diffusivity_exponential_derivative.m

function diffusivity = diffusivity_exponential_derivative(glob, U, params)
% function diffusivity = diffusivity_exponential_derivative(glob, U, params)
%
% function computing derivative of an exponential nonlinear diffusivity with
% respect to `u`.  ``k(x,u) = k_0 + m u^p ``.
%
% parameters:
%      U                      : solution at points in 'glob'
%
% required fields of params:
%      diff_k0                : constant part `k_0 \in [0.1,0.5]`
%      diff_m                 : steepness factor of curve `m \in [0, 0.5]`.
%      diff_p                 : exponent `p \in [1/100, 100]`
%
% See also diffusivity_exponential().
%
% generated fields of diffusivity:
%     epsilon: upper bound on diffusivity value
%     K: vector with diffusivity values

% glob column check
if params.debug
  if ~isempty(glob) && size(glob,1) < size(glob,2)
    warning('coordinates in variable glob are given row-wise, but expected them to be column-wise');
    if params.debug > 2
      keyboard;
    end
  end
end

if(params.diff_p < 1 && any(U<0))
  error(['some values of U are too small for derivative for small', ...
         'exponents. This leads to infinite values']);
end
diffusivity.K = params.diff_p * params.diff_m ...
                 * real(real(U) .^(params.diff_p - 1));

diffusivity.epsilon = max(diffusivity.K);

if params.debug
  if ( params.diff_m ~= 0 && params.diff_p < 1 && min(U) - eps < 0 )
                                    %(max(U)+eps > 1 || min(U) - eps < 0 ) )
    error('U is outside admissable bounds [0,1]');
  end
  if ( max(abs(imag(U))) > 1e-6 )
    error('U has non-trivial imaginary addend.')
  end
end

if params.decomp_mode>0
  error('function is nonlinear and does not support affine decomposition!');
end