A new Krylov subspace method based on rational approximation to solve stiff burnup equation

A burnup equation can be solved with matrix exponential method and its solution can be written as n(t)=eAtn(0). In burnup calculation, general Krylov Subspace Method can solute a matrix-vector efficiently in a subspace but fails to keep a high precision. To solve this problem, a new kind of Krylov Subspace Method, Generalized Minimal Residual Method (GMRES) is implemented, based on a rational approximation method. It shows its great advantage in computation speed, which is more than four times faster than the same kind of rational approximation solved in a whole space while its accuracy is also guaranteed. Some optimizations, such as shift-Invariant technique, precondition technique and restart technique, are also implemented on burnup calculation.