Communications in Applied Mathematics and Computational Science最新文献_第3页

A semi-implicit multiscale scheme for shallow water flows at low Froude number 低弗劳德数下浅水流动的半隐式多尺度格式

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2018-09-25 DOI: 10.2140/CAMCOS.2018.13.303

S. Vater, R. Klein

引用次数: 9

2D force constraints in the method of regularized Stokeslets 正则化Stokeslets方法中的二维力约束

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2018-06-19 DOI: 10.2140/camcos.2019.14.149

O. Maxian, Wanda Strychalski

引用次数: 2

An adaptive local discrete convolution methodfor the numerical solution of Maxwell’s equations 麦克斯韦方程组数值解的自适应局部离散卷积方法

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2018-04-29 DOI: 10.2140/camcos.2019.14.105

B. Lo, P. Colella

引用次数: 3

A theoretical study of aqueous humor secretion based on a continuum model coupling electrochemical and fluid-dynamical transmembrane mechanisms 基于电化学和流体动力学跨膜机制耦合的连续介质模型的房水分泌理论研究

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2017-12-08 DOI: 10.2140/camcos.2019.14.65

Lorenzo Sala, A. Mauri, R. Sacco, D. Messenio, G. Guidoboni, A. Harris

{"title":"A theoretical study of aqueous humor secretion based on a continuum model coupling electrochemical and fluid-dynamical transmembrane mechanisms","authors":"Lorenzo Sala, A. Mauri, R. Sacco, D. Messenio, G. Guidoboni, A. Harris","doi":"10.2140/camcos.2019.14.65","DOIUrl":"https://doi.org/10.2140/camcos.2019.14.65","url":null,"abstract":"Intraocular pressure, resulting from the balance of aqueous humor (AH) production and drainage, is the only approved treatable risk factor in glaucoma. AH production is determined by the concurrent function of ionic pumps and aquaporins in the ciliary processes but their individual contribution is difficult to characterize experimentally. In this work, we propose a novel unified modeling and computational framework for the finite element simulation of the role of the main ionic pumps involved in AH secretion, namely, the sodium potassium pump, the calcium-sodium pump, the anion channel and the hydrogenate-sodium pump. The theoretical model is developed at the cellular scale and is based on the coupling between electrochemical and fluid-dynamical transmembrane mechanisms characterized by a novel description of the electric pressure exerted by the ions on the intrachannel fluid that includes electrochemical and osmotic corrections. Considering a realistic geometry of the ionic pumps, the proposed model is demonstrated to correctly predict their functionality as a function of (1) the permanent electric charge density over the channel pump surface; (2) the osmotic gradient coefficient; (3) the stoichiometric ratio between the ionic pump currents enforced at the inlet and outlet sections of the channel. In particular, theoretical predictions of the transepithelial membrane potential for each simulated pump/channel allow us to perform a first significant model comparison with experimental data for monkeys. This is a significant step for future multidisciplinary studies on the action of molecules on AH production.","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2017-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82217518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Simple second-order finite differences for elliptic PDEs with discontinuous coefficients and interfaces 具有不连续系数和界面的椭圆偏微分方程的简单二阶有限差分

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2017-11-01 DOI: 10.2140/camcos.2019.14.121

C. Tzou, S. Stechmann

{"title":"Simple second-order finite differences for elliptic PDEs with discontinuous coefficients and interfaces","authors":"C. Tzou, S. Stechmann","doi":"10.2140/camcos.2019.14.121","DOIUrl":"https://doi.org/10.2140/camcos.2019.14.121","url":null,"abstract":"In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise due to changes in material properties at an immersed interface or embedded boundary, which may have an irregular shape. Consequently, the solution and its gradient can be discontinuous, and numerical methods can be difficult to design. Here a new method is presented and analyzed, using a simple formulation of one-dimensional finite differences on a Cartesian grid, allowing for a relatively easy setup for one-, two-, or three-dimensional problems. The method preserves a sharp interface with discontinuous solutions, obtained from a small number of iterations (approximately five) of solving a symmetric linear system with updates to the right- hand side. Second-order accuracy is rigorously proven in one spatial dimension and demonstrated through numerical examples in two and three spatial dimensions. The method is tested here on the variable-coefficient Poisson equation, and it could be extended for use on time-dependent problems of heat transfer, fluid dynamics, or other applications.","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85380532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Symmetrized importance samplers for stochastic differential equations 随机微分方程的对称重要抽样

