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Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients
Blanca Ayuso De Dios, Michael Holst, Yunrong Zhu +1
We introduce and analyze two-level and multi-level preconditioners for a family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic proble…
Semilinear mixed problems on Hilbert complexes and their numerical approximation
Michael Holst, Ari Stern
Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite ele…
Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
Michael Holst, James Andrew McCammon, Zeyun Yu +2
We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen…
Local Multilevel Preconditioners for Elliptic Equations with Jump Coefficients on Bisection Grids
Long Chen, Michael Holst, Jinchao Xu +1
The goal of this paper is to design optimal multilevel solvers for the finite element approximation of second order linear elliptic problems with piecewise constant coefficients on…
Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces
Michael Holst, Ari Stern
A recent paper of Arnold, Falk, and Winther [Bull AMS, 47 (2010)] showed that a large class of mixed finite element methods can be formulated naturally on Hilbert complexes, where…
Local Refinement and Multilevel Preconditioning: Implementation and Numerical Experiments
Burak Aksoylu, Stephen Bond, Michael Holst
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While st…