INTLAG_LGL Computes matrix "a" to evaluate 1D Lagrange interpolant at LGL
(Legendre Gauss Lobatto) nodes in [-1,1] at another mesh x_new in [-1,1]
(formula (1.2.55) pag. 17 CHQZ2)
[a]=intlag_lgl(x_lgl, x_new)
Input: x_lgl = array of np_lgl LGL nodes in [-1,1]
x_new = array of np_new another set in [-1,1]
Output: a = matrix of size (np_new,np_lgl)
If u_lgl is the array with evaluations of a function u at nodes
x_lgl, it holds: u_new = a * u_lgl, i.e. u_new=u(x_new)
Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
"Spectral Methods. Fundamentals in Single Domains"
Springer Verlag, Berlin Heidelberg New York, 2006.0001 function [a]=intlag_lgl(x_lgl, x_new); 0002 % INTLAG_LGL Computes matrix "a" to evaluate 1D Lagrange interpolant at LGL 0003 % (Legendre Gauss Lobatto) nodes in [-1,1] at another mesh x_new in [-1,1] 0004 % (formula (1.2.55) pag. 17 CHQZ2) 0005 % 0006 % [a]=intlag_lgl(x_lgl, x_new) 0007 % 0008 % Input: x_lgl = array of np_lgl LGL nodes in [-1,1] 0009 % x_new = array of np_new another set in [-1,1] 0010 % 0011 % Output: a = matrix of size (np_new,np_lgl) 0012 % 0013 % If u_lgl is the array with evaluations of a function u at nodes 0014 % x_lgl, it holds: u_new = a * u_lgl, i.e. u_new=u(x_new) 0015 % 0016 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, 0017 % "Spectral Methods. Fundamentals in Single Domains" 0018 % Springer Verlag, Berlin Heidelberg New York, 2006. 0019 0020 % Written by Paola Gervasio 0021 % $Date: 2007/04/01$ 0022 0023 np_lgl=length(x_lgl); 0024 np_new=length(x_new); 0025 n_lgl=np_lgl-1; 0026 a=zeros(np_new,np_lgl); 0027 nnp1=1/(n_lgl*np_lgl); 0028 0029 pn=pnleg(x_lgl,n_lgl); 0030 pn1=pnleg1(x_new,n_lgl); 0031 for i=1:np_new 0032 for j=1:np_lgl 0033 if abs(x_lgl(j)-x_new(i))>1.e-14 0034 a(i,j)=nnp1*(1-x_new(i)^2)*pn1(i)/((x_lgl(j)-x_new(i))*pn(j)); 0035 else 0036 a(i,j)=1; 0037 end 0038 end 0039 end 0040 0041 return