On the use of Runge-Kutta time-marching and multigrid for the solution of steady adjoint equations

摘要

This paper considers the solution of steady adjoint equations using a class of iterative methods which includes preconditioned Runge-Kutta time-marching with multigrid. It is shown that, if formulated correctly, equal numbers of iterations of the direct and adjoint iterative solvers will result in the same value for the linear functional being sought. The precise details of the adjoint iteration are formulated for the case of Runge-Kutta time-marching with partial updates, which is commonly used in CFD computations. The theory is supported by numerical results from a MATLAB program for two model problems, and from programs for the solution of the linear and adjoint 3D Navier-Stokes equations.udud(This report is an expanded version of a paper presented at the AD2000 Conference in Nice, France on June 19-23, 2000.)ududThis research was supported by EPSRC research grant GR/L95700.