Keynote Speaker: Pascal
Frey, Universite Pierre & Marie Curie
Pascal Frey is a professor of applied maths at the Universite Pierre et Marie Curie, member of the Jacques Louis Lions laboratory (Y. Maday dir.), former member of the Gamma group (P.L. George, dir.) at INRIA research center. Research areas: surface and volume mesh generation, mesh adaptation, scientific computing, visualisation.
Perspectives of local anisotropic
Delaunay mesh adaptation
In this lecture, we will focuss on h-adaptation based on the anisotropic Delaunay kernel in view of numerical simulations based on finite element methods. An application of this scheme will be presented in the area of rigid-body mesh movement. The robustness of the approach relies heavily on preserving mesh quality during each adaptation stage.
Use of Digital Topology
for Robust Geometric Computation
Geometric algorithms are fragile if they are implemented naively because numerical errors generate inconsistency in geometric structures. To overcome this difficulty, many approaches to robust implementation have been proposed, and those that survive till now can be classified into two groups: an exact computation approach and a topology-based approach. The exact computation approach uses high precision arithmetic that is sufficient to judge the topological structures always correctly. This approach is usually used together with symbolic perturbation to cope with degeneracy and a lazy evaluation scheme to decrease computational cost. The topology-based approach, on the other hand, uses floating-point arithmetic while placing higher priority on topological consistency than on numerical values and thus avoids failures.
The topology-based approach has many good merits; it never fails because the consistency is guaranteed from a topological point of view, it is fast because we can use floating-point arithmetic, it is simple because degeneracy never arises, etc. However, the use of this approach is not so automatic as the exact computation approach, because we have to extract topological invariants from each individual geometric problem. This has been a bottleneck for common use of this approach.
Recently, we could improve this approach so that it can be used even by beginners. The basic idea is the use of digital topology. That is, instead of finding topological invariants for a given problem, we first generate an approximate solution of the problem in terms of digital picture, then extract the topological structure from the approximation, and finally use it in the topology-based approach. We show this approach with examples, and discuss about the applicability to mesh generation.
Professor Holst's general research background and interests are in a broad area called computational and applied mathematics; his specific research areas are partial differential equations (PDE), numerical analysis, approximation theory, applied analysis, and mathematical physics. His research projects center around developing mathematical techniques (theoretical techniques in PDE and approximation theory) and mathematical algorithms (numerical methods) for using computers to solve certain types of mathematical problems called nonlinear PDE. These types of problems arise in nearly every area of science and engineering; this is just a reflection of the fact that physical systems that we try to manipulate (e.g., the flow of air over an airplane wing, or the chemical behavior of a drug molecule), or build (e.g., the wing itself, or a semiconductor), or simply study (such as the global climate, or the gravitational field around a black hole) are described mathematically by nonlinear PDE. In simple cases, these problems can be simplified so that purely mathematical techniques can be used to solve them, but in most cases they can only be solved using sophisticated mathematical algorithms designed for use with computers. Computational simulation of PDE is now critical to almost all of science and engineering; the mathematicians provide the mathematical tools and understanding so that scientists in physics, chemistry, biology, engineering, and other areas can confidently use the modern techniques of computational science in the pursuit of new understanding in their fields of study. To learn more about Professor Holst's particular research program, please see his webpage: http://cam.ucsd.edu/~mholst
Parallel Adaptive Finite Element Techniques
We describe a low-communication approach to the use of adaptive finite element methods with parallel computers, developed jointly with R. Bank at UCSD. The algorithm deals with load balancing in an a priori manner, and decouples the coupled elliptic problem into a set of independent subproblems. We give some numerical examples illustrating the approach, and then provide a rigorous analysis of the resulting solution quality. We give local and global error estimates for the solutions produced by the parallel algorithm by reinterpreting it as a partition of unity method, and by using some local estimates from the approximation theory literature. The algorithm is applicable to general elliptic equations in 2D and 3D polyhedral domains.
Banquet Speaker: Dipankar Choudhury, Fluent Inc.
|Dr. Dipankar Choudhury
is the Chief Technology Office at Fluent Incorporated, a leading Computational
Fluid Dynamics software and solutions provider.
He is responsible for directing Fluent Inc.'s R&D and funded development
activities. Prior to his appointment in his current CTO role, Dr. Choudhury
has held positions in software development, product management, overseas
business development, consulting, and customer support.
Dr. Choudhury obtained his Ph.D. in the area of Computational Fluid
Dynamics and Heat Transfer from the University of Minnesota in 1987.
He is a member of the ASME and of the AIAA and has CFD related publications
in journals, conference proceedings and trade magazines.
The Central Role of Mesh
in Commercial Computational Fluid Dynamics Applications
The use of commercial CFD analysis tools is now in its third decade. This talk provides a perspective on how CFD analysis has been applied in industry, the current status of the business, technology and software tools and their relevance to the needs of end users. Some thoughts are provided on evolving trends (both in technology as well as market needs and usage patterns) and the major mesh generation challenges that have to be overcome in order for CFD software to be employed more broadly in industrial applications.
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