This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

In this paper we have investigated via experimental and simulations techniques the transport properties, in terms of total ionic conductivity and ion diffusion coefficients, of ionic liquids and lithium salt mixtures composed of two anions, bis(fluorosulfonyl)imide (FSI) and bis(trifluoromethanesulfonyl)imide (TFSI), and two cations, N-ethyl-N-methylimidazolium (emim) and lithium. The comparison of the experimental results with the simulations shows an exceptional agreement over a wide temperature range. Of particular interest is the high agreement achieved at lower temperature, which is a result of the extended simulation length of, at least, a factor of 5 compared with previous work. The results show as the addition of TFSI favor the formation of lithium dimers (Li+ - TFSI- - Li+). A closer analysis of such dimers shows that involved lithium ions move nearly as fast as single lithium ions although they have a different coordination and much slower TFSI exchange rates.

A combined theoretical and experimental study of the influence of different anion ratios on lithium ion dynamics in ionic liquids

This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. This method combines the Zain Ul Abadin Zafar-transform (ZZ-T) and the homotopy perturbation technique (HPT) to show the validation and efficiency of this technique to investigate three examples. It is also shown that the fractional and integer-order solutions have closed contact with the exact result. The suggested technique is found to be reliable, efficient, and straightforward to use for many related models of engineering and several branches of science, such as modeling nonlinear waves in different plasma models.

/pdf/analytical-investigation-of-fractional-order-korteweg-de-vg44lyx0.pdf

Analytical Investigation of Fractional-Order Korteweg-De-Vries-Type Equations under Atangana-Baleanu-Caputo Operator: Modeling Nonlinear Waves in a Plasma and Fluid

Stress analysis in functionally graded rotating disks with non-uniform thickness and variable angular velocity

In this work, the novel iterative transformation technique and homotopy perturbation transformation technique are used to calculate the fractional-order gas dynamics equation. In this technique, the novel iteration method and homotopy perturbation method are combined with the Elzaki transformation. The current methods are implemented with four examples to show the efficacy and validation of the techniques. The approximate solutions obtained by the given techniques show that the methods are accurate and easy to apply to other linear and nonlinear problems.

https://downloads.hindawi.com/journals/jfs/2022/3341754.pdf

On Solutions of Fractional-Order Gas Dynamics Equation by Effective Techniques

Solvation behavior of glycine and diglycine in aqueous 1-butyl-3-methylimidazolium chloride ionic liquid solutions at different temperatures

Solvation behavior of glycine and glycyl dipeptide in aqueous 1-butyl-3-methylimidazolium bromide ionic liquid solutions at different temperatures

The two point boundary value problems with Neumann and mixed Robbin's boundary conditions have great importance in chemical engineering, deflection of beams etc. It is not easy task to solve numer- ically such type of problems. In this paper, Galerkin-finite element method is proposed for the numerical solution of the boundary value problem having mixed Robbin's and Dirichlet's conditions. Two test prob- lems are taken to show the accuracy of the result. The numerical solutions are compared with the analytic solution available in the literature and found very similar to the analytic solution.

Numerical Solution of Two Point Boundary Value Problems Using Galerkin-Finite Element Method

This paper concentrates on the finite element analysis of thermoe- lastic stresses, displacements and strains in a thin circular functionally graded material (FGM) disk subjected to thermal loads. Further the temperature pro- files have been modeled with the help of heat conduction equation. The model has been solved numerically for an Al2O3/Al FGM disk. The numerical re- sults reveal that these quantities are significantly influenced by temperature

/pdf/stress-and-strain-analysis-of-rotating-fgm-thermoelastic-2nickoam8e.pdf

Stress and strain analysis of rotating fgm thermoelastic circular disk by using fem

Abstract We apply homotopy perturbation transformation method (combination of homotopy perturbation method and Laplace transformation) and homotopy perturbation Elzaki transformation method on nonlinear fractional partial differential equation (fpde) to obtain a series solution of the equation. In this case, the fractional derivative is described in Caputo sense. To avow the adequacy and authenticity of the technique, we have applied both the techniques to Fractional Fisher’s equation, time-fractional Fornberg-Whitham equation and time fractional Inviscid Burgers’ equation. Finally, we compare the results obtained from homotopy perturbation transformation technique with homotopy perturbation Elzaki transformation.

/pdf/comparative-study-of-homotopy-perturbation-transformation-1us5no41vf.pdf

Dinkar Sharma

Papers

Solvation behavior of glycine and diglycine in aqueous 1-butyl-3-methylimidazolium chloride ionic liquid solutions at different temperatures

Solvation behavior of glycine and glycyl dipeptide in aqueous 1-butyl-3-methylimidazolium bromide ionic liquid solutions at different temperatures

Numerical Solution of Two Point Boundary Value Problems Using Galerkin-Finite Element Method

Stress and strain analysis of rotating fgm thermoelastic circular disk by using fem

Comparative study of homotopy perturbation transformation with homotopy perturbation Elzaki transform method for solving nonlinear fractional PDE