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    Convergence analysis of yee-fdtd schemes for 3d maxwell’s equations in linear dispersive media
    (2021-01-01) ;
    Bokil, Vrushali A.
    In this paper, we develop and analyze finite difference methods for the 3D Maxwell’s equations in the time domain in three different types of linear dispersive media described as Debye, Lorentz and cold plasma. These methods are constructed by extending the Yee-Finite Difference Time Domain (FDTD) method to linear dispersive materials. We analyze the stability criterion for the FDTD schemes by using the energy method. Based on energy identities for the continuous models, we derive discrete energy estimates for the FDTD schemes for the three dispersive models. We also prove the convergence of the FDTD schemes with perfect electric conducting boundary conditions, which describes the second order accuracy of the methods in both time and space. The discrete divergence-free conditions of the FDTD schemes are studied. Lastly, numerical examples are given to demonstrate and confirm our results.
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    The Adaptive Reducing Methods of Calculating Determinant
    This paper introduces a method for determinant computation in square matrices. Our approach utilized recursion and the Schur formula to partition the matrix into submatrices. Determinant calculations were performed using the condensation method. To evaluate its computational efficiency, we conducted a floating-point operation per second (FLOPS) analysis, using FLOPS to compare the efficiency of all reduction methods. Pseudocode was provided to demonstrate the computational efficiency of our method in terms of flops and execution time for square matrix determinant calculations.
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    Hydrolytic degradation of poly(lactic acid): Population balance modelling for simulating molecular weight distribution
    (2025-04-01)
    Limsukon, Wanwarang
    ;
    Rubino, Maria
    ;
    Rabnawaz, Muhammad
    ;
    Lim, Loong Tak
    ;
    Poly (lactic acid) (PLA) is one of the most promising biobased and biodegradable polymers able to replace several fossil-based plastics for packaging and other applications. However, PLA is susceptible to hydrolytic degradation, impacting its overall service performance and end-of-life. The molecular weight distribution (MWD) is a critical parameter that provides insights during hydrolytic degradation. In this study, we introduced a population balance model, utilizing the high-order moment-conserving method of classes, to describe the MWD during the hydrolytic degradation of amorphous PLA film at 45 °C and 65 °C and expanded to 85 °C. The phenomenological model provided hydrolysis constants that clarified noncatalytic and autocatalytic reaction mechanisms and information on specific chain scission of a particular length. Our predictions demonstrate a promising alignment in weight location and distribution shape with the experimental MWDs observed throughout the hydrolytic process of PLA. One notable advantage is the MWD simulation, conducted over an extended time frame. Furthermore, this predictive capability extends to forecasting the lifetime of PLA films at various temperatures within the tested range, thereby fostering insights into PLA hydrolysis applicable to real-life scenarios and supporting environmentally conscious degradation practices.
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    Item type:Publication,
    Convergence analysis of operator splitting methods for Maxwell’s equations in dispersive media of Debye type
    (2023-12-01)
    In this paper, two new effective operator splitting methods (SS-MD and SM-MD) for the Maxwell’s equations for dispersive media in two dimensions transverse electric polarization (the 2D Maxwell–Debye TE model) are presented and analyzed. The splitting schemes consist of two sub-stages in each time step, each of which requires solving a number of 1D discrete sub-problems. The Crank–Nicolson approach is used to solve each sub-problem’s time discretization. Both splitting methods satisfy the energy decay and are unconditionally stable. The convergence result of the SS-MD scheme is shown to be of first order in time and of second order in space based on the energy technique, whereas the SM-MD scheme is of second order in both time and space. We also analyze numerical dispersion analysis to obtain two identities of the discrete numerical dispersion relations of both splitting schemes. Examples and numerical experiments are provided to demonstrate and support our theoretical results.