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2017-07-10 DOI: 10.2140/camcos.2018.13.215

Andrew B. Leach, Kevin K. Lin, M. Morzfeld

引用次数: 2

On the convergence of spectral deferred correction methods 关于光谱延迟校正方法的收敛性

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2017-06-20 DOI: 10.2140/camcos.2019.14.33

Mathew F. Causley, David C. Seal

{"title":"On the convergence of spectral deferred correction methods","authors":"Mathew F. Causley, David C. Seal","doi":"10.2140/camcos.2019.14.33","DOIUrl":"https://doi.org/10.2140/camcos.2019.14.33","url":null,"abstract":"In this work we analyze the convergence properties of the Spectral Deferred Correction (SDC) method originally proposed by Dutt et al. [BIT, 40 (2000), pp. 241--266]. The framework for this high-order ordinary differential equation (ODE) solver is typically described wherein a low-order approximation (such as forward or backward Euler) is lifted to higher order accuracy by applying the same low-order method to an error equation and then adding in the resulting defect to correct the solution. Our focus is not on solving the error equation to increase the order of accuracy, but on rewriting the solver as an iterative Picard integral equation solver. In doing so, our chief finding is that it is not the low-order solver that picks up the order of accuracy with each correction, but it is the underlying quadrature rule of the right hand side function that is solely responsible for picking up additional orders of accuracy. Our proofs point to a total of three sources of errors that SDC methods carry: the error at the current time point, the error from the previous iterate, and the numerical integration error that comes from the total number of quadrature nodes used for integration. The second of these two sources of errors is what separates SDC methods from Picard integral equation methods; our findings indicate that as long as difference between the current and previous iterate always gets multiplied by at least a constant multiple of the time step size, then high-order accuracy can be found even if the underlying \"solver\" is inconsistent the underlying ODE. From this vantage, we solidify the prospects of extending spectral deferred correction methods to a larger class of solvers to which we present some examples.","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86417574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 16

Computation of volume potentials on structured grids with the method of local corrections 用局部修正法计算结构网格上的体积势

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2017-02-26 DOI: 10.2140/camcos.2019.14.1

C. Kavouklis, P. Colella

{"title":"Computation of volume potentials on structured grids with the method of local corrections","authors":"C. Kavouklis, P. Colella","doi":"10.2140/camcos.2019.14.1","DOIUrl":"https://doi.org/10.2140/camcos.2019.14.1","url":null,"abstract":"We present a new version of the Method of Local Corrections (MLC) cite{mlc}, a multilevel, low communications, non-iterative, domain decomposition algorithm for the numerical solution of the free space Poisson's equation in 3D on locally-structured grids. In this method, the field is computed as a linear superposition of local fields induced by charges on rectangular patches of size $O(1)$ mesh points, with the global coupling represented by a coarse grid solution using a right-hand side computed from the local solutions. In the present method, the local convolutions are further decomposed into a short-range contribution computed by convolution with the discrete Green's function for an $Q^{th}$-order accurate finite difference approximation to the Laplacian with the full right-hand side on the patch, combined with a longer-range component that is the field induced by the terms up to order $P-1$ of the Legendre expansion of the charge over the patch. This leads to a method with a solution error that has an asymptotic bound of $O(h^P) + O(h^Q) + O(epsilon h^2) + O(epsilon)$, where $h$ is the mesh spacing, and $epsilon$ is the max norm of the charge times a rapidly-decaying function of the radius of the support of the local solutions scaled by $h$. Thus we have eliminated the low-order accuracy of the original method (which corresponds to $P=1$ in the present method) for smooth solutions, while keeping the computational cost per patch nearly the same with that of the original method. Specifically, in addition to the local solves of the original method we only have to compute and communicate the expansion coefficients of local expansions (that is, for instance, 20 scalars per patch for $P=4$). Several numerical examples are presented to illustrate the new method and demonstrate its convergence properties.","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2017-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75449886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

