I am looking at the Equity Option example of QuantLib: http://quantlib.org/reference/_equity_option_8cpp-example.html and more particularly the FDAmericanEngine. However, I am not interested in the point value of the Finite Difference evaluation that is provided by the NPV function, but rather the full value function, for all asset prices (in [x_min, x_max]) and times to maturity (in [0, T]) in some grid of times and asset prices that I can define.
Surely the Finite Difference solver produces the full value function on a mesh of points in order to produce point value, how can I access this value function?