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Title: Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis

Abstract

The dissertation examines spectral transform algorithms for the solution of the shallow water equations on the sphere and studies their implementation and performance on shared memory vector multiprocessors. Beginning with the standard spectral transform algorithm in vorticity divergence form and its implementation in the Fortran based parallel programming language Force, two modifications are researched. First, the transforms and matrices associated with the meridional derivatives of the associated Legendre functions are replaced by corresponding operations with the spherical harmonic coefficients. Second, based on the fast Fourier transform and the fast multipole method, a lower complexity algorithm is derived that uses fast transformations between Legendre and interior Fourier nodes, fast surface spherical truncation and a fast spherical Helmholz solver. Because the global shallow water equations are similar to the horizontal dynamical component of general circulation models, the results can be applied to spectral transform numerical weather prediction and climate models. In general, the derived algorithms may speed up the solution of time dependent partial differential equations in spherical geometry.

Authors:
Publication Date:
Research Org.:
National Center for Atmospheric Research, Boulder, CO (United States)
OSTI Identifier:
5479370
Alternate Identifier(s):
OSTI ID: 5479370
Report Number(s):
PB-94-115029/XAB; NCAR/CT--144
Resource Type:
Technical Report
Resource Relation:
Other Information: Doctoral thesis
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; AIR-WATER INTERACTIONS; CLIMATE MODELS; ATMOSPHERIC CIRCULATION; COMPUTERIZED SIMULATION; MATHEMATICAL MODELS; SIMULATION 540120* -- Environment, Atmospheric-- Chemicals Monitoring & Transport-- (1990-); 990200 -- Mathematics & Computers

Citation Formats

Jakob, R. Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis. United States: N. p., 1993. Web.
Jakob, R. Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis. United States.
Jakob, R. Fri . "Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis". United States. doi:.
@article{osti_5479370,
title = {Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis},
author = {Jakob, R.},
abstractNote = {The dissertation examines spectral transform algorithms for the solution of the shallow water equations on the sphere and studies their implementation and performance on shared memory vector multiprocessors. Beginning with the standard spectral transform algorithm in vorticity divergence form and its implementation in the Fortran based parallel programming language Force, two modifications are researched. First, the transforms and matrices associated with the meridional derivatives of the associated Legendre functions are replaced by corresponding operations with the spherical harmonic coefficients. Second, based on the fast Fourier transform and the fast multipole method, a lower complexity algorithm is derived that uses fast transformations between Legendre and interior Fourier nodes, fast surface spherical truncation and a fast spherical Helmholz solver. Because the global shallow water equations are similar to the horizontal dynamical component of general circulation models, the results can be applied to spectral transform numerical weather prediction and climate models. In general, the derived algorithms may speed up the solution of time dependent partial differential equations in spherical geometry.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 1993},
month = {Fri Jan 01 00:00:00 EST 1993}
}

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  • Short communication.
  • The spectral transform method is a standard numerical technique for solving partial differential equations on a sphere and is widely used in atmospheric circulation models. Recent research has identified several promising algorithms for implementing this method on massively parallel computers; however, no detailed comparison of the different algorithms has previously been attempted. In this paper, we describe these different parallel algorithms and report on computational experiments that we have conducted to evaluate their efficiency on parallel computers. The experiments used a testbed code that solves the nonlinear shallow water equations or a sphere; considerable care was taken to ensure thatmore » the experiments provide a fair comparison of the different algorithms and that the results are relevant to global models. We focus on hypercube- and mesh-connected multicomputers with cut-through routing, such as the Intel iPSC/860, DELTA, and Paragon, and the nCUBE/2, but also indicate how the results extend to other parallel computer architectures. The results of this study are relevant not only to the spectral transform method but also to multidimensional FFTs and other parallel transforms.« less
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