Multiscale Modeling & Simulation最新文献

Extending the Regime of Linear Response with Synthetic Forcings 用综合强迫扩展线性响应域

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-11-14 DOI: 10.1137/23m1557611

Renato Spacek, Gabriel Stoltz

引用次数: 0

FMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three Dimensions FMM-LU:三维多尺度边界积分方程的快速直接求解器

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-11-03 DOI: 10.1137/22m1514040

Daria Sushnikova, Leslie Greengard, Michael O’Neil, Manas Rachh

{"title":"FMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three Dimensions","authors":"Daria Sushnikova, Leslie Greengard, Michael O’Neil, Manas Rachh","doi":"10.1137/22m1514040","DOIUrl":"https://doi.org/10.1137/22m1514040","url":null,"abstract":"We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our algorithm computes an ${LU}$-like hierarchical factorization of the dense system matrix, permitting application of the inverse in $mathcal O(n)$ time, where $n$ is the number of unknowns on the surface. The factorization itself also scales linearly with the system size, albeit with a somewhat larger constant. The scheme is built on a level-restricted adaptive octree data structure, and therefore it is compatible with highly nonuniform discretizations. Furthermore, the scheme is coupled with high-order accurate locally-corrected Nystr\"om quadrature methods to integrate the singular and weakly-singular Green's functions used in the integral representations. Our method has immediate applications to a variety of problems in computational physics. We concentrate here on studying its performance in acoustic scattering (governed by the Helmholtz equation) at low to moderate frequencies, and provide rigorous justification for compression of submatrices via proxy surfaces.","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Homogenization and Dimension Reduction of the Stokes Problem with Navier-Slip Condition in Thin Perforated Layers 薄射孔层中navier -滑移条件下Stokes问题的均匀化与降维

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-10-24 DOI: 10.1137/22m1528860

John Fabricius, Markus Gahn

引用次数: 1

Large Deviation Principle and Thermodynamic Limit of Chemical Master Equation via Nonlinear Semigroup 非线性半群化学主方程的大偏差原理与热力学极限

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-10-24 DOI: 10.1137/22m1505633

Yuan Gao, Jian-Guo Liu

引用次数: 0

Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization 数值均匀化中粗尺度代物的神经网络逼近

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-10-20 DOI: 10.1137/22m1524278

Fabian Kröpfl, Roland Maier, Daniel Peterseim

{"title":"Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization","authors":"Fabian Kröpfl, Roland Maier, Daniel Peterseim","doi":"10.1137/22m1524278","DOIUrl":"https://doi.org/10.1137/22m1524278","url":null,"abstract":"Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale subproblems on local subdomains whose solutions are then employed to deduce appropriate coarse contributions to the surrogate model. However, in the absence of periodicity and scale separation, the reliability of such models requires the local subdomains to cover the whole domain which may result in high offline costs, in particular for parameter-dependent and stochastic problems. This paper justifies the use of neural networks for the approximation of coarse-scale surrogate models by analyzing their approximation properties. For a prototypical and representative numerical homogenization technique, the Localized Orthogonal Decomposition method, we show that one single neural network is sufficient to approximate the coarse contributions of all occurring coefficient-dependent local subproblems for a nontrivial class of diffusion coefficients up to arbitrary accuracy. We present rigorous upper bounds on the depth and number of nonzero parameters for such a network to achieve a given accuracy. Further, we analyze the overall error of the resulting neural network enhanced numerical homogenization surrogate model.","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135569348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0

On the Periodic Homogenization of Elliptic Equations in Nondivergence Form with Large Drifts 大漂移非发散型椭圆方程的周期均匀化

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-10-20 DOI: 10.1137/23m1550906

Wenjia Jing, Yiping Zhang

引用次数: 2

An Effective Fractional Paraxial Wave Equation for Wave-Fronts in Randomly Layered Media with Long-Range Correlations 具有长程相关的随机分层介质中波前的有效分数阶傍轴波动方程

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-10-18 DOI: 10.1137/22m1525594

Christophe Gomez

{"title":"An Effective Fractional Paraxial Wave Equation for Wave-Fronts in Randomly Layered Media with Long-Range Correlations","authors":"Christophe Gomez","doi":"10.1137/22m1525594","DOIUrl":"https://doi.org/10.1137/22m1525594","url":null,"abstract":"This work concerns the asymptotic analysis of high-frequency wave propagation in randomly layered media with fast variations and long-range correlations. The analysis takes place in the three-dimensional physical space and weak-coupling regime. The role played by the slow decay of the correlations on a propagating pulse is twofold. First we observe a random travel time characterized by a fractional Brownian motion that appears to have a standard deviation larger than the pulse width, which is in contrast with the standard O’Doherty–Anstey theory for random propagation media with mixing properties. Second, a deterministic pulse deformation is described as the solution of a paraxial wave equation involving a pseudodifferential operator. This operator is characterized by the autocorrelation function of the medium fluctuations. In case of fluctuations with long-range correlations this operator is close to a fractional Weyl derivative whose order, between 2 and 3, depends on the power decay of the autocorrelation function. In the frequency domain, the pseudodifferential operator exhibits a frequency-dependent power-law attenuation with exponent corresponding to the order of the fractional derivative, and a frequency-dependent phase modulation, both ensuring the causality of the limiting paraxial wave equation as well as the Kramers–Kronig relations. The mathematical analysis is based on an approximation-diffusion theorem for random ordinary differential equations with long-range correlations.","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1

Elastic Far-Field Decay from Dislocations in Multilattices 多晶格中位错的弹性远场衰减

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-10-12 DOI: 10.1137/22m1502021

Derek Olson, Christoph Ortner, Yangshuai Wang, Lei Zhang

引用次数: 2

Electronic Observables for Relaxed Bilayer Two-Dimensional Heterostructures in Momentum Space 动量空间中松弛双层二维异质结构的电子观测

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-10-11 DOI: 10.1137/21m1451208

Daniel Massatt, Stephen Carr, Mitchell Luskin

引用次数: 0

Stochastic Continuum Models for High-Entropy Alloys with Short-range Order 高熵合金短阶随机连续统模型

4区数学

Multiscale Modeling & Simulation Pub Date : 2023-10-10 DOI: 10.1137/22m1496335

Yahong Yang, Luchan Zhang, Yang Xiang

{"title":"Stochastic Continuum Models for High-Entropy Alloys with Short-range Order","authors":"Yahong Yang, Luchan Zhang, Yang Xiang","doi":"10.1137/22m1496335","DOIUrl":"https://doi.org/10.1137/22m1496335","url":null,"abstract":"High entropy alloys (HEAs) are a class of novel materials that exhibit superb engineering properties. It has been demonstrated by extensive experiments and first principles/atomistic simulations that short-range order in the atomic level randomness strongly influences the properties of HEAs. In this paper, we derive stochastic continuum models for HEAs with short-range order from atomistic models. A proper continuum limit is obtained such that the mean and variance of the atomic level randomness together with the short-range order described by a characteristic length are kept in the process from the atomistic interaction model to the continuum equation. The obtained continuum model with short-range order is in the form of an Ornstein--Uhlenbeck (OU) process. This validates the continuum model based on the OU process adopted phenomenologically by Zhang et al. [Acta Mater., 166 (2019), pp. 424--434] for HEAs with short-range order. We derive such stochastic continuum models with short-range order for both elasticity in HEAs without defects and HEAs with dislocations (line defects). The obtained stochastic continuum models are based on the energy formulations, whose variations lead to stochastic partial differential equations.","PeriodicalId":49791,"journal":{"name":"Multiscale Modeling & Simulation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0