Title: High-order mesh generation
Prof. Paul Louis George is currently heading the Gamma3 team at INRIA, Paris-Rocquencourt center and keeps working actively as Researcher in this team. He has been focussing on unstructured mesh generation algorithms with a special emphasis on tet meshing since the early 1980's. Main achievements of this activity include a series of comprehensive books, a fast and robust tet mesher world-wide distributed together with more advanced tet meshers with size control and/or anisotropic features. Recent work of Paul Louis George considers quadratic simplicial finite element. Paul Louis George is graduated from Universite Pierre et Marie Curie (Paris 6) in 1980
There is a need for finite elements of degree 2 or more to solve various P.D.E. problems. This talk discusses the theoretical issues about Lagrange simplicial finite elements of arbitrary order and dimension. The purpose is to give the theoretical frame to be applied in actual cases (2 and 3 dimension, degree 2, 3 , ...). We show the way in which finite elements and Bezier patches are related to eachother and we deduce a validity condition which is then refined. At the same time, a series of a priori surprising things are exhibited. We use this materials in the effective development of a P2 tet mesher which is demonstrated by means of concrete examples. Conclusions and remarks about more higher element end the talk
Title: Delaunay Refinement and Its Localization for Meshing
Tamal K. Dey is professor of computer science at The Ohio State University. His research interest includes computational geometry, computational topology and their applications to graphics, meshing, and geometric modeling in general. After finishing his PhD from Purdue University in 1991 he spent a year in University of Illinois at Urbana Champaign as a post doctoral fellow. He has held academic positions in Indiana University-Purdue University at Indianapolis, Indian Institute of Technology, Kharagpur, India, Max-Planck Institute, Germany, and INRIA, France.
In the past ten years, Dey has focused his research on three topics, namely surface reconstruction, mesh generation, and feature extraction. His work on curve and surface reconstruction is widely known. He authored a book ``Curve and surface reconstruction: Algorithms with mathematical analysis" published by Cambridge University Press.
In mesh generation, his work emphasized on developing algorithms for producing Delaunay meshes of three dimensional domains which have mathematical guarantees. In feature extraction, he used topological techniques to derive meaningful features from shapes. He has authored more than one hundred scientific articles some of which are highly cited. He leads the Jyamiti group which has developed various software including the well known Cocone software for surface reconstruction and DelPSC software for mesh generation. Details can be found at http://www.cse.ohio-state.edu/~tamaldey.
The technique of Delaunay refinement has been recognized as a versatile tool for generating Delaunay meshes for a variety of geometries. The sampling theory for surfaces coupled with the Delaunay refinement paradigm has led to effective algorithms for meshing smooth surfaces and volumes. The technique has even been extended to piecewise smooth cases where input angles can be arbitrarily small. The first part of this talk focuses on these recent developments giving the theoretical as well as empirical results.
The Delaunay refinement paradigm, despite its usefulness, suffers from one lacuna that limits its application. It does not scale well with the mesh size. As the sample point set grows, the Delaunay triangulation starts stressing the available memory space which ultimately stalls any effective progress. To this end, we develop a localized version of Delaunay refinement which still retains theoretical guarantees. The second part of this talk focuses on this work. Experimental results show that the method can avoid memory thrashing while computing large meshes and thus scales much better than the standard Delaunay refinement method.
Title: Tailored unstructured meshes for efficient aerospace engineering simulations
Professor Hassan obtained a Masters Degree from the University of Wales Swansea in finite element methods, before completing his PhD on the simulation of hypersonic flows. He subsequently was employed in a consultancy company, where he developed computer methods based upon unstructured mesh technology for a wide variety of applications. In 1994, he was appointed as a lecturer in the Department of Civil Engineering at Swansea, obtaining a personal chair in 2003. He has developed software, in collaboration with the aerospace industry, for over 20 years. He has extensive experience in the areas of unstructured mesh generation and adaptivity and in the development and implementation of solution algorithms for computational fluid dynamics and computational electromagnetic and has an extensive list of publication in those areas. In 2002 he was awarded the DSc degree by University of Wales for his contribution to computational engineering in aerospace. He was also awarded the MBE in January 1998 for his contribution to the aerodynamic design of THRUST SSC, the car which broke the World Land Speed Record in 1997.
The talk will give an overview of the quality of unstructured meshes and their effect on the quality of the solution algorithm. The restriction that is imposed by the geometry definition which has a direct effect on the final quality of the mesh and the convergence speed will also be addressed.
The talk will also highlight the mesh quality required for a special class of algorithms that are based on the Co-volume methods, which are staggered in both time and space, and exhibit a high degree of computationally efficiency, in terms of both CPU and memory requirements compared to, for example, finite element methods. Despite the fact that real progress has been achieved in unstructured mesh generation methods since late 1980s, co-volume schemes have not generally proved to be effective for the simulations involving general domains of complex shape. This is due to the difficulties encountered when attempting to generate the high quality meshes that are needed to satisfy the mesh requirements necessary for co-volume methods. A Review of the various mechanisms that can be used to achieve the required properties that the mesh must satisfy for Co-volume methods will be given. A new optimisation procedures based on a modified Cuckoo Search coupled to a reduced order model using Proper Orthogonal Decomposition (POD) will be described. The improved quality of the overall resulting Voronoi-Delaunay dual diagram will also be described. Practical test cases which utilise the generated meshes to demonstrate the efficiency that can be achieved for the simulation of unsteady incompressible flows using the extended MAC algorithm and electromagnetic scattering in two and three dimension using the modified YEE algorithm on unstructured meshes will be presented.
