function A = mesh2d1 (n)
% create an n-by-n 2D mesh for the 2nd difference operator
% Example:
%   A = mesh2d1 (30) ;  % a 30-by-30 mesh
% See also: cs_demo

% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+

ii = zeros (5*n^2, 1) ;     % preallocate ii, jj, and xx
jj = zeros (5*n^2, 1) ;
xx = zeros (5*n^2, 1) ;
k = 1 ;
for j = 0:n-1
    for i = 0:n-1
        s = j*n+i + 1 ;
        ii (k:k+4) = [(j-1)*n+i j*n+(i-1) j*n+i j*n+(i+1) (j+1)*n+i ] + 1 ;
        jj (k:k+4) = [s s s s s] ;
        xx (k:k+4) = [-1 -1 4 -1 -1] ;
        k = k + 5 ;
    end
end
% remove entries beyond the boundary
keep = find (ii >= 1 & ii <= n^2 & jj >= 1 & jj <= n^2) ;
A = sparse (ii (keep), jj (keep), xx (keep)) ;