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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Automated Parameter Tuning based on RMS Errors for nonequispaced FFTs

Nestler, Franziska 16 February 2015 (has links) (PDF)
In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the L2-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.
2

Automated Parameter Tuning based on RMS Errors for nonequispaced FFTs

Nestler, Franziska 16 February 2015 (has links)
In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the L2-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.
3

Algorithms for Molecular Dynamics Simulations

Hedman, Fredrik January 2006 (has links)
<p>Methods for performing large-scale parallel Molecular Dynamics(MD) simulations are investigated. A perspective on the field of parallel MD simulations is given. Hardware and software aspects are characterized and the interplay between the two is briefly discussed. </p><p>A method for performing <i>ab initio </i>MD is described; the method essentially recomputes the interaction potential at each time-step. It has been tested on a system of liquid water by comparing results with other simulation methods and experimental results. Different strategies for parallelization are explored.</p><p>Furthermore, data-parallel methods for short-range and long-range interactions on massively parallel platforms are described and compared. </p><p>Next, a method for treating electrostatic interactions in MD simulations is developed. It combines the traditional Ewald summation technique with the nonuniform Fast Fourier transform---ENUF for short. The method scales as <i>N log N</i>, where <i>N </i>is the number of charges in the system. ENUF has a behavior very similar to Ewald summation and can be easily and efficiently implemented in existing simulation programs.</p><p>Finally, an outlook is given and some directions for further developments are suggested.</p>
4

Algorithms for Molecular Dynamics Simulations

Hedman, Fredrik January 2006 (has links)
Methods for performing large-scale parallel Molecular Dynamics(MD) simulations are investigated. A perspective on the field of parallel MD simulations is given. Hardware and software aspects are characterized and the interplay between the two is briefly discussed. A method for performing ab initio MD is described; the method essentially recomputes the interaction potential at each time-step. It has been tested on a system of liquid water by comparing results with other simulation methods and experimental results. Different strategies for parallelization are explored. Furthermore, data-parallel methods for short-range and long-range interactions on massively parallel platforms are described and compared. Next, a method for treating electrostatic interactions in MD simulations is developed. It combines the traditional Ewald summation technique with the nonuniform Fast Fourier transform---ENUF for short. The method scales as N log N, where N is the number of charges in the system. ENUF has a behavior very similar to Ewald summation and can be easily and efficiently implemented in existing simulation programs. Finally, an outlook is given and some directions for further developments are suggested.

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