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Your search keyword '"Galerkin weak form"' showing total 2 results
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2 results on '"Galerkin weak form"'

1. A weighted combination of reproducing kernel particle shape functions with cardinal functions of scalable polyharmonic spline radial kernel utilized in Galerkin weak form of a mathematical model related to anti-angiogenic therapy.

Author

Narimani, Niusha, Dehghan, Mehdi, and Mohammadi, Vahid

Subjects
*POLYHARMONIC functions, *MATHEMATICAL forms, *SPLINES, *NEOVASCULARIZATION inhibitors, *MATHEMATICAL models, *BIOLOGICAL mathematical modeling, *MESHFREE methods, *SPLINE theory
Abstract

In this manuscript, a new localized meshfree (meshless) approximation, i.e., a combination of the reproducing kernel particle (RKP) shape functions with the cardinal functions of the scalable polyharmonic spline radial kernel with polynomial augmentation (PHS+poly) is introduced. It is called the RKP+PHS+poly approximation, and its convergence rate is of order O (h m + 1) , where m is the total degree of polynomials. We apply this method to construct the spaces of trial and test functions in a Galerkin scheme of an extended version of the biological mathematical model in two dimensions describing the interactions between endothelial cells, fibronectin, angiogenic growth factors, and fasentin concentrations. By considering the row-sum method, the eigenvalue stability is also numerically carried out for the discrete equations corresponding to the obtained weak formulation. Accordingly, a semi-implicit form of the backward difference method of order 1 (SBDF1) has been utilized to approximate the weak form in time. We complete our numerical algorithm by solving the obtained full-discretized problem overtime via the biconjugate gradient stabilized (BiCGSTAB) solver with a proper preconditioner. Some simulation results are investigated by estimating the maximum velocity parameter of an enzymatic reaction from the experimental dose–response curve of fasentin to demonstrate the effect of using fasentin drug. [ABSTRACT FROM AUTHOR]

Published
2024
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2. Modeling, simulation and analysis of groundwater flow captured by the horizontal reactive media well using the cell-based smoothed radial point interpolation method.

Author

Li, Wen, Nzeribe, Blossom Nwedo, Liu, G.R., Yao, Guangming, Crimi, Michelle, Rubasinghe, Kalani, Divine, Craig, Mcdonough, Jeff, and Wang, Jack

Subjects
*GROUNDWATER flow, *GROUNDWATER analysis, *ADVECTION, *HORIZONTAL wells, *INTERPOLATION, *HYDRAULIC conductivity, *FINITE element method
Abstract

The Horizontal Reactive Media Treatment (HRX) well is a novel technology for in situ treatment of contaminated groundwater. The most significant technical performance risk associated with field-scale implementation of the HRX well is the potential for water to bypass the well untreated. Therefore, the groundwater capture simulation plays a very important role in the design of the HRX well. We build a model based on a cell-based smoothed radial point interpolation method (CS-RPIM) for simulating groundwater flow captured by the HRX well in both 3D test pit pilot scale and field scale. This method is compared with the finite element method and measured values. Capture width and groundwater velocity obtained by CS-RPIM are consistent with the measured values. We further develop MATLAB software modules to analyze the effects of the hydraulic conductivities, dimension of well and other parameters on the groundwater capture zone, velocity and residence time in the reactive media. The results show that increase of well diameter has a significant effect on enlargement of the capture zone and the extension of media treatment time. When well diameter increases by 100%, horizontal and vertical capture width increase by 57% and 50% respectively, and media treatment time can be extended by 68%. • A realistic 3D model was built for simulating groundwater captured by the HRX well. • The simulation results outperform FEM or the average capture width formula results. • MATLAB software modules are developed for hydraulic capture zone simulation. • Impact of various factors on the capture zone, groundwater flow velocity and treatment time are analyzed. [ABSTRACT FROM AUTHOR]

Published
2022
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