Multiscale Modeling and Simulation

To make the investigation of electronic structure of incommensurate heterostructures computationally tractable, effective alternatives to Bloch theory must be developed. In [Multiscale Model. Simul., 15(2017), pp. 476--499] we developed and analyzed a real space scheme that exploits spatial ergodicity and near-sightedness. In the present work, we present an analogous scheme formulated in momentum space, which we prove has significant computational advantages in specific incommensurate systems of physical interest, e.g., bilayers of a specified class of materials with small rotation angles. We use our theoretical analysis to obtain estimates for improved rates of convergence with respect to total CPU time for our momentum space method that are confirmed in computational experiments.

Daniel Massatt

Stephen Carr

Mitchell Luskin

Christoph Ortner

Incommensurate Heterostructures in Momentum Space

动量空间中的非公度异质结构

We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis for a variety of existing iterative methods. Applications to geometry/texture image decomposition schemes are also discussed. A novelty of our framework is to use extensively the notion of a proximity operator, which was introduced by Moreau in the 1960s.

Patrick L. Combettes

Valérie R. Wajs

Multiscale Model. Simul.

Signal Recovery by Proximal Forward-Backward Splitting

通过近端前向后向分裂实现信号恢复

We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy cut-off for planewave discretizations, for both linear and nonlinear eigenvalue problems. The method is error controllable for linear eigenvalue problems in the sense that for a given required accuracy, an energy cut-off for which the solution matches the target accuracy can be reached efficiently. Further, the method is particularly promising for nonlinear eigenvalue problems in electronic structure calculations as it shall reduce the cost of early iterations in self-consistent algorithms. We present some numerical experiments for both linear and nonlinear eigenvalue problems. In particular, we provide electronic structure calculations for some insulator and metallic systems simulated with the Kohn--Sham density functional theory and the projector augmented wave method, illustrating the efficiency and potential of the algorithm.

Geneviève Dusson

Beilei Liu

Huajie Chen

Jun Fang

Xingyu Gao

An Adaptive Planewave Method for Electronic Structure Calculations

一种用于电子结构计算的自适应平面波方法

One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the simplest representation (i.e., the smallest amount of terms). One such approach is the sparse identification of nonlinear dynamics framework [6], which uses a sparsity-promoting algorithm that iterates between a partial least-squares fit and a thresholding (sparsity-promoting) step. In this work, we provide some theoretical results on the behavior and convergence of the algorithm proposed in [S. L. Brunton, J. L. Proctor, and J. N. Kutz, Proc. Nat. Acad. Sci. USA, 113 (2016), pp. 3932--3937]. In particular, we prove that the algorithm approximates local minimizers of an unconstrained $\ell^0$-penalized least-squares problem. From this, we provide sufficient conditions for general convergence, rate of convergence, conditions for one-step recovery, and a recovery result with respect to the condition number and noise. Examples illustrate that the rates of convergence are sharp. In addition, our results extend to other algorithms related to the algorithm in [S. L. Brunton, J. L. Proctor, and J. N. Kutz, Proc. Nat. Acad. Sci. USA, 113 (2016), pp. 3932--3937], and provide theoretical verification of several observed phenomena.

Linan Zhang

Hayden Schaeffer

On the Convergence of the SINDy Algorithm

关于SINDy算法收敛性的研究

We develop and analyze QM/MM (quantum/classic) hybrid methods for crystalline defects within the context of the tight-binding model. QM/MM methods employ accurate quantum mechanics (QM) models only in regions of interest (defects) and switch to computationally cheaper interatomic potential molecular mechanics (MM) models to describe the crystalline bulk. We propose new energy-based and force-based QM/MM methods, building on two principles: (i) locality of the QM model; and (ii) constructing the MM model as an explicit and controllable approximation of the QM model. This approach enables us to rigorously establish convergence rates in terms of the size of the QM region.

QM/MM Methods for Crystalline Defects. Part 2: Consistent Energy and Force-Mixing

晶体缺陷的QM/MM方法。第2部分：一致的能量和力混合

Wei Xie

Yin Yang

Eric Chung

Yunqing Huang

CEM-GMsFEM for Poisson Equations in Heterogeneous Perforated Domains

异质多孔区域泊松方程的CEM-GMsFEM方法

Richard D. James

Kunlun Qi

Li Wang

On the Kinetic Description of the Objective Molecular Dynamics

关于目标分子动力学的动力学描述

Maxime Krier

Julia Orlik

Grigory Panasenko

Konrad Steiner

Asymptotically Proved Numerical Coupling of a 2D Flexural Porous Plate with the 3D Stokes Fluid

渐近证明的二维弯曲多孔板与三维斯托克斯流体的数值耦合

Patrick E. Farrell

Giovanni Russo

Umberto Zerbinati

Kinetic Derivation of an Inviscid Compressible Leslie–Ericksen Equation for Rarified Calamitic Gases

稀薄 calamitic 气体无粘可压缩 Leslie-Ericksen 方程的动力学推导

Jianliang Qian

Timo Sprekeler

Hung V. Tran

Yifeng Yu

Optimal Rate of Convergence in Periodic Homogenization of Viscous Hamilton-Jacobi Equations

粘性Hamilton-Jacobi方程周期均匀化中的最优收敛率

Abbreviation	Multiscale Model. Simul.
Journal Impact	1.90
Quartiles(Global)	PHYSICS, MATHEMATICAL(Q2)

ISSN	1540-3459, 1540-3467
h-index	75

Publication Information	Publisher: Society for Industrial and Applied Mathematics Publications，Publishing cycle: Quarterly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2003，Proportion of original research papers: 100.00%，Self Citation Rate:5.30%， Gold OA Rate: 0.57%
Average review cycle	网友分享经验：较慢,6-12周
Average recruitment ratio	网友分享经验：较易

Multiscale Modeling and Simulation

Journal Citation Format

A journal article with 1 author

A journal article with 2 authors

A journal article with 3 authors

A journal article with 5 or more authors

Books Citation Format

Thesis Citation Format

Web sites Citation Format

Patent Citation Format

Staying up late manually editing references? ivySCI automatically matches journals and helps you generate references with a single click.

Share Submission Experience