bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment
Authors: Meng Da , Zheng Bin , Lin Guang , Sushko Maria L. 
Published: July 2016

AbstractWe have developed efficient numerical algorithms for solving 3D steady-state Poisson-Nernst-Planck (PNP) equations with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by a finite difference scheme and solved iteratively using the Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Then, the algebraic multigrid method is applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed, which reduces computational complexity from O(N2) to O(NlogN), where N is the number of grid points. Integrals involving the Dirac delta function are evaluated directly by coordinate transformation, which yields more accurate results compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for lithiumion (Li-ion) batteries are shown to be in good agreement with the experimental data and the results from previous studies.
Efficient Variable-Coefficient Finite-Volume Stokes Solvers
Authors: Cai Mingchao , Nonaka Andy , Bell John B. , Griffith Boyce E. , Donev Aleksandar 
Published: July 2016

AbstractWe investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the success of using the classical projection method as a preconditioner for the coupled velocity pressure system [B. E. Griffith, J. Comp. Phys., 228 (2009), pp. 7565-7595], as well; established techniques for steady and unsteady Stokes flow in the finite-element literature, we construct preconditioners that employ independent generalized Helmholtz and Poisson solvers for the velocity and pressure subproblems. We demonstrate that only a single cycle of a standard geometric multigrid algorithm serves as an effective inexact solver for each of these subproblems. Contrary to traditional wisdom, we find that the Stokes problem can be solved nearly as efficiently as the independent pressure and velocity subproblems, making the overall cost of solving the Stokes system comparable to the cost of classical projection or fractional step methods for incompressible flow, even for steady flow and in the presence of large density and viscosity contrasts. Two of the five preconditioners considered here are found to be robust to GMRES restarts and to increasing problem size, making them suitable for large-scale problems. Our work opens many possibilities for constructing novel unsplit temporal integrators for finite-volume spatial discretizations of the equations of low Mach and incompressible flow dynamics.
Immersed Interface CIP for One Dimensional Hyperbolic Equations
Authors: Ito Kazufumi , Takeuchi Tomoya 
Published: July 2016

AbstractThe immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients. The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities, which is the same order of accuracy of the standard CIP scheme. Some numerical tests are given to verify the accuracy of the proposed method.
Radar Cross Section Reduction of a Cavity in the Ground Plane
Authors: Bao Gang , Lai Jun 
Published: July 2016

AbstractThis paper investigates the reduction of backscatter radar cross section (RCS) for a rectangular cavity embedded in the ground plane. The bottom of the cavity is coated by a thin, multilayered radar absorbing material (RAM) with possibly different permittivities. The objective is to minimize the backscatter RCS by the incidence of a plane wave over a single or a set of incident angles. By formulating the scattering problem as a Helmholtz equation with artificial boundary condition, the gradient with respect to the material permittivities is determined efficiently by the adjoint state method, which is integrated into a nonlinear optimization scheme. Numerical example shows the RCS may be significantly reduced.
A Frequency Determination Method for Digitized NMR Signals
Authors: Yan H. , Li K. , Khatiwada R. , Smith E. , Snow W. M. , Fu C. B. , Chu P.-H. , Gao H. , Zheng W. 
Published: July 2016

AbstractWe present a high precision frequency determination method for digitized NMR FID signals. The method employs high precision numerical integration rather than simple summation as in many other techniques. With no independent knowledge of the other parameters of a NMR FID signal (phase ф, amplitude A, and transverse relaxation time T2) this method can determine the signal frequency f0 with a precision of if the observation time T ≫ T2. The method is especially convenient when the detailed shape of the observed FT NMR spectrum is not well defined. When T2 is +∞ and the signal becomes pure sinusoidal, the precision of the method is which is one order more precise than the ±1 count error induced precision of a typical frequency counter. Analysis of this method shows that the integration reduces the noise by bandwidth narrowing as in a lock-in amplifier, and no extra signal filters are needed. For a pure sinusoidal signal we find from numerical simulations that the noise-induced error in this method reaches the Cramer-Rao Lower Band (CRLB) on frequency determination. For the damped sinusoidal case of most interest, the noise-induced error is found to be within a factor of 2 of CRLB when the measurement time T is 2 or 3 times larger than T2. We discuss possible improvements for the precision of this method.
A High-Order Accurate Gas-Kinetic Scheme for One- and Two-Dimensional Flow Simulation
Authors: Liu Na , Tang Huazhong 
Published: July 2016

