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
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Akbariyeh, Ashkan, "Multi-mesh reduced-order basis method for finite element analysis" (2017). Mechanical and Aerospace Engineering Dissertations. 305.
https://mavmatrix.uta.edu/mechaerospace_dissertations/305
Comments
Degree granted by The University of Texas at Arlington