An equation-by-equation method for solving the multidimensional moment constrained maximum entropy problem 求解多维矩约束最大熵问题的一种逐方程方法

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2017-02-08 DOI: 10.2140/camcos.2018.13.189

Wenrui Hao, J. Harlim

{"title":"An equation-by-equation method for solving the multidimensional moment constrained maximum entropy problem","authors":"Wenrui Hao, J. Harlim","doi":"10.2140/camcos.2018.13.189","DOIUrl":"https://doi.org/10.2140/camcos.2018.13.189","url":null,"abstract":"An equation-by-equation (EBE) method is proposed to solve a system of nonlinear equations arising from the moment constrained maximum entropy problem of multidimensional variables. The design of the EBE method combines ideas from homotopy continuation and Newton's iterative methods. Theoretically, we establish the local convergence under appropriate conditions and show that the proposed method, geometrically, finds the solution by searching along the surface corresponding to one component of the nonlinear problem. We will demonstrate the robustness of the method on various numerical examples, including: (1) A six-moment one-dimensional entropy problem with an explicit solution that contains components of order $10^0-10^3$ in magnitude; (2) Four-moment multidimensional entropy problems with explicit solutions where the resulting systems to be solved ranging from $70-310$ equations; (3) Four- to eight-moment of a two-dimensional entropy problem, which solutions correspond to the densities of the two leading EOFs of the wind stress-driven large-scale oceanic model. In this case, we find that the EBE method is more accurate compared to the classical Newton's method, the MATLAB generic solver, and the previously developed BFGS-based method, which was also tested on this problem. (4) Four-moment constrained of up to five-dimensional entropy problems which solutions correspond to multidimensional densities of the components of the solutions of the Kuramoto-Sivashinsky equation. For the higher dimensional cases of this example, the EBE method is superior because it automatically selects a subset of the prescribed moment constraints from which the maximum entropy solution can be estimated within the desired tolerance. This selection feature is particularly important since the moment constrained maximum entropy problems do not necessarily have solutions in general.","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2017-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79625054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 12

A numerical study of the extended Kohn–Shamground states of atoms 原子扩展Kohn-Shamground态的数值研究

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2017-02-03 DOI: 10.2140/camcos.2018.13.139

É. Cancès, Nahia Mourad

{"title":"A numerical study of the extended Kohn–Sham\u0000ground states of atoms","authors":"É. Cancès, Nahia Mourad","doi":"10.2140/camcos.2018.13.139","DOIUrl":"https://doi.org/10.2140/camcos.2018.13.139","url":null,"abstract":"In this article, we consider the extended Kohn-Sham model for atoms subjected to cylindrically-symmetric external potentials. The variational approximation of the model and the construction of appropriate discretization spaces are detailed together with the algorithm to solve the discretized Kohn-Sham equations used in our code. Using this code, we compute the occupied and unoccupied energy levels of all the atoms of the first four rows of the periodic table for the reduced Hartree-Fock (rHF) and the extended Kohn-Sham Xα models. These results allow us to test numerically the assumptions on the negative spectra of atomic rHF and Kohn-Sham Hamiltonians used in our previous theoretical works on density functional perturbation theory and pseudopotentials. Interestingly, we observe accidental degeneracies between s and d shells or between p and d shells at the Fermi level of some atoms. We also consider the case of an atom subjected to a uniform electric-field. For various magnitudes of the electric field, we compute the response of the density of the carbon atom confined in a large ball with Dirichlet boundary conditions, and we check that, in the limit of small electric fields, the results agree with the ones obtained with first-order density functional perturbation theory.","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2017-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85186346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2