Plenary and Semi-Plenary Lectures
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| Title: |
| The Discontinuous Enrichment Method for Multiscale and Higher-Frequency Wave Propagation Problems |
| Lecturer: |
| Charbel Farhat |
| Abstract: |
| Wave propagation problems pertain to many technologies including sonar, radar, geophysical exploration, medical imaging, nondestructive testing, and structural design. In the medium frequency regime, the analysis of these problems by the standard finite element method is either computationally unfeasible or simply unreliable, because of the well-known pollution effect. In practice, the higher-order (or p-type) finite element method alleviates this effect, but only to some extent. Alternative approximation methods based on plane waves have recently emerged to address this issue. The Discontinuous Enrichment Method (DEM) is such an alternative. It distinguishes itself from similar approaches by its ability to evaluate the important system matrices analytically, thereby bypassing the typical accuracy and cost issues associated with high-order quadrature rules. DEM also provides a unique multiscale approach to computation by employing fine scales that contain solutions of the underlying homogeneous partial differential equation in a discontinuous framework. The theoretical and computational underpinnings of this method will be overviewed. Then, recent applications to underwater acoustic and elastoacoustic scattering as well as automotive structural vibrations in the mid-frequency regime will be discussed. One to two orders of magnitude accuracy and/or solution time (CPU) improvement over the higher-order Galerkin method will be demonstrated in three dimensions. |
 Charbel Farhat is Professor of Mechanical Engineering, Professor, by courtesy, of Aeronautics and Astronautics, and Professor in the Institute of Computational and Mathematical Engineering, at Stanford University. He is the recipient of several prestigious awards including the Institute of Electrical and Electronics Engineers Computer Society's Gordon Bell Award, the International Association of Computational Mechanics' Computational Mechanics Award, the Department of Defense Modeling and Simulation Award, the US Association of Computational Mechanics Computational and Applied Sciences Award, the Institute of Electrical and Electronics Engineers Computer Society's Sidney Fernbach Award, the American Society of Mechanical Engineers Aerospace Structures and Materials Award, and the National Science Foundation's Presidential Young Investigator Award. Professor Farhat is currently Vice Chair of the Society for Industrial and Applied Mathematics Activity Group on Supercomputing, and Associate Editor of the International Journal for Numerical Methods in Engineering. He also serves on the editorial board of six international scientific journals, and on the technical assessment board of several national research councils and foundations. He is an elected Fellow of the American Society of Mechanical Engineers, the International Association of Computational Mechanics, the World Innovation Foundation, the US Association of Computational Mechanics, and the American Institute of Aeronautics and Astronautics. |
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