Description of derlgl

DESCRIPTION

DERLGL      Spectral (Legendre Gauss Lobatto) derivative matrix 

    [d]=derlgl(x,np) returns the spectral Legendre Gauss Lobatto derivative
    matrix d at the np LGL nodes x (on [-1,1]). np-1 is the polynomial
    degree used. Legendre Gauss Lobatto (LGL) grid


 Input: x = array of LGL nodes on [-1,1] (computed by xwlgl)
        np = number of LGL nodes (=n+1, n=polynomial interpolation degree)

 Output: D = spectral derivative matrix: formula  (2.3.28), pag. 80 CHQZ2

 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.

CROSS-REFERENCE INFORMATION

pnleg PNLEG Evaluates Legendre polynomial of degree n at x

nonperiodic_burgers NONPERIODIC_BURGERS Numerical solution of non periodic Burgers equation

lgl_eig LGL_EIG Computes eigenvalues of first/second order spectral derivative matrices: collocation/G-NI, LGL nodes, 1D monodomain

adr_1d ADR_1D Numerical solution of the 1D boundary value problem (1.2.52)-(1.2.53), pag. 17, CHQZ2

ell_1d ELL_1D Numerical solution of the 1D elliptic boundary value problem (4.3.17) pag. 208, CHQZ2

ellprecofem_1d ELLPRECOFEM_1D FEM-preconditioned SEM-appx of 1D second order b.v.p.

lap_1d LAP_1D SEM appx of the 1D b.v.p. -nu u''+gam u=f

eig_schur_2d EIG_SCHUR_2D Eigenvalues computation Schur complement matrix

schur_2d SCHUR_2D Numerical solution of the 2D b.v.p. -Delta u + gam u -Schur complement

eig_schwarz_2d EIG_SCHWARZ_2D Eigenvalues computation for the matrix associated to 2D b.v.p. -Delta u + gam u = f + Dirichlet b.c.

schwarz_2d SCHWARZ_2D Numerical solution of the 2D boundary value problem

lap_2d LAP_2D Numerical solution of the 2D b.v.p. -Delta u + gam u = f

lap_3d LAP_3D Numerical solution of the 3D b.v.p. -Delta u + gam u = f

scalar_hyp SCALAR_HYP Numerical solution of scalar linear hyperbolic equations,

stag_scalar_hyp STAG_SCALAR_HYP Numerical solution of scalar linear hyperbolic equations,

stat_scalar_hyp STAT_SCALAR_HYP Numerical solution of a stationary scalar linear hyperbolic equation,

test TEST Script for testing functions of this directory

errors_1d ERRORS_1D Computes errors for 1D b.v.p.

matrices_1d MATRICES_1D Assembles SEM stiffness and mass matrices for 1D b.v.p.

SOURCE CODE

0001 function [d] = derlgl(x,np) 
0002 %DERLGL      Spectral (Legendre Gauss Lobatto) derivative matrix
0003 %
0004 %    [d]=derlgl(x,np) returns the spectral Legendre Gauss Lobatto derivative
0005 %    matrix d at the np LGL nodes x (on [-1,1]). np-1 is the polynomial
0006 %    degree used. Legendre Gauss Lobatto (LGL) grid
0007 %
0008 %
0009 % Input: x = array of LGL nodes on [-1,1] (computed by xwlgl)
0010 %        np = number of LGL nodes (=n+1, n=polynomial interpolation degree)
0011 %
0012 % Output: D = spectral derivative matrix: formula  (2.3.28), pag. 80 CHQZ2
0013 %
0014 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0015 %                    "Spectral Methods. Fundamentals in Single Domains"
0016 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0017 
0018 %   Written by Paola Gervasio
0019 %   $Date: 2007/04/01$
0020  
0021 
0022 d=zeros(np);
0023 n=np-1; 
0024 for j =1:np
0025    lnxj = pnleg(x(j),n);    
0026    for i = 1:np       
0027       if i ~= j          
0028          lnxi = pnleg(x(i),n);
0029          d(i,j) = lnxi/((x(i)-x(j))*lnxj);                 
0030       end       
0031    end 
0032 end 
0033 d(1,1) = -0.25*n*np; 
0034 d(np,np) = -d (1,1); 
0035  
0036 return

derlgl

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SOURCE CODE