15 results
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2. New approach for imposing the nonlinear floating potential boundary condition in the Poisson-continuity coupled system
- Author
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Cheng, Qiwen, Zou, Jun, Li, Benliang, and Lu, Jun
- Published
- 2023
- Full Text
- View/download PDF
3. A note on variation iteration method with an application on Lane–Emden equations
- Author
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Verma, Amit K., Kumar, Narendra, Singh, Mandeep, and Agarwal, Ravi P.
- Published
- 2021
- Full Text
- View/download PDF
4. Analytical model of a T-core coil above a multi-layer conductor with hidden hole using the TREE method for nondestructive evaluation
- Author
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Zhang, Siquan
- Published
- 2021
- Full Text
- View/download PDF
5. An efficient finite element computation using subparametric transformation up to cubic-order for curved triangular elements.
- Author
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Sasikala, J., Shylaja, G., Kesavulu, Naidu V., Venkatesh, B., and Mallikarjunaiah, S.M.
- Subjects
BOUNDARY value problems ,COLLOCATION methods ,FLOW simulations ,FINITE element method ,BLOOD flow - Abstract
Purpose: A finite element computational methodology on a curved boundary using an efficient subparametric point transformation is presented. The proposed collocation method uses one-side curved and two-side straight triangular elements to derive exact subparametric shape functions. Design/methodology/approach: Our proposed method builds upon the domain discretization into linear, quadratic and cubic-order elements using subparametric spaces and such a discretization greatly reduces the computational complexity. A unique subparametric transformation for each triangle is derived from the unique parabolic arcs via a one-of-a-kind relationship between the nodal points. Findings: The novel transformation derived in this paper is shown to increase the accuracy of the finite element approximation of the boundary value problem (BVP). Our overall strategy is shown to perform well for the BVP considered in this work. The accuracy of the finite element approximate solution increases with higher-order parabolic arcs. Originality/value: The proposed collocation method uses one-side curved and two-side straight triangular elements to derive exact subparametric shape functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
6. A FEM in frequency domain for a transient electric field in non-sinusoidal steady state under the non-sinusoidal periodic voltage.
- Author
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Wen, Teng, Wei, Xiaoyun, Li, Xuebao, Cao, Boyuan, and Zhao, Zhibin
- Subjects
ELECTRIC transients ,ELECTRIC fields ,INSULATED gate bipolar transistors ,BOUNDARY value problems ,FINITE element method ,STEADY state conduction ,TRANSISTORS - Abstract
Purpose: This paper aims to focus on the finite element method in the frequency domain (FD-FEM) for the transient electric field in the non-sinusoidal steady state under the non-sinusoidal periodic voltage excitation. Design/methodology/approach: Firstly, the boundary value problem of the transient electric field in the frequency domain is described, and the finite element equation of the FD-FEM is derived by Galerkin's method. Secondly, the constrained electric field equation on the boundary in the frequency domain (FD-CEFEB) is also derived, which can solve the electric field intensity on the boundary and the dielectric interface with high accuracy. Thirdly, the calculation procedures of the FD-FEM with FD-CEFEB are introduced in detail. Finally, a numerical example of the press-packed insulated gate bipolar transistor under the working condition of the repetitive turn-on and turn-off is given. Findings: The FD-CEFEB improves numerical accuracy of electric field intensity on the boundary and interfacial charge density, which can be achieved by modifying the existing FD-FEMs' code in appropriate steps. Moreover, the proposed FD-FEM and the FD-CEFEB will only increase calculation costs by a little compared with the traditional FD-FEMs. Originality/value: The FD-CEFEB can directly solve the electric field intensity on the boundary and the dielectric interface with high accuracy. This paper provides a new FD-FEM for the transient electric field in the non-sinusoidal steady state with high accuracy, which is suitable for combined insulation structure with a long time constant. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
