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1.
Harmonic Surface Mapping Algorithm for Electrostatic Potentials in an Atomistic/Continuum Hybrid Model for Electrolyte Solutions
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Jing Fu & Zecheng Gan 《Communications In Computational Physics》2021,29(2):571-587
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale
model of electrolytes which combines the strengths of atomistic/continuum electrolyte
representations, a harmonic surface mapping algorithm is developed for fast and accurate evaluation of the electrostatic reaction potentials. Our method reformulates the
reaction potential into a sum of image charges for the near-field, and a charge density
on an auxiliary spherical surface for the far-field, which can be further discretized into
point charges. Fast multipole method is used to accelerate the pairwise Coulomb summation. The accuracy and efficiency of our algorithm, as well as the choice of relevant
numerical parameters are demonstrated in detail. As a concrete example, for charges
close to the dielectric interface, our method can improve the accuracy by two orders of
magnitudes compared to the Kirkwood series expansion method. 相似文献
2.
3.
This paper presents a fourth-order Cartesian grid based boundary integral
method (BIM) for heterogeneous interface problems in two and three dimensional
space, where the problem interfaces are irregular and can be explicitly given by parametric curves or implicitly defined by level set functions. The method reformulates the
governing equation with interface conditions into boundary integral equations (BIEs)
and reinterprets the involved integrals as solutions to some simple interface problems
in an extended regular region. Solution of the simple equivalent interface problems for
integral evaluation relies on a fourth-order finite difference method with an FFT-based
fast elliptic solver. The structure of the coefficient matrix is preserved even with the
existence of the interface. In the whole calculation process, analytical expressions of
Green’s functions are never determined, formulated or computed. This is the novelty
of the proposed kernel-free boundary integral (KFBI) method. Numerical experiments
in both two and three dimensions are shown to demonstrate the algorithm efficiency
and solution accuracy even for problems with a large diffusion coefficient ratio. 相似文献
4.
A Simple Solver for the Two-Fluid Plasma Model Based on PseudoSpectral Time-Domain Algorithm
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Benoit Morel Remo Giust Kazem Ardaneh & Francois Courvoisier 《Communications In Computational Physics》2021,29(3):955-978
We present a solver of 3D two-fluid plasma model for the simulation of
short-pulse laser interactions with plasma. This solver resolves the equations of the
two-fluid plasma model with ideal gas closure. We also include the Bhatnagar-Gross-Krook collision model. Our solver is based on PseudoSpectral Time-Domain (PSTD)
method to solve Maxwell's curl equations. We use a Strang splitting to integrate Euler
equations with source term: while Euler equations are solved with a composite scheme
mixing Lax-Friedrichs and Lax-Wendroff schemes, the source term is integrated with
a fourth-order Runge-Kutta scheme. This two-fluid plasma model solver is simple to
implement because it only relies on finite difference schemes and Fast Fourier Transforms. It does not require spatially staggered grids. The solver was tested against
several well-known problems of plasma physics. Numerical simulations gave results
in excellent agreement with analytical solutions or with previous results from the literature. 相似文献
5.
Marco Caliari & Simone Zuccher 《Communications In Computational Physics》2021,29(5):1336-1364
We propose an idea to solve the Gross–Pitaevskii equation for dark structures inside an infinite constant background density $ρ_∞$=${|ψ_∞|}^2$, without the introduction of artificial boundary conditions. We map the unbounded physical domain $\mathbb{R}^3$ into the bounded domain ${(−1,1)}^3$ and discretize the rescaled equation by equispaced
4th-order finite differences. This results in a free boundary approach, which can be
solved in time by the Strang splitting method. The linear part is solved by a new, fast
approximation of the action of the matrix exponential at machine precision accuracy,
while the nonlinear part can be solved exactly. Numerical results confirm existing
ones based on the Fourier pseudospectral method and point out some weaknesses of
the latter such as the need of a quite large computational domain, and thus a consequent critical computational effort, in order to provide reliable time evolution of the
vortical structures, of their reconnections, and of integral quantities like mass, energy,
and momentum. The free boundary approach reproduces them correctly, also in finite
subdomains, at low computational cost. We show the versatility of this method by
carrying out one- and three-dimensional simulations and by using it also in the case of
Bose–Einstein condensates, for which $ψ$→0 as the spatial variables tend to infinity. 相似文献
6.
Explicit Computation of Robin Parameters in Optimized Schwarz Waveform Relaxation Methods for Schrödinger Equations Based on Pseudodifferential Operators
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Xavier Antoine & Emmanuel Lorin 《Communications In Computational Physics》2020,27(4):1032-1052
The Optimized Schwarz Waveform Relaxation algorithm, a domain decomposition method based on Robin transmission condition, is becoming a popular computational method for solving evolution partial differential equations in parallel. Along
with well-posedness, it offers a good balance between convergence rate, efficient computational complexity and simplicity of the implementation. The fundamental question is the selection of the Robin parameter to optimize the convergence of the algorithm. In this paper, we propose an approach to explicitly estimate the Robin parameter which is based on the approximation of the transmission operators at the subdomain interfaces, for the linear/nonlinear Schrödinger equation. Some illustrating
numerical experiments are proposed for the one- and two-dimensional problems. 相似文献
7.
