题  目：A Dual Mesh Finite Domain Method with Applications to Diffusion and Convection-Diffusion Problems

时  间：2019年10月11日14：30－16：00

地  点：交通大楼604会议室

报告人：J.N. Reddy院士（美国德州农工大学）

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                 土木与交通学院

                 2019年10月8日

报告人简介：

       Dr. Reddy is a Distinguished Professor, Regents’ Professor, and inaugural holder of the Oscar S. Wyatt Endowed Chair in Mechanical Engineering at Texas A&M University, College Station, Texas. Dr. Reddy earned a Ph.D. in Engineering Mechanics in 1974 from University of Alabama in Huntsville. He worked as a Post-Doctoral Fellow in Texas Institute for Computational Mechanics (now ICES) at the University of Texas at Austin, Research Scientist for Lockheed Missiles and Space Company, Huntsville, during l974-75, and taught at the University of Oklahoma from 1975 to 1980, Virginia Polytechnic Institute & State University from 1980 to 1992, and at Texas A&M University from 1992.

Dr. Reddy, an ISI highly-cited researcher, is known for his significant contributions to the field of applied mechanics through the authorship of a large number of journal papers and 21 textbooks and the development of shear deformation plate and shell theories and their finite elements. His pioneering works on the development of shear deformation theories (that bear his name in the literature as the Reddy third-order plate theory and the Reddy layerwise theory) have had a major impact and have led to new research developments and applications. In recent years, Reddy's research has focused on the development of locking-free shell finite elements and nonlocal and non-classical continuum mechanics problems, involving couple stresses, surface stress effects, and micropolar cohesive damage.

Recent Honors include: 2019 Timoshenko Medal from the American Society of Mechanical Engineers, 2018 Theodore von Karman Medal from the Engineering Mechanics Institute of the American Society of Civil Engineers, the 2017 John von Neumann Medal from the U.S. Association of Computational Mechanics, the 2016 Prager Medal, Society of Engineering Science, and 2016 ASME Medal from the American Society of Mechanical Engineers. He is a member US National Academy of Engineering and foreign fellow of Indian National Academy of Engineering, the Canadian Academy of Engineering, and the Brazilian National Academy of Engineering. In a recent world ranking of researchers in engineering, he is #13 in all of engineering and #5 in mechanical engineering.

报告摘要：

      A method that employs a dual mesh, one for primary variables and another for the secondary variables, for the numerical solution of differential equations is presented [1].  The formulation makes use of the traditional finite element interpolation [2] of the primary variables (primal mesh) and the subdomain concept akin to the finite volume method [3-5] to satisfy the integral form of the governing differential equations on a dual mesh.  The approach is termed a dual-mesh finite domain method to distinguish it from both the finite element method and the finite volume method, although the method shares some elements of both methods. The method is introduced as applied to representative differential equations in 1-D and 2-D. Numerical examples are presented to illustrate the methodology and accuracy compared to the conventional finite element and finite volume solutions.

 References of additional information

 1.       J. N. Reddy, “A dual mesh finite domain method for the numerical solution of differential equations,” International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 20, No. 3, pp. 212-228, 2019.

2.       J. N. Reddy, An Introduction to the Finite Element Method, 4th ed., McGraw--Hill, New York, NY, 2019.

3.       H. K. Versteeg and W. Malalasekera, Computational Fluid Dynamics, The Finite Volume Method, 2nd ed., Pearson Education (Prentice--Hall), Harlow, England, UK, 2007.

4.       J. H. Ferziger and M. Peric', Computational Methods for Fluid Dynamics, 3rd ed., Springer-Verlag, New York, NY, 2002.

5.  S. Mazumder, Numerical Methods for Partial Differential Equations. Finite Difference and Finite Volume Methods, Elsevier, New York, NY, 2016.