检索结果-内蒙古大学图书馆

Learning Interface Conditions in Domain Decomposition Solvers

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Taghibakhshi, Ali Nytko, Nicolas Zaman, Tareq MacLachlan, Scott Olson, Luke West, Matthew Mechanical Science and Engineering University of Illinois Urbana-Champaign UrbanaIL61801 United States Computer Science University of Illinois Urbana-Champaign UrbanaIL61801 United States Scientific Computing Program Memorial University of Newfoundland and Labrador St. John'sNL Canada Mathematics and Statistics Memorial University of Newfoundland and Labrador St. John'sNL Canada

Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the optimal construction of these methods requires tedious analysis and is often available only in simplified, structured-grid settings, limiting their use for more complex problems. In this work, we generalize optimized Schwarz domain decomposition methods to unstructured-grid problems, using Graph Convolutional Neural Networks (GCNNs) and unsupervised learning to learn optimal modifications at subdomain interfaces. A key ingredient in our approach is an improved loss function, enabling effective training on relatively small problems, but robust performance on arbitrarily large problems, with computational cost linear in problem size. The performance of the learned linear solvers is compared with both classical and optimized domain decomposition algorithms, for both structured- and unstructured-grid problems. © 2022, CC BY.

关键词： Domain decomposition methods

Freezing dynamics of wetting droplet under a uniform electric field

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Huang, Jiangxu Li, Hanqing Che, Jiaqi Chai, Zhenhua Wang, Lei Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Marine Design & Research Institute of China China The State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Physics China University of Geosciences Wuhan430074 China

Electrofreezing is a powerful technique that employs the electric field to control and enhance the freezing process. In this work, a phase-field-based lattice Boltzmann (LB) method is developed to study the electrofreezing process of sessile droplet on a cooled substrate. The accuracy of the present LB method is first validated through performing some simulations of the three-phase Stefan problem, the droplet freezing on a cold wall, and the droplet deformation under a uniform electric field. Then it is used to investigate the effect of an electric field on the freezing of a wetting droplet on a cold substrate, and the numerical results show that the electric field has a significant influence on the freezing time of the droplet mainly through changing the morphology of the droplet. In particular, under the effect of the electric field, the freezing time is increased for the droplet with a prolate pattern, while the freezing time of the droplet with an oblate pattern is decreased. These numerical results bring some new insights on the electrofreezing and provide a valuable guidance for the precise regulation of droplet freezing. Copyright © 2024, The Authors. All rights reserved.

关键词： Wetting

Stellar Blend Image Classification Using Computationally Efficient Gaussian Processes

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Eleh, Chinedu Zhang, Yunli Bidese, Rafael Priest, Benjamin W. Muyskens, Amanda L. Molinari, Roberto Billor, Nedret Department of Mathematics and Statistics Auburn University AuburnAL United States Department of Mechanical Engineering Auburn University AuburnAL United States Department of Biosystems Engineering Auburn University AuburnAL United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA United States Computational Engineering Division Lawrence Livermore National Laboratory LivermoreCA United States

Stellar blends, where two or more stars appear blended in an image, pose a significant visualization challenge in astronomy. Traditionally, distinguishing these blends from single stars has been costly and resource-intensive, involving sophisticated equipment and extensive expert analysis. This is especially problematic for analyzing the vast data volumes from surveys, such as Legacy Survey of Space and Time (LSST), Sloan Digital Sky Survey (SDSS), Dark Energy Spectroscopic Instrument (DESI), Legacy Imaging Survey and the Zwicky Transient Facility (ZTF). To address these challenges, we apply different normalizations and data embeddings on low resolution images of single stars and stellar blends, which are passed as inputs into machine learning methods and to a computationally efficient Gaussian process model (MuyGPs). MuyGPs consistently outperforms the benchmarked models, particularly on limited training data. Moreover, MuyGPs with rth root local min-max normalization achieves 83.8% accuracy. Furthermore, MuyGPs’ ability to produce confidence bands ensures that predictions with low confidence can be redirected to a specialist for efficient human-assisted labeling. © 2024, CC BY.