Kinetic Slip Boundary Condition for Isothermal Rarefied Gas Flows Through Static Non-Planar Geometries Based on the Regularized Lattice-Boltzmann Method
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Jean-Michel Tucny David Vidal Sé bastien Leclaire & Franç ois Bertrand 《Communications In Computational Physics》2022,31(3):816-868
The simulation of rarefied gas flows through complex porous media is challenging due to the tortuous flow pathways inherent to such structures. The Lattice
Boltzmann method (LBM) has been identified as a promising avenue to solve flows
through complex geometries due to the simplicity of its scheme and its high parallel
computational efficiency. It has been proposed to model the stress-strain relationship
with the extended Navier-Stokes equations rather than attempting to directly solve
the Boltzmann equation. However, a regularization technique is required to filter out
non-resolved higher-order components with a low-order velocity scheme. Although
slip boundary conditions (BCs) have been proposed for the non-regularized multiple
relaxation time LBM (MRT-LBM) for planar geometries, previous slip BCs have never
been verified extensively with the regularization technique. In this work, following
an extensive literature review on the imposition of slip BCs for rarefied flows with the
LBM, it is proven that earlier values for kinetic parameters developed to impose slip
BCs are inaccurate for the regularized MRT-LBM and differ between the D2Q9 and
D3Q15 schemes. The error was eliminated for planar flows and good agreement between analytical solutions for arrays of cylinders and spheres was found with a wide
range of Knudsen numbers. 相似文献
8.
Directional $\mathcal{H}^2$ Compression Algorithm: Optimisations and Application to a Discontinuous Galerkin BEM for the Helmholtz Equation
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Nadir-Alexandre Messaï Sebastien Pernet & Abdesselam Bouguerra 《Communications In Computational Physics》2022,31(5):1585-1635
This study aimed to specialise a directional $\mathcal{H}^2
(\mathcal{D}\mathcal{H}^2)$ compression to matrices arising from the discontinuous Galerkin (DG) discretisation of the hypersingular
equation in acoustics. The significant finding is an algorithm that takes a DG stiffness matrix and finds a near-optimal $\mathcal{D}\mathcal{H}^2$ approximation for low and high-frequency
problems. We introduced the necessary special optimisations to make this algorithm
more efficient in the case of a DG stiffness matrix. Moreover, an automatic parameter
tuning strategy makes it easy to use and versatile. Numerical comparisons with a classical Boundary Element Method (BEM) show that a DG scheme combined with a $\mathcal{D}\mathcal{H}^2$ gives better computational efficiency than a classical BEM in the case of high-order finite elements and $hp$ heterogeneous meshes. The results indicate that DG is suitable
for an auto-adaptive context in integral equations. 相似文献
9.
A Highly Scalable Boundary Integral Equation and Walk-on-Spheres (BIE-WOS) Method for the Laplace Equation with Dirichlet Data
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In this paper, we study a highly scalable communication-free parallel domain boundary decomposition algorithm for the Laplace equation based on a hybrid method combining boundary integral equations and walk-on-spheres (BIE-WOS)
method, which provides a numerical approximation of the Dirichlet-to-Neumann
(DtN) mapping for the Laplace equation. The BIE-WOS is a local method on the
boundary of the domain and does not require a structured mesh, and only needs a
covering of the domain boundary by patches and a local mesh for each patch for a local BIE. A new version of the BIE-WOS method with second kind integral equations is
introduced for better error controls. The effect of errors from the Feynman-Kac formula
based path integral WOS method on the overall accuracy of the BIE-WOS method is
analyzed for the BIEs, especially in the calculation of the right hand sides of the BIEs.
For the special case of flat patches, it is shown that the second kind integral equation
of BIE-WOS method can be simplified where the local BIE solutions can be given in
closed forms. A key advantage of the parallel BIE-WOS method is the absence of communications during the computation of the DtN mapping on individual patches of
the boundary, resulting in a complete independent computation using a large number
of cluster nodes. In addition, the BIE-WOS has an intrinsic capability of fault tolerance for exascale computations. The nearly linear scalability of the parallel BIE-WOS
method on a large-scale cluster with 6400 CPU cores is verified for computing the DtN
mapping of exterior Laplace problems with Dirichlet data for several domains. 相似文献
10.
A Non-Ersatz Material Approach for the Topology Optimization of Elastic Structures Based on Piecewise Constant Level Set Method
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Zhengfang Zhang Yanqiang Dong & Weifeng Chen 《Communications In Computational Physics》2021,30(5):1370-1389
The topology optimization of a linearized elasticity system with the area
(volume) constraint is investigated. A non-ersatz material approach is proposed. By
introducing a fixed background domain, the linearized elasticity system is extended
into the background domain by a characteristic function. The piecewise constant level
set (PCLS) method is applied to represent the original material region and the void
region. A quadratic function of PCLS function is proposed to replace the characteristic
function. The functional derivative of the objective functional with respect to PCLS
function is derived, which is zero in the void region and nonzero in the original material region. A penalty gradient algorithm is proposed. Four numerical experiments of
2D and 3D elastic structures with different boundary conditions are presented, illustrating the validity of the proposed algorithm. 相似文献