Parameter estimation with the multigrid-homotopy method for a nonlinear diffusion equation

Liu, Tao

doi:10.1016/j.cam.2022.114393

Cited by 40 publications

(29 citation statements)

References 35 publications

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“…This means the desirabil- ity of analytically solving the diffusion equation. It should be noted that the numerical solutions [24,25] are insufficient because they require the numerical values of the coefficients. At the same time, attempts to determine diffusion coefficients on the basis of numerical modelling of the structure of textile material [23] require a very large amount of preparatory work separately for each material.…”

Section: Figure 1: Porous Materials For Medical Purposesmentioning

confidence: 99%

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Basic Parameters of Medical Textile Materials for Removal and Retention of Exudate from Wounds

Riabchykov

Nazarchuk

Tkachuk

2022

TEKS

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The article focuses on predicting the properties of textile materials intended for the treatment of wounds. The main requirements for medical textile materials for liquid transportation were identified. Exudate from wounds and therapeutic fluids from a dressing must move through material with the necessary efficiency. This ensures that unwanted substances are removed from the wound and the necessary moisture is maintained. These requirements can be provided using a mathematical model of the process. Such a model can be substantiated by solving a non-linear differential diffusion equation. For this purpose, the function of changing the moisture content inside a textile material was approximated using a polynomial function that satisfies the boundary conditions. This approximation made it possible to reduce the problem to the solution of an ordinary differential equation with respect to time. The obtained analytical solution of the change in moisture content with respect to time and coordinate includes two diffusion constants. The results of macro-experiments, together with analytical results, made it possible to determine the diffusion coefficient and the nonlinearity coefficient in an explicit form. The results made it possible to predict the moisture content at a given point of textile material at any given time, the total amount of absorbed liquid and the intensity of absorption. The resulting function can recommend the geometric and physical parameters of medical textile materials for the treatment of wounds with a given intensity of exudate sorption.

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Section: Figure 1: Porous Materials For Medical Purposesmentioning

confidence: 99%

“…In [23], attempts were made to solve nonlinear diffusion equations using exponential and trigonometric series. Study [24] presents numerical methods of finite differences, and study [25] proposes iterative methods. Analysis of research proves the relevance of determining the parameters of the passage of fluid through medical textiles.…”

Section: Introductionmentioning

confidence: 99%

Basic Parameters of Medical Textile Materials for Removal and Retention of Exudate from Wounds

Riabchykov

Nazarchuk

Tkachuk

2022

TEKS

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“…Water resources determine the level of population, agricultural and industrial growth in these five regions. Many authors proposed advanced methods to solve the related problems [1][2][3][4][5][6]. In view of the above situation, it is very necessary and urgent to establish a reasonable water resource allocation plan.…”

Section: Introductionmentioning

confidence: 99%

Based AHP Loss Function Model for Equilibrium Dam Water Use

Xue

Liu

Qiu³

et al. 2023

J. Phys.: Conf. Ser.

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The purpose of this paper is to establish a model to balance water for power generation and domestic use. Dams and reservoirs have been an important part of human production and life since ancient times. In order to make full use of water resources, we have modelled the distribution of water resources in Lake Powell and Lake Mead to help achieve optimal allocation of water resources. Several models are established, Model I: Multiobjective Optimization. Model II: Loss function model based on Analytic Hierarchy Process. The discussion of the above models covers a wealth of industry factors and emergencies, so our model has strong adaptability and flexibility. It can be used not only in the factor we are learning, but also in other factors. Finally, we conduct a sensitivity analysis for extreme climate events. The results show that the model is insensitive to changes in extreme climate events, which means it can deal with water allocation problems in extreme situations. The model can be considered stable.

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“…We also explore the relationship between vehicle allocation, demand change and cost [3]. Many researchers focused on the study of the homotopy method [4], multiscale method [5,6], deep learning [7,8], thermo-hydro-geomechanical modelling [9].…”

Section: Introductionmentioning

confidence: 99%

Emergency Vehicle Intelligent Distribution System

Wang

Xia

Yang³

et al. 2022

J. Phys.: Conf. Ser.

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In this study, we developed a vehicle allocation model that can meet the requirements and cost best, the data related to the number of calls in each zone, and the variability required to respond to different types of calls. First, several indicators are extracted to quantify the advantages of station construction in each zone, and the hierarchical analysis method and TOPSIS are used to score each zone, and then select the stations that need to be built according to the score. Subsequently, according to the call requirements of each zone, its distance from the site, the amount of resources owned, etc, we develop a vehicle allocation model based on integer programming.

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Parameter estimation with the multigrid-homotopy method for a nonlinear diffusion equation

Cited by 40 publications

References 35 publications

Basic Parameters of Medical Textile Materials for Removal and Retention of Exudate from Wounds

Basic Parameters of Medical Textile Materials for Removal and Retention of Exudate from Wounds

Based AHP Loss Function Model for Equilibrium Dam Water Use

Emergency Vehicle Intelligent Distribution System

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