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Home | Seminars and Symposia | Past seminars/symposia: Thursday, July 12, 2012

DTC Seminar Series

Visualization of High-Order Finite Element Methods

by

Mike Kirby
School of Computing
Scientific Computing and Imaging Institute
University of Utah

Thursday, July 12, 2012
10:00 am

405 Walter Library

KirbyThe visualization of high-order methods is an area that is heavily used, but often scientifically marginalized. The aim of this talk is to present new research on visualization techniques that both respect and exploit the mathematical structure of high-order methods. Over the last forty years, tremendous effort has been exerted in the pursuit of numerical methods which are both flexible and accurate, hence providing sufficient fidelity to be employed in the numerical solution of a large number of models and sufficient quantification of accuracy to allow researchers to focus their attention on model refinement and uncertainty quantification. High-order finite element methods (also known as spectral/hp element methods) using either the continuous Galerkin or discontinuous Galerkin formulation have reached a level of sophistication such that they are now commonly applied to a diverse set of real-life engineering problems in computational solid mechanics, fluid mechanics, acoustics and electromagnetics. Unfortunately, there has been little emphasis by the scientific community and, in particular, the visualization community, on providing visualization algorithms and the corresponding software solutions tailored to high-order methods; in particular, almost no research has been done to develop visualization methods based on the a priori knowledge that the data was produced by a high-order finite element simulation. Visualization of computed results is often used as a means of understanding and evaluating the numerical approximation of the mathematical model, and it provides a means of "closing the loop" — that is, of critically evaluating the computational results for refinement of the model and/or numerics or for interpretation of the physical world. Visualizations of high-order finite element results which do not respect the a priori knowledge of how the data were produced and which do not provide a quantification of the visual error produced undermine the scientific process just described. In this talk we describe several efforts at creating accurate and efficient visualization methods for high-order methods. We present recent work on isosurfacing, generating cut-surfaces, and volume rendering within our GPU-based ElVis (Element Visualizer) framework, and discuss some preliminary informal user-studies with applications in aeronautics.

 

Robert M. (Mike) Kirby received the M.S. degree in applied mathematics, the M.S. degree in computer science, and the Ph.D. degree in applied mathematics from Brown University, Providence, RI, in 1999, 2001, and 2002, respectively. He was promoted and received tenure at Utah in 2008. During his 2008-2009 sabbatical year, he taught a Michaelmas term course in High-Performance Scientific Computing at the Cavendish Laboratory at Cambridge University, UK and for the academic year was the Leverhulme Visiting Professor of Aeronautics at Imperial College London, UK. He is currently an Associate Professor of computer science with the School of Computing, University of Utah, Salt Lake City, where he is also an Adjunct Associate Professor in the Departments of Bioengineering and Mathematics and a member of the Scientific Computing and Imaging Institute. His current research interests include scientific computing and visualization.