Orthogonal polynomials and fast multipole method

• Grant number: 14/17357-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 07, 2015
• End date: April 17, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cleonice Fátima Bracciali
• Grantee: Cleonice Fátima Bracciali
• Visiting researcher: Michael Carley
• Visiting researcher institution: University of Bath, England
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 09/13832-9 - Orthogonal polynomials, special functions and applications, AP.TEM

Abstract

This research project aims to establish a collaboration between researchers from the group of Orthogonal Polynomials and Similars from UNESP-São José do Rio Preto and the researcher from the University of Bath, England. The central theme of the project is the development of a method based on Orthogonal Polynomials of Several Variables with the aim of applying it to the numerical calculation of integrals typically occurring in solving problems through Fast Multipole Method. In this method, the orthonormal basis of the polynomial space can be constructed adaptively; as a result, there is an expectation that the method will be computationally efficient as well as be able to prevent pathological settings occurring in the interpolation of the source terms calculated within the domain of integration. We also intend to develop a computational implementation of the method and integrate the code into a general purpose software based on FMM, which is being developed by the visiting researcher with immediate applications to problems in Computational Fluid Dynamics. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BRACCIALI, CLEONICE F.; CARLEY, MICHAEL. Quasi-analytical root-finding for non-polynomial functions. NUMERICAL ALGORITHMS, v. 76, n. 3, p. 639-653, NOV 2017. (14/22571-2, 14/17357-1)