Information-Theoretic Meshfree Approximation Schemes in Solid Mechanics

University Of California-Davis, Davis CA

Investigators

Abstract

PROJECT SUMMARY - N. Sukumar, UC-Davis In this proposal, information-theoretic variational principles are adopted to construct meshfree approximation schemes for the solution of partial differential equations (PDEs). The proposed approach is fundamentally distinct from prior research in meshfree methods, and purports to provide new pathways in the design of approximants as well as in providing novel solution-strategies for PDEs. The shape functions are viewed as a discrete probability distribution, and the polynomial reproducing conditions are the constraints. As a means for least-biased statistical inference, PI uses the maximum entropy principle to derive the approximant, which is adopted within collocation schemes and Galerkin variational formulations. Entropy maximization algorithms are used to compute the shape functions. An entropy functional for the construction of higher-order approximation schemes is also proposed. The external collaboration with Michael Puso at Lawrence Livermore National Laboratory will provide an excellent opportunity for a graduate student to gain valuable research experience at a national laboratory and also to develop a strong foundation in the theory and application of meshfree methods in deformation computations. A new course offering on meshfree methods is planned, and a JAVA applet for visualizing meshfree shape functions will be developed, which will be useful as an effective learning tool to better understand meshfree approximation schemes.