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Uniform estimate of an iterative method for elliptic problems with rapidly oscillating coefficients

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS 2020年第4期8卷 787-818页

作者： Gu, Chenlin Ecole Polytech Palaiseau France PSL Res Univ Ecole Normale Super DMA Paris France

We study the iterative algorithm proposed by Armstrong et al. (An iterative method for elliptic problems with rapidly oscillating coefficients, 2018. arXiv preprint arXiv:1803.03551) to solve elliptic equations in divergence form with stochastic stationary coefficients. Such equations display rapidly oscillating coefficients and thus usually require very expensive numerical calculations, while this iterative method is comparatively easy to compute. In this article, we strengthen the estimate for the contraction factor achieved by one iteration of the algorithm. We obtain an estimate that holds uniformly over the initial function in the iteration, and which grows only logarithmically with the size of the domain.

关键词： Stochastic homogenization Elliptic equation numerical algorithm Iterative method

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Methods of variational data assimilation with application to problems of hydrothermodynamics of marine water areas

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RUSSIAN JOURNAL OF numerical ANALYSIS AND MATHEMATICAL MODELLING 2020年第4期35卷 189-202页

作者： Agoshkov, Valery I. Lezina, Natalia R. Parmuzin, Eugene I. Sheloput, Tatiana O. Shutyaev, Victor P. Zakharova, Natalia B. RAS Marchuk Inst Numer Math Moscow 119333 Russia Moscow Inst Phys & Technol Dolgoprudnyi 141701 Moscow Region Russia

A series of problems related to the class of inverse problems of ocean hydrothermodynamics and problems of variational data assimilation are formulated in the present paper. We propose methods for solving the problems... 详细信息

关键词： Variational assimilation numerical algorithm determination of heat fluxes sea surface temperature liquid boundaries sea level domain decomposition data processing

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Monotone Finite-Difference Schemes With Second Order Approximation Based on Regularization Approach for the Dirichlet Boundary Problem of the Gamma Equation

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IEEE ACCESS 2020年 8卷 45119-45132页

作者： Hieu, Le Minh Hanh, Truong Thi Hieu Thanh, Dang Ngoc Hoang Univ Econ Univ Danang Dept Econ Da Nang 550000 Vietnam Univ Econ Univ Danang Dept Ecommerce Da Nang 550000 Vietnam Univ Econ Ho Chi Minh City Sch Business Informat Technol Dept Informat Technol Ho Chi Minh City 700000 Vietnam

We investigate the initial boundary value problem for the Gamma equation transformed from the nonlinear Black-Scholes equation for pricing option to a quasilinear parabolic equation of second derivative. Furthermore, two-side estimates for the exact solution are also provided. By using regularization principle, the unconditionally monotone second order approximation finite-difference scheme on uniform and nonuniform grids is generalized, in that the maximum principle is satisfied without depending on relations of the coefficients and grid parameters. By using the difference maximum principle, we acquired two-side estimates for difference solution for the arbitrary non-sign-constant input data. Finally, we also provide a proof for a priori estimate. It can be confirmed that the two-side estimates for difference solution are completely consistent with the differential problem. Otherwise, the maximal and minimal values of the difference solution is independent from the diffusion and convection coefficients.

关键词： Gamma equation Black-Scholes equation financial engineering stock price prediction numerical solution numerical algorithm maximum principle two-side estimates finite-difference scheme regularization principle

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Admittance Method for Estimating Local Field Potentials Generated in a Multi-Scale Neuron Model of the Hippocampus

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FRONTIERS IN COMPUTATIONAL NEUROSCIENCE 2020年 14卷 72页

作者： Bingham, Clayton S. Paknahad, Javad Girard, Christopher B. C. Loizos, Kyle Bouteiller, Jean-Marie C. Song, Dong Lazzi, Gianluca Berger, Theodore W. Case Western Reserve Univ Dept Biomed Engn Cleveland OH 44106 USA Univ Southern Calif Dept Elect Engn Los Angeles CA 90007 USA Univ Southern Calif Dept Biomed Engn Los Angeles CA 90007 USA

Significant progress has been made toward model-based prediction of neral tissue activation in response to extracellular electrical stimulation, but challenges remain in the accurate and efficient estimation of distributed local field potentials (LFP). Analytical methods of estimating electric fields are a first-order approximation that may be suitable for model validation, but they are computationally expensive and cannot accurately capture boundary conditions in heterogeneous tissue. While there are many appropriate numerical methods of solving electric fields in neural tissue models, there isn't an established standard for mesh geometry nor a well-known rule for handling any mismatch in spatial resolution. Moreover, the challenge of misalignment between current sources and mesh nodes in a finite-element or resistor-network method volume conduction model needs to be further investigated. Therefore, using a previously published and validated multi-scale model of the hippocampus, the authors have formulated an algorithm for LFP estimation, and by extension, bidirectional communication between discretized and numerically solved volume conduction models and biologically detailed neural circuit models constructed in NEURON. Development of this algorithm required that we assess meshes of (i) unstructured tetrahedral and grid-based hexahedral geometries as well as (ii) differing approaches for managing the spatial misalignment of current sources and mesh nodes. The resulting algorithm is validated through the comparison of Admittance Method predicted evoked potentials with analytically estimated LFPs. Establishing this method is a critical step toward closed-loop integration of volume conductor and NEURON models that could lead to substantial improvement of the predictive power of multi-scale stimulation models of cortical tissue. These models may be used to deepen our understanding of hippocampal pathologies and the identification of efficacious electroceutical treatmen

