function [ ml, mu, m ] = fem_bandwidth ( element_order, element_num, element_node ) %*****************************************************************************80 % %% FEM_BANDWIDTH determines the bandwidth associated with the finite element mesh. % % Discussion: % % The quantity computed here is the "geometric" bandwidth determined % by the finite element mesh alone. % % If a single finite element variable is associated with each node % of the mesh, and if the nodes and variables are numbered in the % same way, then the geometric bandwidth is the same as the bandwidth % of a typical finite element matrix. % % The bandwidth M is defined in terms of the lower and upper bandwidths: % % M = ML + 1 + MU % % where % % ML = maximum distance from any diagonal entry to a nonzero % entry in the same row, but earlier column, % % MU = maximum distance from any diagonal entry to a nonzero % entry in the same row, but later column. % % Because the finite element node adjacency relationship is symmetric, % we are guaranteed that ML = MU. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 23 September 2006 % % Author: % % John Burkardt % % Parameters: % % Input, integer ELEMENT_ORDER, the order of the elements. % % Input, integer ELEMENT_NUM, the number of elements. % % Input, integer ELEMENT_NODE(ELEMENT_ORDER,ELEMENT_NUM); % ELEMENT_NODE(I,J) is the global index of local node I in element J. % % Output, integer ML, MU, the lower and upper bandwidths of the matrix. % % Output, integer M, the bandwidth of the matrix. % ml = 0; mu = 0; for element = 1 : element_num for local_i = 1 : element_order global_i = element_node(local_i,element); for local_j = 1 : element_order global_j = element_node(local_j,element); mu = max ( mu, global_j - global_i ); ml = max ( ml, global_i - global_j ); end end end m = ml + 1 + mu; return end