关键词： Dark energy

A bicriteria perspective on l-penalty approaches a corrigendum to siddiqui and gabriel's L-Penalty Approach for Solving MPECs

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Dächert, D. Siddiqui, Kerstin Saez-Gallego, Sauleh Gabriel, Javier Morales, Steven A. Miguel, Juan University of Duisburg-Essen Faculty of Economics and Business Administration Department for Management Science and Energy Economics Berliner Platz 6-8 Essen45127 Germany Departments of Civil Engineering and Applied Mathematics Statisitics Johns Hopkins University 3400 N Charles Street BaltimoreMD21218 United States Siemens Wind Power A/S Borupvang 9 Ballerup2750 Denmark Department of Mechanical Engineering Applied Mathematics Statistics and Scientific Computation Program University of Maryland College ParkMD20742-3021 United States University of Málaga Department of Applied Mathematics School of Industrial Engineers Málagaroom 2.556L-B

This paper presents a corrigendumto Theorems 2 and 3 in Siddiqui and Gabriel (2013). In brief, we revise the claim that their L-penalty approach yields a so-lution satisfying complementarity for any positive value of L, in general. This becomes evident when interpreting the L-penalty method as a weighted-sum scalarization of a bicriteria optimization problem. We also elaborate further assumptions under which the L-penalty approach yields a solution satisfying complementarity. Copyright © 2018, The Authors. All rights reserved.

关键词： Constrained optimization

Bullen’s parameter as a seismic observable for spin crossovers in the lower mantle

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Valencia-Cardona, Juan J. Williams, Quentin Shukla, Gaurav Wentzcovitch, Renata M. Scientific Computing Program University of Minnesota MinneapolisMN United States Department of Earth and Planetary Sciences University of California Santa Cruz Santa CruzCA United States Department of Earth Ocean and Atmospheric Science Florida State University TallahasseeFL United States Department of Applied Physics and Applied Mathematics Columbia University New York CityNY United States Lamont-Doherty Earth Observatory Columbia University PalisadesNY United States

Elastic anomalies produced by the spin crossover in ferropericlase have been documented by both first principles calculations and high pressure-temperature experiments. The predicted signature of this spin crossover in the lower mantle is, however, subtle and difficult to geophysically observe within the mantle. Indeed, global seismic anomalies associated with spin transitions have not yet been recognized in seismologic studies of the deep mantle. A sensitive seismic parameter is needed to determine the presence and amplitude of such a spin crossover signature. The effects of spin crossovers on Bullen’s parameter, η, are assessed here for a range of compositions, thermal profiles, and lateral variations in temperature within the lower mantle. Velocity anomalies associated with the spin crossover in ferropericlase span a depth range near 1,000 km for typical mantle temperatures. Positive excursions of Bullen’s parameter with a maximum amplitude of ∼ 0.03 are calculated to be present over a broad depth range within the mid-to-deep lower mantle: these are largest for peridotitic and harzburgitic compositions. These excursions are highest in amplitude for model lower mantles with large lateral thermal variations, and with cold downwellings having longer lateral length-scales relative to hot upwellings. We conclude that predicted deviations in Bullen’s parameter due to the spin crossover in ferropericlase for geophysically relevant compositions may be sufficiently large to resolve in accurate seismic inversions of this parameter, and could shed light on both the lateral variations in temperature at depth within the lower mantle, and the amount of ferropericlase at depth. Copyright © 2017, The Authors. All rights reserved.

关键词： Seismology

Phase-field modeling of dendritic growth with gas bubbles in the solidification of binary alloys

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Zhan, Chengjie Chai, Zhenhua Sun, Dongke Shi, Baochang Geng, Shaoning Jiang, Ping School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mechanical Engineering Southeast University Nanjing211189 China The State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan430074 China

In this work, a phase-field model is developed for the dendritic growth with gas bubbles in the solidification of binary alloys. In this model, a total free energy for the complex gas-liquid-dendrite system is proposed through considering the interactions of gas bubbles, liquid melt and solid dendrites, and it can reduce to the energy for gas-liquid flows in the region far from the solid phase, while degenerate to the energy for thermosolutal dendritic growth when the gas bubble disappears. The governing equations are usually obtained by minimizing the total free energy, but here some modifications are made to improve the capacity of the conservative phase-field equation for gas bubbles and convection-diffusion equation for solute transfer. Additionally, through the asymptotic analysis of the thin-interface limit, the present general phase-field model for alloy solidification can match the corresponding free boundary problem, and it is identical to the commonly used models under a specific choice of model parameters. Furthermore, to describe the fluid flow, the incompressible Navier-Stokes equations are adopted in the entire domain including gas, liquid, and solid regions, where the fluid-structure interaction is considered by a simple diffuse-interface method. To test the present phase-field model, the lattice Boltzmann method is used to study several problems of gas-liquid flows, dendritic growth as well as the solidification in presence of gas bubbles, and a good performance of the present model for such complex problems is observed. © 2024, CC BY-NC-ND.