Title: Meshing – A Key Enabling Technology in Computational Simulations, nD Visualization & Mixed Reality
Dr. Soni received his doctoral degree in Applied Mathematics from the University of Texas in 1979. After 9 years in industry and adjunct experience in academic institutions, he joined the academic world at Mississippi State University (MSU) as an Associate Professor of Aerospace Engineering in 1988. Until, June 30, 2002, He was the Director for the Center for Computational Systems (CCS), Engineering Research Center (ERC), and a Professor and Eminent Scholar of Aerospace Engineering at MSU. He joined the University of Alabama at Birmingham (UAB) as a Chair and Professor of Mechanical Engineering in July 2002.
Dr. Soni leads the Department of Mechanical Engineering in teaching, research and development, service/outreach and technology transfer activities. Dr. Soni's group at UAB has a long history of contributions in cross-disciplinary research and education in high fidelity computational simulations and associated enabling technologies (nD visualization, virtual reality, image processing, and high performance computing). The strategic research focus is to build on these technologies to address 21st Century engineering grand challenges: Advance Personalized Learning, Engineer the Tools of Scientific Discovery, Enhance Virtual Reality, and Develop Carbon Sequestration Methods covering a wide-spectrum of disciplines including aerospace, automotive, homeland security, energy and environment, healthcare, biomechanics, and biomedical and medical science. Dr. Soni has led the establishment of the VisCube environment which provides an immersive an immersive three-dimensional and virtual reality experience (http://www.uab.edu/uabmagazine/2009/december/vizcube) with applications to medical, health-care and general education and training, rehabilitation, engineering design, analysis, evaluation and marketing, and homeland security (http://main.uab.edu/Sites/MediaRelations/articles/71060/). He has provided a leadership in building UAB High Performance Computing capabilities from less than 1 TeraFlops in 2002 to 11+ TeraFlops combined performance in 2011.
Dr. Soni's group has well established collaborations with academic institutions and industry in the US, China, India, and Europe. These collaborative activities have resulted in the initiation of the Mixed Reality Medical Simulation Training Center in collaboration with the UAB School of Medicine, US Army, and US Air Force and the Regional Carbon Sequestration Center in collaboration with the Southern Company and NEPRI (China). Also, through collaboration with four junior colleges (CACC, ESCC, WSCC, and SSCC) and Tuskegee University, Dr. Soni plans to develop visual educational contents for middle school teachers and students. Additionally, the intellectual properties generated by the group have resulted in two spin-off commercial companies in Birmingham: VIPAAR (integrates remote expertise directly and indirectly into local field of operation) and Amplicode (provides consulting and engineering support associated with computer aided geometry design and meshing to the engineering simulation community).
Dr. Soni has been instrumental in the growth of the Department of Mechanical Engineering from $300K in annual research expenditure, 6 faculty members, and 70 undergraduate and 6 graduate students in 2002 to $3.0-3.5M in annual sponsored research expenditure, 18 faculty members, 7 research associates, and 189 undergraduate and 39 graduate students in 2011. Dr. Soni has been internationally recognized for his research, educational and professional services and contributions in the area of numerical grid generation and computational fluid dynamics. He has authored more than 170 publications and is a co-editor of the CRC Handbook of Grid Generation, published in 1999.
The National Academy of Engineering (NAE) has identified the following as five of the fourteen greatest engineering challenges humanity will face in the 21st century: Enhance Virtual Reality, Advanced Personalized Learning, Engineer the Tools for Scientific Discovery, Develop Carbon Sequestration Methods, and Engineer Better Medicine (Engineer Better Health Care Practice). High fidelity computational simulations and associated enabling technologies (meshing, computer-aided geometry design, image processing, visualization, virtual and augmented reality) integrated with experiments/observations and theoretical advances provide an efficient approach in addressing these challenges. To this end, the University of Alabama at Birmingham (UAB) has developed a strategic interdisciplinary education and research program focusing on the core areas of high fidelity computational simulations and associated enabling technologies applicable to related scientific disciplines. Meshing is a key enabling infrastructure technology critical to success of this highly collaborative program where a wide spectrum of applications from aerospace, automotive, energy, homeland security, environmental and health sciences as well as healthcare are being researched and developed.
The hardware/software and human expertise infrastructure will be described along with progress realized in the development of tools and technologies and associated applications in the disciplines mentioned above. Computational and associated enabling technology tools will be presented with an emphasis on historical perspectives and future directions of meshing algorithms, associated software, and applications in education, training, diagnostics, research, analysis, and design. Future program directions will be described emphasizing a recently initiated Mixed Reality Medical Simulation Training Center, Alabama Collaborative Center on Energy Sustainability (ACCESS), and 3D Content Development System.