Chapter 1
Introduction

Welcome to the tutorial on the fundamentals of the Nektar++ framework where we will look at how to perform 1D and 2D Gaussian Quadrature using the Nektar++ LibUtilities library. If you have not already downloaded and installed Nektar++, please do so by visiting http://www.nektar.info, where you can also find the User-Guide with the instructions on how to install the library.

This tutorial requires:

• Nektar++ compiled libraries and include files compiled from source so additional code can be compiled with the framework libraries

Goals

After completing this tutorial, you should be familiar with:

• The concept of Gaussian integration using classical Gauss and Gauss-Lobatto rules in a standard interval ξ ∈ [-1,1];
• Using the Nektar++ programming concepts of an Array, PointsKey and the PointsManager to generate Gaussian quadrature weights;
• Integrating in the standard segment (ξ ∈ [-1,1]) and quadrilateral region (ξ ∈ [-1,1] × [-1,1]);
• The mathematical concept of mapping a general quadrilateral region to the standard region, evaluating the jacobian of this mapping and using this to evaluate an integral in a general straight sided quadrilateral region.