关键词： Solidification

A diffuse-interface lattice Boltzmann method for the dendritic growth with thermosolutal convection

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Zhan, Chengjie Chai, Zhenhua Shi, Baochang Jiang, Ping Geng, Shaoning Sun, Dongke School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China The State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan430074 China School of Mechanical Engineering Southeast University Nanjing211189 China

In this work, we proposed a diffuse interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter governed by the phase-field equation for the dendritic growth. The governing equations for solute and heat transfer are modified such that the previous special treatments for source term can be avoided. To solve the model for the dendritic growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are developed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, to test the present diffuse-interface LB method, we performed some simulations of the dendritic growth, and found that the numerical results are in good agreements with some previous works. © 2022, CC BY-NC-ND.

关键词： Navier Stokes equations

A field guide to cultivating computational biology

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Carpenter, Anne E. Greene, Casey S. Carninci, Piero Carvalho, Benilton S De Hoon, Michiel Finley, Stacey Lê Cao, Kim-Anh Lee, Jerry S.H. Marchionni, Luigi Sindi, Suzanne S. Theis, Fabian J. Way, Gregory P. Yang, Jean Y.H. Fertig, Elana J. Imaging Platform Broad Institute of Mit and Harvard CambridgeMA United States Center for Health Ai University of Colorado School of Medicine AuroraCO United States Human Technopole Via Belgioioso 171 Milano MI20157 Italy Department of Statistics Institute of MathematicsStatistics and Scientific Computing University of Campinas Campinas Brazil Riken Center for Integrative Medical Sciences Yokohama Kanagawa Japan Department of Biomedical Engineering Quantitative and Computational Biology Chemical Engineering & Materials Science University of Southern California United States Melbourne Integrative Genomics School of Mathematics and Statistics University of Melbourne Australia Departments of Medicine/Oncology Chemical Engineering and Material Sciences University of Southern California CA United States Department of Pathology and Laboratory Medicine Weill-Cornell Medicine New YorkNY United States Department of Applied Mathematics University of CaliforniaMerced MercedCA United States Helmholtz Center Munich and Department of Mathematics Institute of Computational Biology Technical University of Munich Germany Charles Perkins Centre and School of Mathematics and Statistics University of Sydney Australia Departments of Oncology Convergence Institute Biomedical Engineering and Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD United States

Biomedical research centers can empower basic discovery and novel therapeutic strategies by leveraging their large-scale datasets from experiments and patients. This data, together with new technologies to create and analyze it, has ushered in an era of data-driven discovery which requires moving beyond the traditional individual, single-discipline investigator research model. This interdisciplinary niche is where computational biology thrives. It has matured over the past three decades and made major contributions to scientific knowledge and human health, yet researchers in the field often languish in career advancement, publication, and grant review. We propose solutions for individual scientists, institutions, journal publishers, funding agencies, and educators. © 2021, CC BY-SA.

关键词： Large dataset

Nonlinear multigrid based on local spectral coarsening for heterogeneous difiusion problems

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Leea, Chak Shing Hamon, Francois Castelletto, Nicola Vassilevski, Panayot S. White, Joshua Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Total EandP Research and Technology HoustonTX77002 United States Atmospheric Earth and Energy Division Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Energy Resources Engineering Stanford University StanfordCA94305 United States Fariborz Maseeh Department of Mathematics and Statistics Portland State University PortlandOR97201 United States

This work develops a nonlinear multigrid method for difiusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of freedom and spectral decomposition of reference linear operators associated with the aggregates. For rapid convergence, it is important that the resulting coarse spaces have good approximation properties. In our approach, the approximation quality can be directly improved by including more spectral degrees of freedom in the coarsening process. Further, by exploiting local coarsening and a piecewise-constant approximation when evaluating the nonlinear component, the coarse level problems are assembled and solved without ever re-visiting the fine level, an essential element for multigrid algorithms to achieve optimal scalability. Numerical examples comparing relative performance of the proposed nonlinear multigrid solvers with standard single-level approaches-Picard's and Newton's methods-are presented. Results show that the proposed solver consistently outperforms the single-level methods, both in effciency and robustness. Copyright © 2020, The Authors. All rights reserved.

关键词： Finite volume method