Physical Sciences and Mathematics Commons^™

Non-Equispaced Fast Fourier Transforms In Turbulence Simulation, Aditya M. Kulkarni

Masters Theses

Fourier pseudo-spectral method on equispaced grid is one of the approaches in turbulence simulation, to compute derivative of discrete data, using fast Fourier Transform (FFT) and gives low dispersion and dissipation errors. In many turbulent flows the dynamically important scales of motion are concentrated in certain regions which requires a coarser grid for higher accuracy. A coarser grid in other regions minimizes the memory requirement. This requires the use of Non-equispaced Fast Fourier Transform (NFFT) to compute the Fourier transform, by solving a system of linear equations.

To achieve similar accuracy, the NFFT needs to return more Fourier coefficients than …

Information Metrics For Predictive Modeling And Machine Learning, Kostantinos Gourgoulias

Doctoral Dissertations

The ever-increasing complexity of the models used in predictive modeling and data science and their use for prediction and inference has made the development of tools for uncertainty quantification and model selection especially important. In this work, we seek to understand the various trade-offs associated with the simulation of stochastic systems. Some trade-offs are computational, e.g., execution time of an algorithm versus accuracy of simulation. Others are analytical: whether or not we are able to find tractable substitutes for quantities of interest, e.g., distributions, ergodic averages, etc. The first two chapters of this thesis deal with the study of the …