Implicit Gradient for Numerical Solution of PDEs



题目:Implicit Gradient for Numerical Solution of PDEs

报告人:J. S. Chen教授University of California, San Diego





Implicit gradient (IG) is expressed in an integral equation with embedded gradient consistency without explicit derivatives. It offers a paradigm for constructing approximation of function derivatives for the numerical solution of PDEs, either by using strong forms or weak forms.  A straightforward application of IG is for the gradient typed regularization of ill-posed problems, such as the strain localization problems. GI can also be used to construct stabilization of convection dominated problems and as the stabilization of nodally integrated Galerkin equation. Without the need of taking directives of approximation functions, GI also offers computational efficiency for Meshfree based numerical solution of PDEs. This talk will introduce continuous and discrete GI for approximation of derivatives, discuss the gradient consistency of GI and its convergence properties in solving PDEs, and demonstrate its applications to strain localization, convection dominated problems, and modeling of damage and fracture processes in solids subjected to extreme loadings.


J. S. Chen is currently the Inaugural William Prager Chair Professor of Structural Engineering Department and the Director of Center for Extreme Events Research at UC San Diego. Before joining UCSD in October 2013, he was the Chancellor’s Professor of UCLA Civil & Environmental Engineering Department where he served as the Department Chair during 2007-2012. J. S. Chen’s research is in computational mechanics and multiscale materials modeling with specialization in the development of meshfree methods. He is the Past President of US Association for Computational Mechanics (USACM) and the Past President of ASCE Engineering Mechanics Institute (EMI). He has received numerous awards, including the Computational Mechanics Award from International Association for Computational Mechanics (IACM), ICACM Award from International Chinese Association for Computational Mechanics (ICACM), the Ted Belytschko Applied Mechanics Award from ASME Applied Mechanics Division, the Belytschko Medal, US Association for Computational Mechanics (USACM), among others. He is the Fellow of USACM, IACM, ASME, EMI, ICACM, and ICCEES.