International Journal of Mathematical Modelling and Numerical Optimisation
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International Journal of Mathematical Modelling and Numerical Optimisation (5 papers in press)
Finite Element Tearing and Interconnecting-1 method for the solution of the topology optimization problem by Ouafaa Raibi, Abdelilah Makrizi Abstract: The algebraic system derived from the descritization of problems arising in physical field and engineering science appears to be challenging to solve due to the strong nonlinearity and the large size of such problems. Parallel processing is shown to be an efficient technique to handle the computational complexity associated with solving large linear systems and this is readily obtained by using one of the most popular methods which is known to be suitable for parallelization, namely, domain decomposition methods. In this work we apply Finite Element Tearing and Interconnecting method within the framework of topology optimization, we describe a methodology that brings together existing fast algorithms for topology optimization and FETI for solving the resulting large-scale linear systems. Keywords: Domain decomposition; FETI-1 method; minimum compliance; Topology optimization.
A virtual class of nonconforming finite elements and its applications to Poisson\'s equation by Hammou El-Otmany Abstract: In this paper, we develop and analyze the virtual class of nonconforming Finite Element inspired from the classical Crouzeix-Raviart element in two and three-dimensions. We focus on Poisson\'s equation for theoretical and numerical results. We show that the discrete problem is stable and the a priori error estimates are optimal. Two numerical tests are presented to demonstrate the theoretical results. Keywords: Nonconforming finite element; element of Crouzeix-Raviart; interpolation error; consistency error; a priori error estimates.
Haar wavelet collocation method for the investigation of micropolar fluid flow in a porous channel with suction and injection by Harinakshi Karkera, Nagaraj N. Katagi Abstract: In this paper, the problem of micropolar fluid flow in a porous channel is analysed using a novel concept of Haar wavelet-based numerical method. Haar wavelet approach is explored first time for the solution of higher order coupled nonlinear boundary value problems without employing linearisation technique. The objective is to demonstrate the simplicity and efficiency of the proposed numerical scheme to find the approximate solution for governing problem. Using suitable similarity transformations, the resulting nonlinear coupled differential equations of fourth order are solved to acquire a complete description of the micropolar fluid flow in a porous channel. Error analysis is performed to authenticate the accuracy of the results obtained. The behaviour of velocity and microrotation profiles in the flow channel driven by the influence of wall porosity are explained in detail through graphs and tables for pertinent parameters like Reynolds number Re and microrotation boundary parameter s ? [0, 1/2]. The new method presented in this study found to be powerful and promising to obtain solutions of different nonlinear boundary value problems. Keywords: mass transfer; micropolar flow; nonlinear coupled differential equations; Haar wavelets. DOI: 10.1504/IJMMNO.2022.10042869
Optimum Economic Ordering and Preservation Technology Expenditure Strategy facing Non-instantaneous degrading Inventory as a consequence of composite impact of Advertisement, Trade-credit besides Inflation by Chanda Nautiyal Abstract: The Present paper accommodates an Inventory model for advertisement as well as price sensitive demand. The paper deals with the Non-instantaneous degrading products as a composite impact appertaining to trade-credit besides Inflation. Also preservation Technology is infused to mitigate the rate of deterioration. The paper rules out the prevailing supposition of zero reaching inventory. Hence shortages are permitted and backlogged partly. The model's principal motive is to determine the optimal plan of ordering which dwindles the sum of expenditure of retailer per unit time. The solution procedure includes derivation of lemmas and theorems to achieve optimal policy. Four numerical examples and a sensitivity analysis are administered to elucidate the conclusions of the inventory models and managerial perspectives have also been addressed. Keywords: Inflation; trade credit; preservation technology; advertisement; non-instantaneous deterioration ; partial backlogging; price dependent demand. DOI: 10.1504/IJMMNO.2022.10043097
Modelling the potential role of super spreaders on COVID-19 transmission dynamics by Josiah Mushanyu, Williams Chukwu, Farai Nyabadza, Gift Muchatibaya Abstract: Superspreading phenomenon has been observed in many infectious diseases and contributes significantly to public health burden in many countries. Superspreading events have recently been reported in the transmission of the COVID-19 pandemic. The present study uses a set of nine ordinary differential equations to investigate the impact of superspreading on COVID-19 dynamics. The model developed in this study addresses the heterogeineity in infectiousness by taking into account two forms of transmission rate functions for superspreaders based on clinical (infectivity level) and social or environmental (contact level). The basic reproduction number has been derived and the contribution of each infectious compartment towards the generation of new COVID-19 cases is ascertained. Data fitting was performed and parameter values were estimated within plausible ranges. Numerical simulations performed suggest that control measures that decrease the effective contact radius and increase the transmission rate exponent will be greatly beneficial in the control of COVID-19 in the presence of superspreading phenomena. Keywords: COVID-19; superspreaders; model analysis; numerical simulations. DOI: 10.1504/IJMMNO.2022.10043816