GeoPDEs: A research tool for Isogeometric Analysis of PDEs
نویسندگان
چکیده
GeoPDEs (http://geopdes.sourceforge.net) is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of the many IGA methods for the discretization of partial differential equations currently studied, mainly based on B-Splines and Non-Uniform Rational B-Splines (NURBS), while being flexible enough to allow users to implement new and more general methods with a relatively small effort. This paper presents the philosophy at the basis of the design of GeoPDEs and its relation to a quite comprehensive, abstract definition of IGA. 2011 Elsevier Ltd. All rights reserved.
منابع مشابه
Isogeometric Analysis
We present an introduction to Isogeometric Analysis, a new methodology for solving partial differential equations (PDEs) based on a synthesis of Computer Aided Design (CAD) and Finite Element Analysis (FEA) technologies. A prime motivation for the development of Isogeometric Analysis is to simplify the process of building detailed analysis models for complex engineering systems from CAD represe...
متن کاملIsogeometric analysis and error estimates for high order partial differential equations in fluid dynamics
In this paper, we consider the numerical approximation of high order Partial Differential Equations (PDEs) by means of NURBS–based Isogeometric Analysis (IGA) in the framework of the Galerkin method, for which global smooth basis functions with degree of continuity higher than C can be used. We derive a priori error estimates for high order elliptic PDEs under h–refinement, by extending existin...
متن کاملIsogeometric analysis for second order partial differential equations on surfaces
We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitates the encapsulation of the exact geometrical description of the manifold in the analysis when this is represented by B–splines or NURBS. Our ...
متن کاملDiscontinuous Galerkin Isogeometric Analysis of Elliptic PDEs on Surfaces
The Isogeometric Analysis (IGA) was introduced by Hughes et al. [2005] and has since been developed intensively, see also monograph Cottrell et al. [2009], is a very suitable framework for representing and discretizing Partial Differential Equations (PDEs) on surfaces. We refer the reader to the survey paper by Dziuk and Elliot [2013] where different finite element approaches to the numerical s...
متن کاملOn Isogeometric Subdivision Methods for PDEs on Surfaces
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an isogeometric discretization approach to partial differential equations on surfaces using subdivision methodology. Elliptic equations with the Laplace-Beltra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Advances in Engineering Software
دوره 42 شماره
صفحات -
تاریخ انتشار 2011