Fast methods for simulation of biomolecule electrostatics

Kuo, Shih-Hsien; Altman, Michael D.; Bardhan, Jaydeep P.; Tidor, Bruce; White, Jacob K.

doi:10.1145/774572.774640

Cited by 19 publications

(20 citation statements)

References 45 publications

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“…It can be seen as a domain decomposition method on the two non-overlapping domains Ω 0 and Ω ∞ where only problems on the bounded domain Ω 0 are solved. Similar property has been obtained for the integral equation formulation of implicit solvation models, see for example [12,11,29,4].…”

Section: Global Strategysupporting

confidence: 75%

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A domain decomposition method for the polarizable continuum model based on the solvent excluded surface

Quan

Stamm

Maday

2018

Math. Models Methods Appl. Sci.

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In this paper, an efficient solver for the polarizable continuum model in quantum chemistry is developed which takes the solvent excluded surface (the smooth molecular surface) as the solute–solvent boundary. This model requires to solve a generalized Poisson (GP) equation defined in [Formula: see text] with a space-dependent dielectric permittivity function. First, the original GP-equation is transformed into a system of two coupled equations defined in a bounded domain. Then, this domain is decomposed into overlapping balls and the Schwarz domain decomposition method is used. This method involves a direct Laplace solver and an efficient GP-solver to solve the local sub-equations in balls. For each solver, the spherical harmonics are used as basis functions in the angular direction of the spherical coordinate system. A series of numerical experiments are presented to test the performance of this method.

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Section: Global Strategysupporting

confidence: 75%

“…[2] Solve the following Dirichlet boundary problem for W k ∞ : 29) and derive similarly its Neumann boundary trace…”

Section: Global Strategymentioning

confidence: 99%

A domain decomposition method for the polarizable continuum model based on the solvent excluded surface

Quan

Stamm

Maday

2018

Math. Models Methods Appl. Sci.

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“…Our solution makes use of a surface integral formulation derived from Laplace's equation for each homogeneous layer in the substrate; this system is derived as found in [4], [3], [5]. We discretize this coupled system using the method of moments technique [6] on a uniform, rectangular grid overlaid on the surfaces of the substrate, and its interface between layers.…”

Section: Methodsmentioning

confidence: 99%

Substrate resistance extraction using a multi-domain surface integral formulation

Vithayathil

White

2003

International Conference on Simulation of Semiconductor Processes and Devices, 2003. SISPAD 2003.

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In recent years, mixed-signal designs have become more pervasive, due to their efficient use of area and power. Unfortunately, with sensitive analog and fast digital circuits sharing a common, non-ideal substrate, such designs carry the additional design burden of electromagnetic coupling between contacts.This thesis presents a method that quickly extracts the electroquasistatic coupling resistances between contacts on a planar, rectangular, two-layer lossy substrate, using an FFT-accelerated multi-domain surface integral formulation. The multi-domain surface integral formulation allows for multi-layered substrates, without meshing the volume. This method has the advantages of easy meshing, simple implementation, and FFT-accelerated iterative methods. Also, a three-dimensional variant of this method allows for more complex substrate geometries than some other surface integral techniques, such as multilayered Green's functions; this three-dimensional problem and its solution are presented in parallel with the planar substrate problem and solution. Results from a C++ implementation are presented for the planar problem.Thesis Supervisor: Jacob K. White Title: Professor AcknowledgmentsAn Acknowledgements section is supposed to be one page long, but really, what is the cost of printing one extra page? I've been lucky enough to have many supporters, and I'd be remiss to omit one.I have Prof. Jacob White to thank for the inspiration of this thesis, as well as innumerable suggestions, encouragements and chastisements. Also to be thanked profusely is Xin Hu, a good friend, but more more importantly for the purposes of this thesis, a collaborator in much of the substrate coupling work, in particular the fundamentals and gruntwork of the two-dimensional problem. I must acknowledge that I couldn't have done it without our collaboration. It is imperative that 5I have my friends to thank for dragging me out of the lab, and keeping me sane.In particular, thank you to those of you who (horror!) are not in Engineering and/or (horror!) not at MIT. You guys have provided an amusing reality check, and great a cheerleading squad, even when you couldn't remember what my major is (it's Electrical Engineering, by the way). Speaking of sanity and reality, for the past nine months,

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“…Work has been done on numerically solving nonlinear elliptic partial differential equations (PDEs). For example, Schwarz alternating methods (see [14] and references therein), multigrid methods [5], and preconditioned FFT [12]. In this work, we explore the convergence of the discretization method, and also the convergence behaviour of the Newton-Krylov method for solving the nonlinear algebraic equations [7,8].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear elliptic problems with the method of finite volumes

Khattri

2006

International Journal of Differential Equations

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We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.

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Fast methods for simulation of biomolecule electrostatics

Cited by 19 publications

References 45 publications

A domain decomposition method for the polarizable continuum model based on the solvent excluded surface

A domain decomposition method for the polarizable continuum model based on the solvent excluded surface

Substrate resistance extraction using a multi-domain surface integral formulation

Nonlinear elliptic problems with the method of finite volumes

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