The main difficulty is solving the discrete constrained problem is its poor and even ill condition. In this paper, we transform the discrete constrained problems on de Rham complex to Laplace-like problems. This transformation not only make the constrained problems solvable, but also make it easy to use the existing iterative methods and preconditioning techniques to solving large-scale discrete constrained problems.

翻译：主要困难在于如何解决被限制的离散问题,即贫困甚至条件差。 在本文中,我们把位于德赖姆(De Rham)综合体的离散问题转变为类似拉皮尔(Laplace)的问题。 这种转变不仅使被限制的问题可以解决,而且使使用现有的迭接方法和先决条件技术解决大规模离散受限问题变得容易。