7. Three-dimensional data-driven magnetostatic field computation using real-world measurement data.
- Author
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Galetzka, Armin, Loukrezis, Dimitrios, and De Gersem, Herbert
- Subjects
MAGNETIC fields ,MAXWELL equations ,MISSING data (Statistics) ,LAGRANGE problem ,BOUNDARY value problems ,LAGRANGE multiplier - Abstract
Purpose: The purpose of this paper is to present the applicability of data-driven solvers to computationally demanding three-dimensional problems and their practical usability when using real-world measurement data. Design/methodology/approach: Instead of using a hard-coded phenomenological material model within the solver, the data-driven computing approach reformulates the boundary value problem such that the field solution is directly computed on raw measurement data. The data-driven formulation results in a double minimization problem based on Lagrange multipliers, where the sought solution must conform to Maxwell's equations while at the same time being as close as possible to the available measurement data. The data-driven solver is applied to a three-dimensional model of a direct current electromagnet. Findings: Numerical results for data sets of increasing cardinality verify that the data-driven solver recovers the conventional solution. Additionally, the practical usability of the solver is shown by using real-world measurement data. This work concludes that the data-driven magnetostatic finite element solver is applicable to computationally demanding three-dimensional problems, as well as in cases where a prescribed material model is not available. Originality/value: Although the mathematical derivation of the data-driven problem is well presented in the referenced papers, the application to computationally demanding real-world problems, including real measurement data and its rigorous discussion, is missing. The presented work closes this gap and shows the applicability of data-driven solvers to challenging, real-world test cases. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
8. An extended variational iteration method for fractional BVPs encountered in engineering applications.
- Author
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Khuri, Suheil and Assadi, Reem
- Subjects
BOUNDARY value problems ,INITIAL value problems ,FRACTIONAL differential equations - Abstract
Purpose: The purpose of this paper is to find approximate solutions for a general class of fractional order boundary value problems that arise in engineering applications. Design/methodology/approach: A newly developed semi-analytical scheme will be applied to find approximate solutions for fractional order boundary value problems. The technique is regarded as an extension of the well-established variation iteration method, which was originally proposed for initial value problems, to cover a class of boundary value problems. Findings: It has been demonstrated that the method yields approximations that are extremely accurate and have uniform distributions of error throughout their domain. The numerical examples confirm the method's validity and relatively fast convergence. Originality/value: The generalized variational iteration method that is presented in this study is a novel strategy that can handle fractional boundary value problem more effectively than the classical variational iteration method, which was designed for initial value problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
9. Numerical simulation of Bratu's problem using a new form of the Adomian decomposition technique.
- Author
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Umesh
- Subjects
BOUNDARY value problems ,COMPUTER simulation ,NONLINEAR equations ,DECOMPOSITION method - Abstract
Purpose: This paper aims to discuss a new form of the Adomian decomposition technique for the numerical treatment of Bratu's type one-dimensional boundary value problems (BVPs). Moreover, the author also addresses convergence and error analysis for the completeness of the proposed technique. Design/methodology/approach: First, the author discusses the standard Adomian decomposition method and an algorithm based on Duan's corollary and Rach's rule for the fast calculation of the Adomian polynomials. Then, a new form of the Adomian decomposition technique is present for the numerical simulation of Bratu's BVPs. Findings: The reliability and validity of the proposed technique are examined by calculating the absolute errors of Bratu's problem for some different values of Bratu parameter λ. Numerical simulation demonstrates that the proposed technique yields higher accuracy than the Bessel collocation and other known methods. Originality/value: Unlike the other methods, the proposed technique does not need linearization, discretization or perturbation to handle the non-linear problems. So, the results obtained by the present technique are more physically realistic. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
10. Numerical solution for high-order ordinary differential equations using H-ELM algorithm.
- Author
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Lu, Yanfei, Weng, Futian, and Sun, Hongli
- Subjects
BOUNDARY value problems ,HERMITE polynomials ,LINEAR orderings ,ORDINARY differential equations ,MACHINE learning ,ALGORITHMS ,RANDOM forest algorithms - Abstract
Purpose: This paper aims to introduce a novel algorithm to solve initial/boundary value problems of high-order ordinary differential equations (ODEs) and high-order system of ordinary differential equations (SODEs). Design/methodology/approach: The proposed method is based on Hermite polynomials and extreme learning machine (ELM) algorithm. The Hermite polynomials are chosen as basis function of hidden neurons. The approximate solution and its derivatives are expressed by utilizing Hermite network. The model function is designed to automatically meet the initial or boundary conditions. The network parameters are obtained by solving a system of linear equations using the ELM algorithm. Findings: To demonstrate the effectiveness of the proposed method, a variety of differential equations are selected and their numerical solutions are obtained by utilizing the Hermite extreme learning machine (H-ELM) algorithm. Experiments on the common and random data sets indicate that the H-ELM model achieves much higher accuracy, lower complexity but stronger generalization ability than existed methods. The proposed H-ELM algorithm could be a good tool to solve higher order linear ODEs and higher order linear SODEs. Originality/value: The H-ELM algorithm is developed for solving higher order linear ODEs and higher order linear SODEs; this method has higher numerical accuracy and stronger superiority compared with other existing methods. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
11. Shear and normal stresses of electroosmotic magnetized physiological nanofluid on curved artery with moderate Reynolds number: application on electroshock therapy.
