A polynomial approach to determine the time-dependent electric and magnetic fields in anisotropic materials by symbolic computations

Yakhno, V. G.; Altunkaynak, Meltem

doi:10.1108/compel-07-2015-0245

Cited by 3 publications

(7 citation statements)

References 28 publications

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“…This type of solution is called a PS. Substituting (21) into (8) and (9) and using (19), (20) we get…”

Section: The Computation Of An Explicit Formula For a Solution When Dmentioning

confidence: 99%

“…Moreover, a new procedure of the recovering all unknown coefficients of PSs of this symmetric hyperbolic system has been developed in the present paper. We note that this procedure is different from the procedure of finding E k , m , n ( t ) in Yakhno and Altunkaynak because the first one is related with the solution of the symmetric hyperbolic system of the first order and the second one is solving the second‐order hyperbolic equations.…”

Section: Introductionmentioning

confidence: 99%

“…These equations are solved independently. For these equations the procedure of recovering all unknown coefficients E k , m , n ( t ) of PSs has been developed in Section 3 of the work . Unfortunately, the Maxwell's equations in bi‐anisotropic materials cannot be decomposed to the partial differential equations of the second (or higher) order for the electric and, separately, to magnetic fields.…”

Section: Introductionmentioning

confidence: 99%

“…17,18 Further, this technique has been applied for solving the initial value problem (IVP) of the Maxwell's equations in general electrically and magnetically anisotropoic media. 19 We note that in the work 19 Maxwell's equations in isotropic and anisotropic materials have been reduced to the hyperbolic partial differential equations of the second order for electric and magnetic fields. Moreover, equations for electric fields are disconnected from equations for magnetic fields.…”

mentioning

confidence: 99%

“…For these equations the procedure of recovering all unknown coefficients E k,m,n (t) of PSs has been developed in Section 3 of the work. 19 Unfortunately, the Maxwell's equations in bi-anisotropic materials cannot be decomposed to the partial differential equations of the second (or higher) order for the electric and, separately, to magnetic fields. For this reason, we suggest a different method for computation of the time-dependent electric and magnetic fields in bi-anisotropic materials with polynomial inputs, which is based on the reduction of Maxwell's equations to a symmetric hyperbolic system of the first order.…”

mentioning

confidence: 99%

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Symbolic computation of the time‐dependent electric and magnetic fields in bi‐anisotropic media with polynomial inputs

Yakhno

Altunkaynak

2018

Int J Numerical Modelling

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A new method for the computation of a solution of the Maxwell's equations in bi‐anisotropic media with polynomial input is suggested. This method consists of the reduction of Maxwell's equations to a symmetric hyperbolic system of the first‐order partial differential equations. The solutions of the obtained system are constructed by symbolic computation in Maple for the given polynomial data in an explicit form. For the case when input data are given as smooth functions, an interpolation of the data has been made by polynomials and then an approximate solution has been computed by our method. The robustness of the method is confirmed by computational experiments. The comparison of the suggested method with finite difference time domain method has been done.

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“…This type of solution is called a PS. Substituting (21) into (8) and (9) and using (19), (20) we get…”

Section: The Computation Of An Explicit Formula For a Solution When Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Symbolic computation of the time‐dependent electric and magnetic fields in bi‐anisotropic media with polynomial inputs

Yakhno

Altunkaynak

2018

Int J Numerical Modelling

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From Iterative Balance Models to Directly Calculating Explicit Models for Real-time Process Optimization and Scheduling

Björkqvist

Suominen

Vilkko

et al. 2018

Linköping Electronic Conference Proceedings

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Optimal utilization of complex processes involves realtime operational optimization and scheduling, especially in cases where the production line consists of both continuous and batch operated unit processes. This kind of real-time optimization requires process models which can be computed significantly faster than realtime. Iterative balance calculation is typically far too slow for these cases. This paper presents a method for converting an iterative balance model to a directly calculating model suitable for on-line process optimization. The approach is demonstrated with the first unit process in the copper smelting line, the flash smelting furnace (FSF). The method consisted of formulating an equation group based on the constrained FSF HSC-Sim model and solving the unknown parameters and static states with use of a symbolic calculation software. The solution was implemented as a function whose calculation time fulfilled the requirements for scheduling use.

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Polynomial Solutions of Electric Field Equations in Anisotropic Media

Altunkaynak

2024

MANAS Journal of Engineering

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The time-dependent system of partial differential equations of the second order describing the electric wave propagation in electrically and magnetically anisotropic homogeneous media is considered in the paper. A method for the computation of the polynomial solutions of the initial value problem for the considered system is proposed. Symbolic computations are used and these symbolic computations are implemented in Maple. It is proved also that these polynomial solutions are approximate solutions of the considered initial value problem with smooth initial data and the inhomogeneous term. The computational experiments confirm the robustness of the suggested method for the computation of electric fields in general electrically and magnetically anisotropic media.

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A polynomial approach to determine the time-dependent electric and magnetic fields in anisotropic materials by symbolic computations

Cited by 3 publications

References 28 publications

Symbolic computation of the time‐dependent electric and magnetic fields in bi‐anisotropic media with polynomial inputs

Symbolic computation of the time‐dependent electric and magnetic fields in bi‐anisotropic media with polynomial inputs

From Iterative Balance Models to Directly Calculating Explicit Models for Real-time Process Optimization and Scheduling

Polynomial Solutions of Electric Field Equations in Anisotropic Media

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