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Charbel Farhat is the Vivian Church Hoff Professor of Aircraft Structures in the School of Engineering at Stanford University, where from 2008 to 2023, he chaired the Department of Aeronautics and Astronautics. From 2022 to 2023, he chaired this department as the inaugural James and Anna Marie Spilker Chair of Aeronautics and Astronautics. He is also Professor in the Institute for Computational and Mathematical Engineering, and Director of the Stanford-King Abdulaziz City for Science and Technology Center of Excellence for Aeronautics and Astronautics. From 2017 to 2023, he served on the Space Technology Industry-Government-University Roundtable; from 2015 to 2019, he served on the United States Air Force Scientific Advisory Board (SAB); from 2008 to 2018, he served on the United States Bureau of Industry and Security's Emerging Technology and Research Advisory Committee (ETRAC) at the United States Department of Commerce; and from 2007 to 2018, he served as the Director of the Army High Performance Computing Research Center at Stanford University. He was designated by the US Navy recruiters as a Primary Key-Influencer and flew with the Blue Angels during Fleet Week 2014.
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In numerical analysis, multi-time-step integration, also referred to as multiple-step or asynchronous time integration, is a numerical time-integration method that uses different time-steps or time-integrators for different parts of the problem. There are different approaches to multi-time-step integration. They are based on domain decomposition and can be classified into strong (monolithic) or weak (staggered) schemes. Using different time-steps or time-integrators in the context of a weak algorithm is rather straightforward, because the numerical solvers operate independently. However, this is not the case in a strong algorithm. In the past few years a number of research articles have addressed the development of strong multi-time-step algorithms. In either case, strong or weak, the numerical accuracy and stability needs to be carefully studied. Other approaches to multi-time-step integration in the context of operator splitting methods have also been developed; i.e., multi-rate GARK method and multi-step methods for molecular dynamics simulations.
The proper generalized decomposition (PGD) is an iterative numerical method for solving boundary value problems (BVPs), that is, partial differential equations constrained by a set of boundary conditions, such as the Poisson's equation or the Laplace's equation.
Michel Bercovier is a French-Israeli Professor (Emeritus) of Scientific Computing and Computer Aided Design (CAD) in The Rachel and Selim Benin School of Computer Science and Engineering at the Hebrew University of Jerusalem. Bercovier is also the head of the School of Computer Science at the Hadassah Academic College, Jerusalem.
References
- ↑ C. Farhat and F. X. Roux, A method of finite element tearing and interconnecting and its parallel solution algorithm, Internat. J. Numer. Meths. Engrg. 32, 1205-1227 (1991)
- ↑ Charbel Farhat, Jan Mandel, and François-Xavier Roux, Optimal convergence properties of the FETI domain decomposition method, Comput. Meth. Appl. Mech. Engrg. 115(1994)365-385
- ↑ J. Mandel and R. Tezaur, On the Convergence of a Substructuring Method with Lagrange multipliers, Numerische Mathematik 73 (1996) 473-487
- ↑ C. Farhat, A. Macedo, M. Lesoinne, A two-level domain decom- position method for the iterative solution of high-frequency exterior Helmholtz problems, Numerische Mathematik 85 (2000) 283-303 DOI 10.1007/PL00005389
- ↑ C. Farhat, A. Macedo, M. Lesoinne, F. X. Roux, F. Magoules, A. D. L. Bourdonnaye, Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems, Computer Methods in Applied Mechanics and Engineering 184(2-4) (2000) 213-240 DOI 10.1016/s0045-7825(99)00229-7 hal-00624498
- ↑ B. Vereecke, H. Bavestrello, D. Dureisseix, An extension of the FETI domain decomposition method for incompressible and nearly incompressible problems, Computer Methods in Applied Mechanics and Engineering 192 (2003) 3409-3429 DOI 10.1016/S0045-7825(03)00313-X hal-00141163
- ↑ D. Dureisseix, C. Farhat, A numerically scalable domain decomposition method for the solution of frictionless contact problems, International Journal for Numerical Methods in Engineering 50 (2001) 2643-2666 DOI 10.1002/nme.140 hal-00321391
- ↑ Z. Dostál, F. A.M. Gomes Neto, S. A. Santos, Solution of contact problems by FETI domain decomposition with natural coarse space projections. Computer Methods in Applied Mechanics and Engineering 190 (2000) 1611-1627 DOI 10.1016/s0045-7825(00)00180-8
- ↑ Philip Avery, Charbel Farhat, The FETI family of domain decomposition methods for inequality-constrained quadratic programming: Application to contact problems with conforming and nonconforming interfaces. Computer Methods in Applied Mechanics and Engineering 198 (2009) 1673-1683, DOI 10.1016/j.cma.2008.12.014