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- N A Baker, D Sept, S Joseph, M J Holst, J A McCammon
- Proceedings of the National Academy of Sciences…
- 2001

Evaluation of the electrostatic properties of biomolecules has become a standard practice in molecular biophysics. Foremost among the models used to elucidate the electrostatic potential is the Poisson-Boltzmann equation; however, existing methods for solving this equation have limited the scope of accurate electrostatic calculations to relatively small… (More)

- Michael J. Holst, Faisal Saied
- Journal of Computational Chemistry
- 1993

A multigrid method is presented for the numerical solution of the linearized Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the finite volume method, and the numerical solution of the discrete equations is accomplished with multiple grid techniques originally developed for two-dimensional interface problems… (More)

- Long Chen, Michael J. Holst, Jinchao Xu
- Math. Comput.
- 2009

The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure of orthogonal-ity. A quasi-orthogonality property is proved using the fact that the error is orthogonal to the… (More)

- Randolph E. Bank, Michael J. Holst
- SIAM Review
- 2000

We present a new approach to the use of parallel computers with adaptive finite element methods. This approach addresses the load balancing problem in a new way, requiring far less communication than current approaches. It also allows existing sequential adaptive PDE codes such as PLTMG and MC to run in a parallel environment without a large investment in… (More)

- Donald J. Estep, Michael J. Holst, Mats Larson
- SIAM J. Scientific Computing
- 2005

One well-known approach to a posteriori analysis of finite element solutions of elliptic problems estimates the error in a quantity of interest in terms of residuals and a generalized Green's function. The generalized Green's function solves the adjoint problem with data related to a quantity of interest and measures the effects of stability, including any… (More)

- Takeharu Hayashi, Maryann E Martone, +5 authors Masahiko Hoshijima
- Journal of cell science
- 2009

In the current study, the three-dimensional (3D) topologies of dyadic clefts and associated membrane organelles were mapped in mouse ventricular myocardium using electron tomography. The morphological details and the distribution of membrane systems, including transverse tubules (T-tubules), junctional sarcoplasmic reticulum (SR) and vicinal mitochondria,… (More)

- Michael J. Holst, Faisal Saied
- Journal of Computational Chemistry
- 1995

We present a robust and efficient numerical method for solution of the nonlinear Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact-Newton method, combined with linear multilevel techniques we have described in a paper… (More)

- Michael J. Holst
- Adv. Comput. Math.
- 2001

Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first reviewed, and then adaptive multilevel finite element methods for approximating solutions to this class of problems are… (More)

- M. J. Holst
- 1994

- Long Chen, Michael J. Holst, Jinchao Xu
- SIAM J. Numerical Analysis
- 2007

A widely used electrostatics model in the biomolecular modeling community , the nonlinear Poisson–Boltzmann equation, along with its finite element approximation , are analyzed in this paper. A regularized Poisson–Boltzmann equation is introduced as an auxiliary problem, making it possible to study the original nonlinear equation with delta distribution… (More)