an:01417823
Zbl 0960.82035
Richardson, W. B. jun.
Sobolev preconditioning for the Poisson-Boltzmann equation
EN
Comput. Methods Appl. Mech. Eng. 181, No. 4, 425-436 (2000).
00062879
2000
j
82D37 65M60 65F35
least-squares steepest descent; Sobolev gradients; Poisson-Boltzmann equation; semiconductor device modeling
Summary: 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 Poisson-Boltzmann equation from semiconductor device modeling.