Related papers: Piece-wise Multipole-expansion Implicit Solvation …
In this paper we discuss the extention of MPE methods to nonlinear differential equations. We concentrate on nonlinear systems of differential equations and generalize the recent MPE method, see the work of Chin and Geiser 2010.
We consider the construction of semi-implicit linear multistep methods which can be applied to time dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As…
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…
The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of…
In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace equation in layered media. The potential due to charges embedded in layered media is decomposed into a free space component and four types of reaction field…
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
Efficient, accurate, and adaptable implicit solvent models remain a significant challenge in the field of molecular simulation. A recent implicit solvent model, IS-SPA, based on approximating the mean solvent force using the superposition…
Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite…
Recent studies on the solvation of atomistic and nanoscale solutes indicate that a strong coupling exists between the hydrophobic, dispersion, and electrostatic contributions to the solvation free energy, a facet not considered in current…
We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…
Relative free energy calculations are now widely used in academia and industry, but the accuracy is often limited by poor sampling of the complexes conformational ensemble. To address this, we have developed a novel method termed…
We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Accurate modelling of electrostatic interactions and charge transfer is fundamental to computational chemistry, yet most machine learning interatomic potentials (MLIPs) rely on local atomic descriptors that cannot capture long-range…
Point multipole expansions are widely used to gain physical insight into complex distributions of charges and to reduce the cost of computing interactions between such distributions. However, practical applications that typically retain…
In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…
The ab-initio computational treatment of electrochemical systems requires an appropriate treatment of the solid/liquid interfaces. A fully quantum mechanical treatment of the interface is computationally demanding due to the large number of…
A transferable potential energy function for describing the interaction between water molecules is presented. The electrostatic interaction is described rigorously using a multipole expansion. Only one expansion center is used per molecule…
This review describes the theory and implementation of implicit solvation models based on continuum electrostatics. Within quantum chemistry this formalism is sometimes synonymous with the polarizable continuum model, a particular…