On finite element domain imbedding methods
SIAM Journal on Numerical Analysis
Diagonal scalings of the Laplacian as preconditioners for other elliptic differential operators
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Sobolev Space Preconditioning of Strongly Nonlinear 4th Order Elliptic Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Recursive form of Sobolev gradient method for ODEs on long intervals
International Journal of Computer Mathematics
Journal of Computational Physics
Energy minimization related to the nonlinear Schrödinger equation
Journal of Computational Physics
Journal of Computational Physics
Computers & Mathematics with Applications
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Sobolev gradient type preconditioning is proposed for the numerical solution of the electrostatic potential equation. A constructive representation of the gradients leads to efficient Laplacian preconditioners in the iteration thanks to the available fast Poisson solvers. Convergence is then verified for the corresponding sequence in Sobolev space, implying mesh independent convergence results for the discretized problems. A particular study is devoted to the case of a ball: due to the radial symmetry of this domain, a direct realization without discretization is feasible. The simplicity of the algorithm and the fast linear convergence are finally illustrated in a numerical test example.