I have read the papers written by Dr.Zhibin Ren :“NANOSCALE MOSFETS: PHYSICS, SIMULATION AND DESIGN”. and trying to realize the non-linear Poisson solver by myself. when solving for the non-linear Poisson, I always need to solve for linear equations like: Jx=b. where J is the jacobi matrix defined in the paper. so I have a question, is this matrix positive-definite? If yes, then a variety of algorithms can be implemented to solve this linear equation.