Parallel computation of normalized legendre polynomials using graphics processors

Abstract

To carry out some calculations in physics and Earth sciences, for example, to determine spherical harmonics in geodesy or angular momentum in quantum mechanics, it is necessary to compute normalized Legendre polynomials. We consider the solution to this problem on modern graphics processing units, whose massively parallel architectures allow to perform calculations for many arguments, orders and degrees of polynomials simultaneously. For higher degrees of a polynomial, computations are characterized by a considerable spread in numerical values and lead to overflow and/or underflow problems. In order to avoid such problems, support for extended-range arithmetic has been implemented.