We consider the discrete source, eigenvalue and constrained problems of the $ d^*d $ operators on deRham complex. The three kinds of problems can be transformed into some auxiliary problems. The spectra of the auxiliary problems are Laplace-like.Then many existing iterative methods and preconditioning techniques, which are efficient for Laplace problems, can be applied to solving these problems. After the solutions of the auxiliary problems are obtained, the desired solutions of the original problems can be easily recovered oridentified through the basic property of discrete complex.