HIGH-ORDER PCG METHOD SOLVING COMPLEX SYSTEMS

To solve complex systems obtained from 2D nonlinear Schrödinger equation, a method of high-order PCG coupling with BICG has been developed. Meanwhile, the complex systems of order M can be reconstructed as the real systems of order 2M. From the theory of order matrix, the high order approximate LU decompositions are given as the preconditioners to solve the real systems. Numerical results show that the computational efficiency can be nearly doubled by the high-order PCG method comparing with the ICCG method.