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Rational functions are frequently used as efficient yet accurate numerical approximations for real and complex valued special functions. For the complex error function , whose real part is the Voigt function , the rational approximation developed by Hui, Armstrong, and Wray [Rapid computation of the Voigt and complex error functions, J. Quant. Spectrosc. Radiat. Transfer 19 (1978) 509–516] is investigated. Various optimizations for the algorithm are discussed. In many applications, where these functions have to be calculated for a large x grid with constant y, an implementation using real arithmetic and factorization of invariant terms is especially efficient.
Radiative transfer modelling of high resolution infrared (or microwave) spectra still represents a major challenge for the processing of atmospheric remote sensing data despite significant advances in the numerical techniques utilized in line-by-line modelling by, e.g., optimized Voigt function algorithms or multigrid approaches. Special purpose computing hardware such as Field Programmable Gate Arrays (FPGAs) can be used to cope with the dramatic increase of data quality and quantity. Utilizing a highly optimized implementation of an uniform rational function approximation of the Voigt function, the molecular absorption cross section computation-representing the most compute intensive part of radiative transfer codes-has been realized on FPGA. Design and implementation of the FPGA coprocessor is presented along with first performance tests and an outlook for the ongoing further development.
Forschungsbericht 2013
(2014)
Forschungsbericht 2012
(2012)