Multiscale Model. Simul.最新文献_第10页

Multiscale Discrete Framelet Transform for Graph-Structured Signals 图结构信号的多尺度离散小框架变换

Multiscale Model. Simul. Pub Date : 2020-07-22 DOI: 10.1137/19m1259201

Hui Ji, Zuowei Shen, Yufei Zhao

引用次数: 0

Discrete-Time Inference for Slow-Fast Systems Driven by Fractional Brownian Motion 分数阶布朗运动驱动慢速系统的离散时间推理

Multiscale Model. Simul. Pub Date : 2020-07-22 DOI: 10.1137/20m135813x

S. Bourguin, S. Gailus, K. Spiliopoulos

引用次数: 5

Computing the minimal rebinding effect for non-reversible processes 计算非可逆过程的最小再结合效应

Multiscale Model. Simul. Pub Date : 2020-07-16 DOI: 10.1137/20M1334966

Susanne Röhl, Marcus Weber, K. Fackeldey

引用次数: 2

Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions 基于自适应边基函数的多尺度线性椭圆偏微分方程的指数收敛性

Multiscale Model. Simul. Pub Date : 2020-07-15 DOI: 10.1137/20M1352922

Yifan Chen, T. Hou, Yixuan Wang

{"title":"Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions","authors":"Yifan Chen, T. Hou, Yixuan Wang","doi":"10.1137/20M1352922","DOIUrl":"https://doi.org/10.1137/20M1352922","url":null,"abstract":"In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves nearly exponential convergence in the approximation error with respect to the computational degrees of freedom. Our strategy is to perform an energy orthogonal decomposition of the solution space into a coarse scale component comprising $a$-harmonic functions in each element of the mesh, and a fine scale component named the bubble part that can be computed locally and efficiently. The coarse scale component depends entirely on function values on edges. Our approximation on each edge is made in the Lions-Magenes space $H_{00}^{1/2}(e)$, which we will demonstrate to be a natural and powerful choice. We construct edge basis functions using local oversampling and singular value decomposition. When local information of the right-hand side is adaptively incorporated into the edge basis functions, we prove a nearly exponential convergence rate of the approximation error. Numerical experiments validate and extend our theoretical analysis; in particular, we observe no obvious degradation in accuracy for high-contrast media problems.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121286036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

Variational Asymptotic Preserving Scheme for the Vlasov-Poisson-Fokker-Planck System Vlasov-Poisson-Fokker-Planck系统的变分渐近保持格式

Multiscale Model. Simul. Pub Date : 2020-07-03 DOI: 10.1137/20M1350431

J. Carrillo, Li Wang, Wuzhe Xu, Ming Yan

引用次数: 4

Phase Field Modeling of Precipitation and Dissolution Processes in Porous Media: Upscaling and Numerical Experiments 多孔介质中沉淀和溶解过程的相场模拟:升级和数值实验

Multiscale Model. Simul. Pub Date : 2020-06-11 DOI: 10.1137/19m1239003

C. Bringedal, L. Wolff, I. Pop

引用次数: 28

Wave Packets in the Fractional Nonlinear Schrödinger Equation with a Honeycomb Potential 具有蜂窝电位的分数阶非线性Schrödinger方程中的波包

Multiscale Model. Simul. Pub Date : 2020-06-10 DOI: 10.1137/20M1340757

Peng Xie, Yi Zhu

引用次数: 3

Numerical Scheme for Kinetic Transport Equation with Internal State 具有内态的动力学输运方程的数值格式

Multiscale Model. Simul. Pub Date : 2020-06-09 DOI: 10.1137/20M134441X

N. Vauchelet, S. Yasuda

引用次数: 3

Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions 多尺度问题的量化张量有限元:二维和三维扩散问题

Multiscale Model. Simul. Pub Date : 2020-06-02 DOI: 10.1137/20m1341659

V. Kazeev, I. Oseledets, M. Rakhuba, C. Schwab

{"title":"Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions","authors":"V. Kazeev, I. Oseledets, M. Rakhuba, C. Schwab","doi":"10.1137/20m1341659","DOIUrl":"https://doi.org/10.1137/20m1341659","url":null,"abstract":"Homogenization in terms of multiscale limits transforms a multiscale problem with $n+1$ asymptotically separated microscales posed on a physical domain $D subset mathbb{R}^d$ into a one-scale problem posed on a product domain of dimension $(n+1)d$ by introducing $n$ so-called \"fast variables\". This procedure allows to convert $n+1$ scales in $d$ physical dimensions into a single-scale structure in $(n+1)d$ dimensions. We prove here that both the original, physical multiscale problem and the corresponding high-dimensional, one-scale limiting problem can be efficiently treated numerically with the recently developed quantized tensor-train finite-element method (QTT-FEM). \u0000The method is based on restricting computation to sequences of nested subspaces of low dimensions (which are called tensor ranks) within a vast but generic \"virtual\" (background) discretization space. In the course of computation, these subspaces are computed iteratively and data-adaptively at runtime, bypassing any \"offline precomputation\". For the purpose of theoretical analysis, such low-dimensional subspaces are constructed analytically to bound the tensor ranks vs. error $tau>0$. \u0000We consider a model linear elliptic multiscale problem in several physical dimensions and show, theoretically and experimentally, that both (i) the solution of the associated high-dimensional one-scale problem and (ii) the corresponding approximation to the solution of the multiscale problem admit efficient approximation by the QTT-FEM. These problems can therefore be numerically solved in a scale-robust fashion by standard (low-order) PDE discretizations combined with state-of-the-art general-purpose solvers for tensor-structured linear systems. We prove scale-robust exponential convergence, i.e., that QTT-FEM achieves accuracy $tau$ with the number of effective degrees of freedom scaling polynomially in $log tau$.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131372615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Coupling Particle-Based Reaction-Diffusion Simulations with Reservoirs Mediated by Reaction-Diffusion PDEs 基于颗粒的反应扩散模拟与反应扩散偏微分方程介导的储层耦合

Multiscale Model. Simul. Pub Date : 2020-05-29 DOI: 10.1137/20m1352739

Margarita Kostré, C. Schütte, Frank No'e, M. D. Razo

{"title":"Coupling Particle-Based Reaction-Diffusion Simulations with Reservoirs Mediated by Reaction-Diffusion PDEs","authors":"Margarita Kostré, C. Schütte, Frank No'e, M. D. Razo","doi":"10.1137/20m1352739","DOIUrl":"https://doi.org/10.1137/20m1352739","url":null,"abstract":"Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small to be relevant for life processes. Alternatively, particle-based reaction-diffusion models are currently the most accurate and computationally feasible approach at these scales. Their efficiency lies in modeling entire molecules as particles that can diffuse and interact with each other. In this work, we develop modeling and numerical schemes for particle-based reaction-diffusion in an open setting, where the reservoirs are mediated by reaction-diffusion PDEs. We derive two important theoretical results. The first one is the mean-field for open systems of diffusing particles; the second one is the mean-field for a particle-based reaction-diffusion system with second-order reactions. We employ these two results to develop a numerical scheme that consistently couples particle-based reaction-diffusion processes with reaction-diffusion PDEs. This allows modeling open biochemical systems in contact with reservoirs that are time-dependent and spatially inhomogeneous, as in many relevant real-world applications.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128901665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8