Utilization of meshless techniques in a computational code for data interpolation

• Grant number: 14/05300-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2014
• End date: June 30, 2016
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Dimas Betioli Ribeiro
• Grantee: Luiz Felipe Pedão
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The objective of this project is to develop a computer program for multidimensional scattered data interpolation, using a strategy commonly employed in meshless methods. Such strategy consists on defining the interpolation function as a summation of predefined functions multiplied by unknown coefficients. Imposing that the interpolation function equals the known data at its coordinates a system of equations is obtained, which solution are the unknown coefficients. Once the coefficients are determined, it is possible to return to the interpolation function to obtain values for any other coordinates.One type of interpolation widely used in meshless methods uses radial based functions (RBF). As they are based only at the Euclidean distance between points, they are easy to obtain for any dimension. In this project will be used, more specifically, Wendland´s functions, which have the advantage of being polynomial and always generate positive-definite matrices for the system of equations.Among the problems that would be considered, we cite the prediction of the depth of soil layers from two dimensional and tridimensional data obtained at the field and also predicting the limit load of piles. In future work, the numerical tool to be developed could be used as a starting point for a program that uses meshless methods to solve engineering problems.