Bell, I.
(2024),
Efficient Approximation with Space Filling Quadtrees: Application to Phase Equilibria in Binary Mixtures, Industrial and Engineering Chemistry Research, [online], https://doi.org/10.1021/acs.iecr.4c01631, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=957529
(Accessed December 16, 2024)
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Efficient Approximation with Space Filling Quadtrees: Application to Phase Equilibria in Binary Mixtures
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Abstract
The use of quadtrees to tile rectangular domains is a well accepted numerical technique. If each leaf of the quadtree is in turn a two-dimensional bi-variate approximation, a representation of a function $z(x,y)$ can be constructed that covers the entire rectangular domain. Through the use of adaptive subdivision, the function can be practically represented to any desired level of accuracy. Bi-variate Chebyshev expansions are used in each leaf due to their favorable convergence characteristics and availability in existing numerical libraries. Evaluation of the approximation function requires only a few bisection steps to identify the leaf of interest such that evaluation of the approximation data structure takes less than a microsecond. The technique is demonstrated by application to the vapor-liquid-equilibria evaluated with two different models (COSMO-SAC activity coefficient model and multi-fluid model). For the more expensive COSMO-SAC case, the approximation function is more than 2000 times faster to evaluate, and deviations in pressure are less than a part in $10^8}$ which is practically equal to the iteration convergence criterionCitation
Industrial and Engineering Chemistry Research
Volume
63
Pub Type
Journals
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Created July 25, 2024, Updated September 10, 2024