AbstractThis paper develops a high-order accurate gas-kinetic scheme in the framework of the finite volume method for the one- and two-dimensional flow simulations, which is an extension of the third-order accurate gas-kinetic scheme [Q.B. Li, K. Xu, and S. Fu, J. Comput. Phys., 229(2010), 6715-6731] and the second-order accurate gas-kinetic scheme [K. Xu, J. Comput. Phys., 171(2001), 289-335]. It is formed by two parts: quartic polynomial reconstruction of the macroscopic variables and fourth-order accurate flux evolution. The first part reconstructs a piecewise cell-center based quartic polynomial and a cell-vertex based quartic polynomial according to the “initial” cell average approximation of macroscopic variables to recover locally the non-equilibrium and equilibrium single particle velocity distribution functions around the cell interface. It is in view of the fact that all macroscopic variables become moments of a single particle velocity distribution function in the gas-kinetic theory. The generalized moment limiter is employed there to suppress the possible numerical oscillation. In the second part, the macroscopic flux at the cell interface is evolved in fourth-order accuracy by means of the simple particle transport mechanism in the microscopic level, i.e. free transport and the Bhatnagar-Gross-Krook (BGK) collisions. In other words, the fourth-order flux evolution is based on the solution (i.e. the particle velocity distribution function) of the BGK model for the Boltzmann equation. Several 1D and 2D test problems are numerically solved by using the proposed high-order accurate gas-kinetic scheme. By comparing with the exact solutions or the numerical solutions obtained the second-order or third-order accurate gas-kinetic scheme, the computations demonstrate that our scheme is effective and accurate for simulating invisid and viscous fluid flows, and the accuracy of the high-order GKS depends on the choice of the (numerical) collision time.
Computational Modeling of Solvent Effects on Protein-Ligand Interactions Using Fully Polarizable Continuum Model and Rational Drug Design
Authors: Zheng Fang , Zhan Chang-Guo 
Published: July 2016

AbstractThis is a brief review of the computational modeling of protein-ligand interactions using a recently developed fully polarizable continuum model (FPCM) and rational drug design. Computational modeling has become a powerful tool in understanding detailed protein-ligand interactions at molecular level and in rational drug design. To study the binding of a protein with multiple molecular species of a ligand, one must accurately determine both the relative free energies of all of the molecular species in solution and the corresponding microscopic binding free energies for all of the molecular species binding with the protein. In this paper, we aim to provide a brief overview of the recent development in computational modeling of the solvent effects on the detailed protein-ligand interactions involving multiple molecular species of a ligand related to rational drug design. In particular, we first briefly discuss the main challenges in computational modeling of the detailed protein-ligand interactions involving the multiple molecular species and then focus on the FPCM model and its applications. The FPCM method allows accurate determination of the solvent effects in the first-principles quantum mechanism (QM) calculations on molecules in solution. The combined use of the FPCM-based QM calculations and other computational modeling and simulations enables us to accurately account for a protein binding with multiple molecular species of a ligand in solution. Based on the computational modeling of the detailed protein-ligand interactions, possible new drugs may be designed rationally as either small-molecule ligands of the protein or engineered proteins that bind/metabolize the ligand. The computational drug design has successfully led to discovery and development of promising drugs.
A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs
Authors: Ying Wenjun , Wang Wei-Cheng 
Published: July 2016

AbstractThis work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations (PDEs), including both boundary value and interface problems. The method is kernel-free in the sense that there is no need to know analytical expressions for kernels of the boundary and volume integrals in the solution of boundary integral equations. Evaluation of a boundary or volume integral is replaced with interpolation of a Cartesian grid based solution, which satisfies an equivalent discrete interface problem, while the interface problem is solved by a fast solver in the Cartesian grid. The computational work involved with the generalized boundary integral method is essentially linearly proportional to the number of grid nodes in the domain. This paper gives implementation details for a second-order version of the kernel-free boundary integral method in two space dimensions and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface problems. The interface problems demonstrated include those with piecewise constant and large-ratio coefficients and the heterogeneous interface problem, where the elliptic PDEs on two sides of the interface are of different types.
Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver
Authors: Zhang Bo , Lu Benzhuo , Cheng Xiaolin , Huang Jingfang , Pitsianis Nikos P. , Sun Xiaobai , McCammon J. Andrew 
Published: July 2016

