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SYMPOSIUM MINISYMPOSIA

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FIRST SOUTHERN SYMPOSIUM ON COMPUTING

December 4-5, 1998
University of Southern Mississippi
Hattiesburg, Mississippi


ABSTRACT

Assessing Parallel Bernstein Interpolation in Large Scale Models

S. Fang and J. Kolibal

Ocean models which require the representation of detailed features over large computational domains presents computational challenges which stretch the limits of computability. Such details can include strong currents generated by wind stress over shallow seas; upwellings and downwellings; slope currents; undercurrents; fronts; oceanic eddies impinging upon the shelf break; longshore pressure gradients; filaments; and, the topography of the ocean bottom itself.

The objective of this study is to investigate and develop robust computational methods for efficiently and accurately interpolating large model data, typical in ocean simulations, onto refined grid structures. The approximations must be able to reproduce apparent structures having several resolution scales and preserve essential modeling components in the approximation.

Standard parallel polynomial interpolation techniques are compared to the use of Bernstein functions based on extending the Bernstein polynomials with covariance sxy = 0,

Bn(f;x,y) = n
å
 k = 0 
 n
å
 l = 0 
 æ
ç
è 		n
k
 ö
÷
ø 		æ
ç
è 		n
l
 ö
÷
ø 		f(xk,yl) xk (1-x)n-k yl (1-y)n-l
where x Î [0,1], y Î [0,1] to continuum Gaussian pdf model. These models are highly parallelizable since the approximant Bn(f;x,y) has compact support and is independent of any data structure (requiring any ordering of the data). The techique is also suitable for recovery of missing data. The convergence of these approximations can be adjusted (locally) to obtain substantial variations in the smoothness of the approximant. The approximation, however, are non-interpolating, instead providing optimal estimates in the L1 norm.

Several examples that demonstrate the effectiveness of the code will be given.


Getting More Information

To obtain more information about the meeting send e-mail to: fscc98@pax.st.usm.edu.

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