Optimization Techniques for Entropy-based Moment Models of Linear Transport

Title of dissertation: OPTIMIZATION TECHNIQUES FOR ENTROPY-BASED MOMENT MODELS OF LINEAR TRANSPORT Graham West Alldredge, Doctor of Philosophy, 2012 Dissertation directed by: Professor André Tits Department of Electrical and Computer Engineering Kinetic equations are used to model many physical phenomena, including gas dynamics, semiconductors, radiative transport, and more. However, high dimensionality of the domain of definition of the system makes simulation difficult. The entropy-based moment closure model of the kinetic equation reduces the dimension of the domain and has attractive theoretical and practical properties, but most implementations have avoided numerically solving the defining optimization problem. We use the linear one-dimensional slab-geometry model to expose the main challenges in the use of numerical optimization then propose an isotropic regularization and describe the benefits of using fixed quadrature. A numerical technique using adaptive polynomial bases in the optimization algorithm is also tested. We develop manufactured solutions to test our algorithm and also present its performance on two standard test problems. OPTIMIZATION TECHNIQUES FOR ENTROPY-BASED MOMENT MODELS OF LINEAR TRANSPORT by Graham West Alldredge Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2012 Advisory Committee: Professor André Tits, Chair/Advisor Dr. Cory Hauck, Co-Advisor Professor Dianne O’Leary Professor Isaak Mayergoyz Professor C. David Levermore