AbstractThis paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. The potential of the solver is demonstrated with preliminary numerical results.
Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell’s Equations
Authors: Jiang Xue , Zhang Linbo , Zheng Weiying 
Published: July 2016

AbstractIn this paper, hp-adaptive finite element methods are studied for time-harmonic Maxwell’s equations. We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates. Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities, edge singularities, and an engineering benchmark problem of Maxwell’s equations. The hp-adaptive methods show much better performance than the h-adaptive method.
Variable High-Order Multiblock Overlapping Grid Methods for Mixed Steady and Unsteady Multiscale Viscous Flows, Part II: Hypersonic Nonequilibrium Flows
Authors: Lani Andrea , Sjögreen Björn , Yee H. C. , Henshaw William D. 
Published: July 2016

AbstractThe variable high-order multiblock overlapping (overset) grids method of Sjögreen & Yee [CiCP, Vol. 5, 2009] for a perfect gas has been extended to nonequilibrium flows. This work makes use of the recently developed high-order well-balanced shock-capturing schemes and their filter counterparts [Wang et al., J. Comput. Phys., 2009, 2010] that exactly preserve certain non-trivial steady state solutions of the chemical nonequilibrium governing equations. Multiscale turbulence with strong shocks and flows containing both steady and unsteady components is best treated by mixing of numerical methods and switching on the appropriate scheme in the appropriate subdomains of the flow fields, even under the multiblock grid or adaptive grid refinement framework. While low dissipative sixth- or higher-order shock-capturing filter methods are appropriate for unsteady turbulence with shocklets, second- and third- order shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence. It is anticipated that our variable high-order overset grid framework capability with its highly modular design will allow for an optimum synthesis of these new algorithms in such a way that the most appropriate spatial discretizations can be tailored for each particular region of the flow. In this paper some of the latest developments in single block high-order filter schemes for chemical nonequilibrium flows are applied to overset grid geometries. The numerical approach is validated on a number of test cases characterized by hypersonic conditions with strong shocks, including the reentry flow surrounding a 3D Apollo-like NASA Crew Exploration Vehicle that might contain mixed steady and unsteady components, depending on the flow conditions.
An Unpreconditioned Boundary-Integral for Iterative Solution of Scattering Problems with Non-Constant Leontovitch Impedance Boundary Conditions
Authors: Levadoux D. , Millot F. , Pernet S. 
Published: July 2016

AbstractThis paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition. It has two objectives. Firstly, the intrinsically well-conditioned integral equation (noted GCSIE) proposed in [30] is described focusing on its discretization. Secondly, we highlight the potential of this method by comparison with two other methods, the first being a two currents formulation in which the impedance condition is implicitly imposed and whose the convergence is quasi-optimal for Lipschitz polyhedron, the second being a CFIE-like formulation [14]. In particular, we prove that the new approach is less costly in term of CPU time and gives a more accurate solution than that obtained from the CFIE formulation. Finally, as expected, It is demonstrated that no preconditioner is needed for this formulation.
Simulation of Propagating Acoustic Wavefronts with Random Sound Speed
Authors: Martinelli Sheri L. 
Published: July 2016

AbstractA method for simulating acoustic wavefronts propagating under random sound speed conditions is presented. The approach applies a level set method to solve the Eikonal equation of high frequency acoustics for surfaces of constant phase, instead of tracing rays. The Lagrangian nature often makes full-field ray solutions difficult to reconstruct. The level set method captures multiple-valued solutions on a fixed grid. It is straightforward to represent other sources of uncertainty in the input data using this model, which has an advantage over Monte Carlo approaches in that it yields an expression for the solution as a function of random variables.
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation
Authors: Mu Lin , Wang Junping , Ye Xiu , Zhao Shan 
Published: July 2016

AbstractA weak Galerkin (WG) method is introduced and numerically tested for the Helmholtz equation. This method is flexible by using discontinuous piecewise polynomials and retains the mass conservation property. At the same time, the WG finite element formulation is symmetric and parameter free. Several test scenarios are designed for a numerical investigation on the accuracy, convergence, and robustness of the WG method in both inhomogeneous and homogeneous media over convex and non-convex domains. Challenging problems with high wave numbers are also examined. Our numerical experiments indicate that the weak Galerkin is a finite element technique that is easy to implement, and provides very accurate and robust numerical solutions for the Helmholtz problem with high wave numbers.
Correlation Functions, Universal Ratios and Goldstone Mode Singularities inn-Vector Models
Authors: Kaupužs J. , Melnik R. V. N. , Rimšāns J. 
Published: July 2016

