Sobolev preconditioning for the Poisson–Boltzmann equation Original Research Article

This paper presents an overview of least-squares steepest descent using Sobolev gradients for several prototype differential equations. In the linear case, the method is viewed as a very effective preconditioning strategy for the basic iterative method which arises from steepest descent, in particular, it acts to smooth the Euclidean gradient. Results are given for the one-dimensional Possion–Boltzmann equation from semiconductor device modeling.