Graphics Group. Before he has been a junior professor in the department of computer science at RWTH Aachen University (2014-2018), where he also received his Ph.D. in 2012. Between 2012 and 2014 David Bommes has been a researcher in France at Inria Sophia Antipolis. His research interests include algorithms for geometry processing and specifically mesh generation, (discrete) differential geometry and numerical optimization. David Bommes’ scientific contributions to computer graphics and geometry processing have been recognized by the EUROGRAPHICS Association with two prestigious prizes, the Best Ph.D. Thesis Award in 2013 and the Young Researcher Award in 2016.
Abstract: Automatically generating quadrilateral and hexahedral meshes is a notoriously challenging task, specifically if alignment to freeform surfaces in combination with high mesh regularity and low distorted elements is required. Novel algorithms based on global optimization rely on the construction of integer-grid maps, which pull back a Cartesian grid of integer isolines from a 2D or 3D domain onto a structure aligned quadrilateral or hexahedral mesh. Such global optimization algorithms do not suffer from limitations known from local advancing front methods, as for instance a high rate of irregularity, and enable meshes comparable to manually designed ones by finding a good compromise between regularity and element distortion. The key to efficiently finding high-quality solutions are 3D frame fields that are employed to optimize the orientation and sizing of mesh elements globally. In my talk, I will give an overview of the state of the art and discuss the strengths and weaknesses of available algorithms, including open challenges for hexahedral meshing.
Epic Games, USA
Title: Triangulating the future of 3D Design Tools
Biography: Ryan Schmidt leads the Geometric Modeling team at Epic Games, and has an Adjunct appointment at the University of Toronto. He previously founded Gradientspace Corp, where he wrote the open-source mesh processing library geometry3Sharp, created the open-source 3D Printing app Cotangent, and helped Nia Technologies bring 3D-printed prosthetics to the developing world. From 2011 to 2016 he was head of the Design & Fabrication Group at Autodesk Research, which he joined with the acquisition of his mesh modeling software Meshmixer. Meshmixer has been downloaded millions times, by a userbase ranging from elementary school students to aerospace engineers. He academic research focuses on 3D modeling, 3D user interfaces, and geometry processing. Find him on the web at https://urldefense.proofpoint.com/v2/url?u=http-3A__www.rms80.com&d=DwIFAg&c=slrrB7dE8n7gBJbeO0g-IQ&r=Rzi2u-5rQB71qeVh4_DaQA&m=f0sn77hUsqEsPQQqzw5V9oyLAjUq3AwtnPvno3ooRjo&s=Bgx0QwOnEu3EkPgK-3QOfjkZXZ4JE8VogTNU8kqb6v0&e=, or on twitter @rms80.
Abstract: Historically, triangle meshes have not been held in particularly high regard in the world of 3D design tools. Triangles - sometimes downgraded to "facets" - are more likely to be the source of problems rather than solutions. However, over the past two decades the outlook for triangle meshes has markedly improved. Advances in geometry processing now allow us to solve complex energy minimizations over triangle surfaces, compute robust booleans, and efficiently perform spatial queries like point containment. As a result, the lowly triangle mesh now supports mathematical capabilities far beyond what is practical with traditional CAD B-Reps. Modern rendering, simulation, and manufacturing methods - particularly Additive Manufacturing - are also largely driven by triangle meshes. From this viewpoint, the trimmed NURBS patch appears to primarily be a user interface to, and procedural generator of, a patch of triangles. This leads us to ask, why not cut out the middle-man and design directly with triangles? In this talk I will describe my attempts to do just that, first by embedding some organizational structure into the mesh, and then using this simplified topology to provide novel design interfaces.
Adobe Research, Seattle, WA, USA
Title: Numerical Optimization of Geometric and Physical Behavior on Meshes
Biography: Danny Kaufman is a Senior Research Scientist at Adobe based in Seattle, WA. Previously he was a post-doctoral researcher at Columbia University working with Prof. Eitan Grinspun and before that finished his PhD work at the University of British Columbia advised by Prof. Dinesh Pai. Danny’s research focuses on developing predictive, expressive and efficient computational models and tools for applications in physical simulation, geometry processing, computer animation and design. His work has been broadly applied in domains ranging from from live broadcast (The Late Show with Steve Colbert, The Simpsons) and production (Our Cartoon President) television, to visual effects research (with Weta and Disney), and on to the predictive physical modeling of granular assemblies and passive dynamic robotics.
Abstract: A wide range of core geometry, simulation and design tasks, ranging from surface parameterization to time-stepping elastodynamics, boil down to solving variational problems defined on meshes. Yet the fundamental features of the complex models involved, including strong nonlinearities, nonsmoothness and nonconvexity, pose significant challenges to computation at the high-speed rates required by modern research, entertainment, and industrial applications. To make these applications tractable we often necessarily turn to coarse mesh representations and potentially even low-precision solves. And while classical analysis can sometimes provide guarantees for our solutions at high resolutions with accurate solves, all bets are off when we violate these base assumptions. Nevertheless, systems must be modeled and, in turn, these models will often necessarily be roughly discretized and solved. It is thus critical to consider how algorithms for these rough solutions can best be understood, designed, validated and improved. In turn this leads us to ask: how can we create predictive and compelling solutions to these optimization problems across mesh resolutions?
In this talk I will present some of our recent investigations towards answering these questions. First, I will discuss our development of optimization technologies towards the fast, scalable and convergent minimization of distortion energies over meshes. These are fundamental tasks for applications across geometry processing and deformation and so must necessarily work well for unstructured meshes with widely varying resolutions and shapes. Second, I will discuss our work on designing an algorithm for the efficient and accurate simulation of impacting elastodynamics. The resulting material-aware frictional impact method, designed for coarser space and time meshes, leads to a well over 70X improvement in the predictive simulation of 3D-printed materials. Third, I will present a new optimization method for shape interpolation on meshes that enables interpolation between shapes with extreme deformation and topology changes at interactive rates. Throughout I will focus on the combined and intertwined role that optimization and meshing play in these domains. I will cover a range of applications that our methods enable -- from the design optimization of 3D-printed mechanisms to the live-broadcast animation of performed cartoons. For more details on these and related projects see http://dannykaufman.io.