ORCID Identifier(s)

0000-0002-4806-7883

Graduation Semester and Year

2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mechanical Engineering

Department

Mechanical and Aerospace Engineering

First Advisor

Brian Dennis

Second Advisor

Bo Ping Wang

Abstract

Reduced order modeling of differential equations parametrized over a parameter space can be used to accelerate optimization and parameter estimation problems. The method of snapshots or reduced order basis is well established among researchers as a tool to build reduced order models of ordinary differential equations. The reduced order basis method has been utilized for numerical solution of parametric PDE problems by researchers in recent years and has many advantages over response surface methods. The application of ROB to finite element analysis has been restricted to using a fixed mesh for snapshots. In this work, a new method is developed for construction of ROB from a set of snapshots defined over various meshes. Consistent inner product is defined for the finite dimensional functional spaces and a new general purpose geometric intersection algorithm is developed to enable the inner product computations for all dimensions. Compatible inner products are used to construct the multi-mesh proper orthogonal decomposition method. The newly developed multi-mesh POD method removes the restriction of fixed mesh from ROB method and it can also be applied outside the context of finite element analysis.

Keywords

Multi-mesh, Proper orthogonal decomposition, Reduced basis method, ROB, Finite element analysis, Finite element method, Reduced order model (ROM), Inner product, Vector space, Orthogonal subspace projection, Embedded convex polytope intersection, ECPI, Algorithms, Geometric intersection, Recursive algorithm, Gramian matrix, Super-mesh

Disciplines

Aerospace Engineering | Engineering | Mechanical Engineering

Comments

Degree granted by The University of Texas at Arlington

Download

Share

COinS