2
$\begingroup$

How can I get Gauss-Lobatto points on a quadrilateral or a triangle in $x$-$y$ plane?

I am only getting abscissa coordinates and weights by solving Lobatto polynomials using Lobatto quadrature. Please suggest a method to get the $x$-$y$ coordinates

$\endgroup$
  • $\begingroup$ What do you mean by Gauss-Lobatto points on a triangle? What properties of Gauss-Lobatto do you wish to preserve? $\endgroup$ – Jesse Chan Nov 18 '15 at 16:10
  • $\begingroup$ the distance between points and number of points i get on sides of a quadrilateral should be same on the sides of a triangle as well... $\endgroup$ – Nish Dec 14 '15 at 15:27
  • 1
    $\begingroup$ i see. if that's the only requirement, you can form the nodes a bunch of different ways. One explicit way is in uea.ac.uk/~h007/publications/lobatto.pdf. Others include Hesthaven and Teng's construction, or Warburton's Warp and Blend nodes. Many of these are described in the Nodal DG Methods book @GoHokies mentioned. $\endgroup$ – Jesse Chan Dec 15 '15 at 3:55
6
$\begingroup$

For domains that are logically square or cubic (like your quadrilateral), you can use the tensor product (dimension-by-dimension) approach. That is, generate the 2D Gauss-Lobatto point matrix as the tensor product of your 1D Gauss-Lobatto point vectors.

An example: if your 1D Gauss-Lobatto points are $(x_1,x_2)$, then in 2D you get the following four points: $(x_i,x_j)_{i,j=1,2}$.

Generating the Gauss-Lobatto points on triangular domains is a bit more complicated. Fortunately, there are good references. Here's a couple to get the ball rolling:

  1. The Nodal DG methods book by Hesthaven and Warburton, appendix A (Google Books)
  2. The Matlab code from said book (link).
  3. These lecture notes on multidimensional Gaussian quadrature.
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.