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Hall, Brenton TaylorUsing the Non-Uniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations
Master of Mathematical Sciences, The Ohio State University, 2017, Mathematical Sciences
Partial Differential Equation simulations can produce large amounts of data that are very slow to transfer. There have been many model reduction techniques that have been proposed and utilized over the past three decades. Two popular techniques Proper Orthogonal Decomposition and Dynamic Mode Decomposition have some hindrances. Non-Uniform Dynamic Mode Decomposition (NU-DMD), which was introduced in 2015 by Gueniat et al., that overcomes some of these hindrances. In this thesis, the NU-DMD's mathematics are explained in detail, and three versions of the NU-DMD's algorithm are outlined. Furthermore, different numerical experiments were performed on the NU-DMD to ascertain its behavior with repect to errors, memory usage, and computational efficiency. It was shown that the NU-DMD could reduce an advection-diffusion simulation to 6.0075% of its original memory storage size. The NU-DMD was also applied to a computational fluid dynamics simulation of a NASA single-stage compressor rotor, which resulted in a reduced model of the simulation (using only three of the five simulation variables) that used only about 4.67% of the full simulation's storage with an overall average percent error of 8.90%. It was concluded that the NU-DMD, if used appropriately, could be used to possibly reduce a model that uses 400GB of memory to a model that uses as little as 18.67GB with less than 9% error. Further conclusions were made about how to best implement the NU-DMD.


Ching-Shan Chou (Advisor); Jen-Ping Chen (Committee Member)


Aerospace Engineering; Applied Mathematics; Computer Science; Mathematics; Mechanical Engineering


Fluid Dynamics; Fluid Flow; Model Reduction; Partial Differential Equations; reducing memory; Dynamic Mode Decomposition; Decomposition; memory; Non-Uniform Dynamic Mode Decomposition