关键词： neural network finite-element (FE) local field potential (LFP) multi-scale numerical algorithm volume conduction extracellular current measurements

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Simulations and experiments of mould filling in lost foam casting

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INTERNATIONAL JOURNAL OF CAST METALS RESEARCH 2020年第4-5期33卷 194-200页

作者： Li, Fengjun Zhao, Hua Ren, Fengzhang Song, Shaobiao Shao, Xinghai Volinsky, Alex A. First Tractor Co Ltd Engn Ctr Mfg Technol Luoyang Peoples R China Guangdong Songshan Polytech Coll Dept Mech Engn Shaoguan Peoples R China Henan Univ Sci & Technol Sch Mat Sci & Engn Luoyang 471023 Peoples R China Univ S Florida Dept Mech Engn Tampa FL 33620 USA

A new method for mould filling calculation of lost foam casting (LFC) was developed based on the main hypothesis, which assumes that every point on the melt-pattern interface moves in the radial direction. The value of the normal velocity is calculated by an empirical formula, which is the function of the degree of vacuum, pattern density, pouring temperature, metallic static head, etc. At a given time step, every interface point moves to a new position, and all the points form the shape of the melt-pattern interface. Based on the new position of the interface and the given velocity of the interface cell, the fluid flow and the temperature distribution of the molten metal can be calculated during the mould filling process of LFC. The calculated results were validated by experiments.

关键词： Physical mode numerical algorithm filling speed fluid flow temperature distribution lost foam casting numerical simulation mould filling

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Work recognition model for a higher education unit

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COGENT EDUCATION 2023年第2期10卷

作者： Martinez-Vazquez, P. Univ Birmingham Sch Engn Birmingham B15 2TT England

Higher Education frameworks have a strong focus on increasing students' satisfaction. This vision increases expectations on academic performance that often derive from stringent output measures for staff. The combination of internal and external demands for workers, such as those derived from their interaction with society, could create inadequate working conditions, which highlights the need to develop objective, rational, and robust mechanisms to distribute roles and responsibilities more fairly. This paper introduces a work recognition model for managing higher education units. It accounts for individual effort per discretised academic activity over a range of teaching, research, and administration duties. The model integrates standard academic activities into a mathematical framework characterised by continuous derivable functions that can be used to visualise fluctuations of workload across a complete academic year. The established framework enables optimisation of workloads through redistribution, moving away from diagnosing issues experienced by individuals subject to imbalanced or unfair workloads, to propose a practical solution. It is also possible to enhance the architecture of the proposed model to incorporate further activity or allowances and potentially increase robustness. In addition, the numerical model is relatively easy to implement in a variety of platforms. The proposed model was tested on a case study including 26 academics, mixing three-legged and teaching-focused contracts, showing how it decreases the relative differences of workload by a proportion of 4:1, after redistribution.

关键词： project allocation model staff workload numerical algorithm

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Deep learning of the role of interleukin IL-17 and its action in promoting cancer

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BIO-algorithmS AND MED-SYSTEMS 2020年第4期16卷

作者： Nutini, Alessandro Sohail, Ayesha Comsats Inst Informat Technol Dept Math Lahore 54000 Pakistan Ctr Study Motor Sci Biomech Dept Lucca Italy

In breast cancer patients, metastasis remains a major cause of death. The metastasis formation process is given by an interaction between the cancer cells and the microenvironment that surrounds them. In this article, we develop a mathematical model that analyzes the role of interleukin IL-17 and its action in promoting cancer and in facilitating tissue metastasis in breast cancer, using a dynamic analysis based on a stochastic process that accounts for the local and global action of this molecule. The model uses the Ornstein-Uhlembeck and Markov process in continuous time. It focuses on the oncological expansion and the interaction between the interleukin IL-17 and cell populations This analysis tends to clarify the processes underlying the metastasis expansion mechanism both for a better understanding of the pathological event and for a possible better control of therapeutic strategies. IL-17 is a proinflammatory interleukin that acts when there is tissue damage or when there is a pathological situation caused by an external pathogen or by a pathological condition such as cancer. This research is focused on the role of interleukin IL-17 which, especially in the case of breast cancer, turns out to be a dominant "communication pin" since it interconnects with the activity of different cell populations affected by the oncological phenomenon. Stochastic modeling strategies, specially the Ornstein-Uhlenbeck process, with the aid of numerical algorithms are elaborated in this review. The role of IL-17 is discussed in this manuscript at all the stages of cancer. It is discussed that IL-17 also acts as "metastasis promoter" as a result of its proinflammatory nature. The stochastic nature of IL-17 is discussed based on the evidence provided by recent literature. The resulting dynamical analysis can help to select the most appropriate therapeutic strategy. Cancer cells, in the case of breast cancer, have high level of IL-17 receptors (IL-17R);therefore the interleukin itsel

