Sakkaplangkul, Puttha

Preferred name

Main Affiliation

School of Science

puttha.sa@kmitl.ac.th

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Dispersion analysis of finite difference and discontinuous Galerkin schemes for Maxwell's equations in linear Lorentz media
(2019-10-01)
Jiang, Yan
;
Sakkaplangkul, Puttha
;
Bokil, Vrushali A.
;
Cheng, Yingda
;
Li, Fengyan
In this paper, we consider Maxwell's equations in linear dispersive media described by a single-pole Lorentz model for electronic polarization. We study two classes of commonly used spatial discretizations: finite difference methods (FD) with arbitrary even order accuracy in space and high spatial order discontinuous Galerkin (DG) finite element methods. Both types of spatial discretizations are coupled with second order semi-implicit leap-frog and implicit trapezoidal temporal schemes. By performing detailed dispersion analysis for the semi-discrete and fully discrete schemes, we obtain rigorous quantification of the dispersion error for Lorentz dispersive dielectrics. In particular, comparisons of dispersion error can be made taking into account the model parameters, and mesh sizes in the design of the two types of schemes. This work is a continuation of our previous research on energy-stable numerical schemes for nonlinear dispersive optical media [6,7]. The results for the numerical dispersion analysis of the reduced linear model, considered in the present paper, can guide us in the optimal choice of discretization parameters for the more complicated and nonlinear models. The numerical dispersion analysis of the fully discrete FD and DG schemes, for the dispersive Maxwell model considered in this paper, clearly indicate the dependence of the numerical dispersion errors on spatial and temporal discretizations, their order of accuracy, mesh discretization parameters and model parameters. The results obtained here cannot be arrived at by considering discretizations of Maxwell's equations in free space. In particular, our results contrast the advantages and disadvantages of using high order FD or DG schemes and leap-frog or trapezoidal time integrators over different frequency ranges using a variety of measures of numerical dispersion errors. Finally, we highlight the limitations of the second order accurate temporal discretizations considered.
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Convergence analysis of yee-fdtd schemes for 3d maxwell’s equations in linear dispersive media
(2021-01-01)
Sakkaplangkul, Puttha
;
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
(2024-01-01)
Sakkaplangkul, Puttha
;
Chuenjarern, Nattaporn
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
;
Sakkaplangkul, Puttha
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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A Fully Fourth Order Accurate Energy Stable Finite Difference Method for Maxwell's Equations in Metamaterials
(2019-01-01)
Sakkaplangkul, Puttha
;
Bokil, Vrushali A.
;
Carvalho, Camille
We present a novel fully fourth order in time and space finite difference method (FDM) for the time domain Maxwell's equations in metamaterials. We consider a Drude metamaterial model for the material response to incident electromagnetic fields. We consider the second-order formulation of the system of partial differential equations that govern the evolution in time of electric and magnetic fields along with the evolution of the polarization and magnetization current densities. Our discretization employs fourth-order staggering in space of different field components and the modified equation approach to obtain fourth-order accuracy in time. Using the energy method, we derive energy relations for the continuous models and design numerical schemes that preserve a discrete analogue of the energy relation. Numerical simulations are provided in one- and two-dimensional settings to illustrate fourth-order convergence as well as to compare with second-order schemes.
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Convergence analysis of operator splitting methods for Maxwell’s equations in dispersive media of Debye type
(2023-12-01)
Sakkaplangkul, Puttha
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.

Sakkaplangkul, Puttha

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