Help about the preconditioner in gmres method

Dan Gao

Hi, all, I am importing a implicit time method to my 3D NS finite difference code. I used the Matrix-free method to get the Jaccobi matrix-vector product, and the sparse linear equations are solved by gmres method. Now I am in trouble in constructing a preconditioner for my finite difference code. I hope the preconditioning method is similar with the matrix-free method, that means only the preconditioner-vector product needed. I hope someone can suggest me how to construct a preconditioner for my finite difference code. I read some papers about how to get the preconditioner for finite volume method. But I can not understand it and import them to the finite difference method. I don't know I describe the question clearly. I am poor in English. Thanks for your any help in advance .