New Preconditioners For Optimal Control Problems Of Burgers Equation

Optimization problems with constraints which require the solution of Burgers equations arise widely in many areas of sciences and engineering,such as shock waves, vortex, acoustic transmission。Among them, optimization control problems(OCP) of the one dimensional Burger equation are a important problems that is widely used in computational science.In this literature, the new precondition technology is proposed from the character of the saddle point matrices which is transformed from the Burgers equation by numerical discretization. To the new preditioner, we study it from matrix character, such as operator construction, eigenvalue, prove the efficiency of it, and verify it in computational numerical experiments.