CNR ExploRA

Articolo in rivista, 2015, ENG, 10.1137/140955252

Igatools: An isogeometric analysis library

M.S. Pauletti, M. Martinelli, N. Cavallini, and P. Antolín

Instituto de Matematica Aplicada del Litoral (IMAL) - Consejo Nacional de Investigaciones cientificas y tecnicas (CONICET), Santa Fe, Argentina. Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) "E. Magenes" - Consiglio Nazionale delle Ricerche (CNR). Pavia, Italy. Dipartimento di Matematica "F. Casorati''. Universita' degli Studi di Pavia. Via Ferrata 1, 27100 Pavia, Italy. Dipartimento di Matematica "F. Casorati''. Universita' degli Studi di Pavia. Via Ferrata 1, 27100 Pavia, Italy.

We present the design of an object oriented general purpose library for isogeometric analysis, where the mathematical concepts of the isogeometric method and their relationships are directly mapped into classes and their interactions. The encapsulation of mathematical concepts into interacting building blocks gives flexibility to use the library in a wide range of scientific areas and applications. We provide a precise framework for a lot of loose, available information regarding the implementation of the isogeometric method, and also discuss the similarities and differences between this and the finite element method. We also describe how to implement this proposed design in a C++11 open source library, \textttigatools (http://www.igatools.org). The library uses advanced object oriented and generic programming techniques to ensure reusability, reliability, and maintainability of the source code. It includes isogeometric elements of the h-div and h-curl type, and supports the development of dimension independent code (including manifolds and tensor-valued spaces). We finally present a number of code examples to illustrate the flexibility and power of the library, including surface domains, nonlinear elasticity, and Navier--Stokes computations on nontrivial geometries.

SIAM journal on scientific computing (Online) 37 (4), pp. 465–496