minmaxbdr.m

%MINMAXBDR Calculate minima and maxima of an expression on boundaries.
%
%   [ MIN_VAL, MAX_VAL, MIN_COORD, MAX_COORD ] = MINMAXBDR( S_EXPR, PROB, IND_B, I_CUB, SOLNUM )
%   Evaluates the mimimum and maximum value of expression S_EXPR on
%   boundaries, using FEM interpolation of data given in the FEA
%   model/problem struct PROB.
%
%   The string expression S_EXPR must be valid MATLAB syntax, and may
%   include combinations of dependent variables (defined in PROB.dvar)
%   and derivatives, space dimensions (PROB.sdim), and all common
%   built-in constants and mathematical functions available, such as
%   pi, eps, sqrt, sin, cos, log, exp, abs etc (for example
%   "sin(2*pi*x + ux^2)" where "ux" is the x-derivative of the
%   dependent variable "u").
%
%   The optional vector IND_B are indices to boundaries to include in
%   the evaluation (default all "unique(PROB.grid.b(3,:))").
%
%   SOLNUM is an optional scalar integer indicating the solution/time
%   to use in the evaluation (PROB.sol.u(:,SOLNUM), defaults to the
%   last available solution "size(PROB.sol.u, 2)").
%
%   Returns the computed minima and maxima in MIN_VAL and MAX_VAL, and
%   the corresponding coordinates where the minima/maxima occurs in
%   MIN_COORD and MAX_COORD, respectively.
%
%       Input       Value/[Size]           Description
%       -----------------------------------------------------------------------------------
%       s_expr      string                 Expression to evaluate
%       prob        struct                 FEA model/problem definition struct
%       ind_b       [1,n_bdr]              Boundary numbers (default all)
%       i_cub       scalar int             Evaluation point rule/quadrature order (default 2)
%       solnum      scalar int {n_sols}    Solution number/time to evaluate
%                                                                                         .
%       Output      Value/[Size]           Description
%       -----------------------------------------------------------------------------------
%       min_val     scalar                 Minimum value of expression
%       max_val     scalar                 Maximum value of expression
%       min_coord   scalar                 Coordinates where minima occurs
%       max_coord   scalar                 Coordinates where maxima occurs
%
%
%   Example:
%
%      1) Evaluate minimum and maximum temperature on boundaries at time t=100 s.
%
%      fea = ex_heattransfer5('iplot', false);  % Use example script to generate FEA data struct.
%      solnum = find(fea.sol.t == 100);
%
%      [T_min, T_max, T_min, T_max] = minmaxbdr('T', fea, solnum)
%
%   See also MINMAXSUBD, INTBDR, INTSUBD

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