Before revision:  The coordinate transformation is performed on the semi-discretized level which makes them applicable to a wide range of kinetic schemes and replaces the nonlinear optimization problems by inversion of the positive-definite Hessian matrix.
After revision:  The transformation is performed on the semi-discretized level which makes them applicable to a wide range of kinetic schemes and replaces the nonlinear optimization problems by inversion of the positive-definite Hessian matrix.