关键词： bidimensional Ornstein-Uhlenbeck process deep learning immunotherapy interleukin-17 noise numerical algorithm

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Application of the Fast Automatic Differentiation Technique for Solving Inverse Coefficient Problems

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2020年第1期60卷 15-25页

作者： Albu, A. F. Evtushenko, Yu G. Zubov, V., I Russian Acad Sci Fed Res Ctr Comp Sci & Control Dorodnicyn Comp Ctr Moscow 119333 Russia Moscow Inst Phys & Technol Dolgoprudnyi 141701 Moscow Oblast Russia

Results obtained by the authors in solving inverse coefficient problems are overviewed. The inverse problem under consideration is to determine a temperature-dependent thermal conductivity coefficient from experimental observations of the temperature field in the studied substance and (or) the heat flux on the surface of the object. The study is based on the Dirichlet boundary value problem for the nonstationary heat equation stated in the general -dimensional formulation. For this general case, an analytical expression for the cost functional gradient is obtained. The features of solving the inverse problem and the difficulties encountered in the solution process are discussed.

关键词： heat conduction inverse coefficient problems gradient heat equation numerical algorithm

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Thermophysical aspects of magnetized Williamson fluid flow subject to both porous and non-porous surfaces: A Lie symmetry analysis

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CASE STUDIES IN THERMAL ENGINEERING 2021年 28卷

作者： Rehman, Khalil Ur Shatanawi, Wasfi Abodayeh, Kamaleldin Prince Sultan Univ Dept Gen Sci Riyadh 11586 Saudi Arabia Air Univ Dept Math PAF Complex E-9 Islamabad 44000 Pakistan China Med Univ China Med Univ Hosp Dept Med Res Taichung 40402 Taiwan Hashemite Univ Fac Sci Dept Math POB 330127 Zarqa 13133 Jordan

The present outcomes on thermally magnetized flow fields by way of symmetry analysis will assist the research community to examine fluid dynamics, particular structures of fluids, and their interaction with the homogeneous porous mediums. The new scaling group of transformations is offered rather than using so-called transformations from existing literature to better narrate the thermal fluid interaction with the porous magnetized medium. Symmetry analysis is carried to find the physical quantities at the surface by executing (i) Slip and non-Slip flow fields (ii) Porous and non-porous mediums (iii) Magnetized and non-Magnetized flow fields. Such collective physical effects result in a complicated mathematical differential system. For the solution purpose firstly the concerned scaling group of transformations is obtained by using symmetry analysis and such transformations are used to covert the differential system into an ordinary differential system. The ultimate differential system is solved by using the shooting method along with RK scheme. The observations are shared with the help of line graph study and tabular forms. It is concluded that for the porous and non-porous mediums, resistance towards fluid declines as the Weissenberg number enhances whereas the heat transfer normal to both porous and non-porous surfaces increases as thermal diffusivity declines.

关键词： Thermally magnetized fluid Symmetry analysis Porous surface Slip flow numerical algorithm

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A statistical approach in enhancing the volume prediction of ellipsoidal ham

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JOURNAL OF FOOD ENGINEERING 2021年 290卷 110186-110186页

作者： Gan, Y. S. Wei, Lan Han, Yiming Zhang, Chenyu Huang, Yen-Chang Liong, Sze-Teng Natl Taipei Univ Nursing & Hlth Sci Res Ctr Healthcare Ind Innovat Taipei Taiwan Xiamen Univ Malaysia Sch Elect & Comp Engn Jalan Sunsuria Sepang Selangor Malaysia Natl Univ Tainan Dept Appl Math Tainan Taiwan Feng Chia Univ Dept Elect Engn Taichung Taiwan

In literature, there exist many attempts to determine the surface area and volume of an irregular object using automated image processing techniques. This paper expanded previous work on predicting the volume of ellipsoidal hams by using both image processing techniques and numerical methods. Novel algorithms were proposed to improve the prediction accuracy and robustness of the volume estimation mechanism. Particularly, the work focused on the ham's position in the horizontal viewpoint. An industrial robotic arm was utilized to lift the ham object and rotate it at a fixed controlled speed to maximize data consistency. Then, a Mask Region-based convolutional neural network approach was used to extract the ham object's features. Experiments were conducted on 16 newly collected ham datasets. In this paper, performance comparisons between this and the previous work were reported and detailed analyses presented. Particularly, three numerical algorithms (i.e., based on the minor axis, Y-direction, and k-nearest neighbor) were introduced to enhance volume prediction in the two databases. The new algorithm exhibited a 27% higher performance than that of the previous work's algorithm. Related theoretical and conceptual frameworks were discussed to further provide evidence and insights on the proposed mechanism.

关键词： Mask R-CNN Ham numerical algorithm Volume

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