Courses / ActivitiesA Paradigm for Computational Continuum to Quantum Mechanics
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Mechanics at different length scales exhibit diverse characteristics that require proper regularity in the construction of numerical formulation. Strong and weak discontinuities, topological change in geometry, and singularities are a few examples that render difficulty in the construction of approximation functions with desirable regularity in solving mechanics problems at different length scales. We first review a few finite element and meshfree approximation methods to address these issues. Through three classes of problems at continuum macro-scale, meso-scale, and quantum-scale, we demonstrate the convergence properties of Galerkin meshfree approach and how it can be constructed to alleviate the numerical difficulties associated with the standard finite element methods. The examples include large eformation and fragment impact problems, modeling of icrostructure evolution, and solution of Schrodinger equation in quantum mechanics. We then discuss the possibility of introducing meshfree approximation under the strong form collocation framework, including the local moving least squares reproducing kernel and the nonlocal radial basis collocation methods. We show how to combine the advantages of radial basis function and reproducing kernel function to yield a local approximation that is better conditioned than that of the radial basis collocation method, while at the same time offers a higher rate of convergence than that of Galerkin type reproducing kernel method. J. S. Chen received PhD from Northwestern University in 1989. He is now the Chancellor’s Professor & Department Chair of Civil & Environmental Engineering Department at UCLA. He is also Professor of Mechanical & Aerospace Engineering Department and Professor of Mathematics Department at UCLA. He is the Vice President of US Association for Computational Mechanics. His research activities include development of finite element and meshfree methods for large deformation and contact mechanics, multiscale materials modeling, computational biomechanics, and computational quantum mechanics. He has received numerous awards, including GenCorp Technology Achievement. Award, The Faculty Scholar Award, UCLA Chancellor’s Professor Endowed Chair, Fellow of US Association for Computational Mechanics, Fellow of International Association for Computational Mechanics, Outstanding Alumnus of National Central University, Taiwan, etc. Three of his papers have been cited for more than 100 times (ISI).
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Jiun-Shyan Chen
2009-04-21
11:10:00 - 12:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
Mechanics at different length scales exhibit diverse characteristics that require proper regularity in the construction of numerical formulation. Strong and weak discontinuities, topological change in geometry, and singularities are a few examples that render difficulty in the construction of approximation functions with desirable regularity in solving mechanics problems at different length scales. We first review a few finite element and meshfree approximation methods to address these issues. Through three classes of problems at continuum macro-scale, meso-scale, and quantum-scale, we demonstrate the convergence properties of Galerkin meshfree approach and how it can be constructed to alleviate the numerical difficulties associated with the standard finite element methods. The examples include large eformation and fragment impact problems, modeling of icrostructure evolution, and solution of Schrodinger equation in quantum mechanics. We then discuss the possibility of introducing meshfree approximation under the strong form collocation framework, including the local moving least squares reproducing kernel and the nonlocal radial basis collocation methods. We show how to combine the advantages of radial basis function and reproducing kernel function to yield a local approximation that is better conditioned than that of the radial basis collocation method, while at the same time offers a higher rate of convergence than that of Galerkin type reproducing kernel method. J. S. Chen received PhD from Northwestern University in 1989. He is now the Chancellor’s Professor & Department Chair of Civil & Environmental Engineering Department at UCLA. He is also Professor of Mechanical & Aerospace Engineering Department and Professor of Mathematics Department at UCLA. He is the Vice President of US Association for Computational Mechanics. His research activities include development of finite element and meshfree methods for large deformation and contact mechanics, multiscale materials modeling, computational biomechanics, and computational quantum mechanics. He has received numerous awards, including GenCorp Technology Achievement. Award, The Faculty Scholar Award, UCLA Chancellor’s Professor Endowed Chair, Fellow of US Association for Computational Mechanics, Fellow of International Association for Computational Mechanics, Outstanding Alumnus of National Central University, Taiwan, etc. Three of his papers have been cited for more than 100 times (ISI).