I am trying to solve 2D Poisson equations with Neumann boundary conditions. When the mesh is uniform, Poisson equation is singular and symmetric, so the method listed in Null Space Projection for Singular Systems works well. But when the mesh is non uniform and sharp immersed boundary method is implemented to treat the curved boundary, discretized Poisson equation is singular and asymmetric based on finite difference method. In this case, the pervious method seems not working well. So can someone help me and tell me how to solve this kind of problem, or just provide me some references? Thanks a lot!