AbstractCorrelation functions in the(n) models below the critical temperature are considered. Based on Monte Carlo (MC) data, we confirm the fact stated earlier by Engels and Vogt, that the transverse two-plane correlation function of the(4) model for lattice sizes aboutL= 120 and small external fieldshis very well described by a Gaussian approximation. However, we show that fits of not lower quality are provided by certain non-Gaussian approximation. We have also tested larger lattice sizes, up toL= 512. The Fourier-transformed transverse and longitudinal two-point correlation functions have Goldstone mode singularities in the thermodynamic limit atk→ 0 andh= +0, i.e.,G⊥(k) ≃ak–λ⊥andG‖(k)≃bk–λ‖, respectively. Hereaandbare the amplitudes,k= |k| is the magnitude of the wave vectork. The exponents λᚆ, λ‖and the ratiobM2/a2, whereMis the spontaneous magnetization, are universal according to the GFD (grouping of Feynman diagrams) approach. Here we find that the universality follows also from the standard (Gaussian) theory, yieldingbM2/a2=(n−1)/16. Our MC estimates of this ratio are 0.06±0.01 forn=2, 0.17±0.01 forn= 4 and 0.498±0.010 forn= 10. According to these and our earlier MC results, the asymptotic behavior and Goldstone mode singularities are not exactly described by the standard theory. This is expected from the GFD theory. We have found appropriate analytic approximations forG⊥(k) andG‖(k), well fitting the simulation data for smallk. We have used them to test the Patashinski-Pokrovski relation and have found that it holds approximately.
Feature-Scale Simulations of Particulate Slurry Flows in Chemical Mechanical Polishing by Smoothed Particle Hydrodynamics
Authors: Wang Dong , Shao Sihong , Yan Changhao , Cai Wei , Zeng Xuan 
Published: July 2016

AbstractIn this paper, the mechanisms of material removal in chemical mechanical polishing (CMP) processes are investigated in detail by the smoothed particle hydrodynamics (SPH) method. The feature-scale behaviours of slurry flow, rough pad, wafer defects, moving solid boundaries, slurry-abrasive interactions, and abrasive collisions are modelled and simulated. Compared with previous work on CMP simulations, our simulations incorporate more realistic physical aspects of the CMP process, especially the effect of abrasive concentration in the slurry flows. The preliminary results on slurry flow in CMP provide microscopic insights on the experimental data of the relation between the removal rate and abrasive concentration and demonstrate that SPH is a suitable method for the research of CMP processes.
Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential
Authors: Araújo Adérito , Das Amal K. , Neves Cidália , Sousa Ercília 
Published: July 2016

AbstractNumerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and mean-square-displacement (covering both inertial and diffusive regimes) are presented.
Strong Convergence and Speed up of Nested Stochastic Simulation Algorithm
Authors: Huang Can , Liu Di 
Published: July 2016

AbstractIn this paper, we revisit the Nested Stochastic Simulation Algorithm (NSSA) for stochastic chemical reacting networks by first proving its strong convergence. We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes, for which strong error estimates can also be obtained. Numerical experiments are presented to demonstrate the validity of our analysis.
An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations
Authors: Mirzadeh Mohammad , Theillard Maxime , Helgadöttir Asdís , Boy David , Gibou Frédéric 
Published: July 2016

AbstractWe present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set framework to represent sharp, complex interfaces in a simple and robust manner. It also uses non-graded, adaptive octree grids which, in comparison to uniform grids, drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16,27], and here is extended to address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule’s surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.
Simulation with Fluctuating and Singular Rates
Authors: Barekat Farzin , Caflisch Russel 
Published: July 2016

AbstractIn this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the Acceptance-Rejection method, and it is particularly useful for kinetic simulation in which the rates are fluctuating in time and have singular limits, as occurs for example in simulation of recombination interactions in a plasma. Although it depends on some additional requirements, the new method is easy to implement and rejects less samples than the Acceptance-Rejection method.