Accurate solar-power integration: Solar-weighted Gaussian quadrature

Abstract

In this technical note, we explain how to construct Gaussian quadrature rules for efficiently and accurately computing integrals of S(x)f(x) where S(x) is the solar irradiance function tabulated in the ASTM standard and f(x) is an arbitary application-specific smooth function. This allows the integral to be computed accurately with a relatively small number of f(x) evaluations despite the fact that S(x) is non-smooth and wildly oscillatory. Julia software is provided to compute solar-weighted quadrature rules for an arbitrary bandwidth or number of points. We expect that this technique will be useful in solar-energy calculations, where f(x) is often a computationally expensive function such as an absorbance calculated by solving Maxwell's equations.