- Author
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Alsemiry, Reima Daher, Abo Elkhair, Rabea E., Alarabi, Taghreed H., Alharbi, Sana Abdulkream, Allogmany, Reem, and Elsaid, Essam M.
- Subjects
ELECTROCONVULSIVE therapy ,NANOFLUIDS ,REYNOLDS number ,SHEARING force ,EQUATIONS of motion ,TURBULENT shear flow ,BOUNDARY value problems ,ZETA potential - Abstract
Purpose: Studying the shear stress and pressure resulting on the walls of blood vessels, especially during high-pressure cases, which may lead to the explosion or rupture of these vessels, can also lead to the death of many patients. Therefore, it was necessary to try to control the shear and normal stresses on these veins through nanoparticles in the presence of some external forces, such as exposure to some electromagnetic shocks, to reduce the risk of high pressure and stress on those blood vessels. This study aims to examines the shear and normal stresses of electroosmotic-magnetized Sutterby Buongiorno's nanofluid in a symmetric peristaltic channel with a moderate Reynolds number and curvature. The production of thermal radiation is also considered. Sutterby nanofluids equations of motion, energy equation, nanoparticles concentration, induced magnetic field and electric potential are calculated without approximation using small and long wavelengths with moderate Reynolds numbers. Design/methodology/approach: The Adomian decomposition method solves the nonlinear partial differential equations with related boundary conditions. Graphs and tables show flow features and biophysical factors like shear and normal stresses. Findings: This study found that when curvature and a moderate Reynolds number are present, the non-Newtonian Sutterby fluid raises shear stress across all domains due to velocity decay, resulting in high shear stress. Additionally, modest mobility increases shear stress across all channel domains. The Sutterby parameter causes fluid motion resistance, which results in low energy generation and a decrease in the temperature distribution. Originality/value: Equations of motion, energy equation, nanoparticle concentration, induced magnetic field and electric potential for Sutterby nano-fluids are obtained without any approximation i.e. the authors take small and long wavelengths and also moderate Reynolds numbers. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
12. A generalized CAS wavelet method for solving ψ-Caputo fractional differential equations.
- Author
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Saeed, Umer
- Subjects
BOUNDARY value problems ,INITIAL value problems ,COSINE function ,NONLINEAR equations ,QUASILINEARIZATION ,FRACTIONAL differential equations - Abstract
Purpose: The purpose of the present work is to introduce a wavelet method for the solution of linear and nonlinear psi-Caputo fractional initial and boundary value problem. Design/methodology/approach: The authors have introduced the new generalized operational matrices for the psi-CAS (Cosine and Sine) wavelets, and these matrices are successfully utilized for the solution of linear and nonlinear psi-Caputo fractional initial and boundary value problem. For the nonlinear problems, the authors merge the present method with the quasilinearization technique. Findings: The authors have drived the orthogonality condition for the psi-CAS wavelets. The authors have derived and constructed the psi-CAS wavelets matrix, psi-CAS wavelets operational matrix of psi-fractional order integral and psi-CAS wavelets operational matrix of psi-fractional order integration for psi-fractional boundary value problem. These matrices are successfully utilized for the solutions of psi-Caputo fractional differential equations. The purpose of these operational matrices is to make the calculations faster. Furthermore, the authors have derived the convergence analysis of the method. The procedure of implementation for the proposed method is also given. For the accuracy and applicability of the method, the authors implemented the method on some linear and nonlinear psi-Caputo fractional initial and boundary value problems and compare the obtained results with exact solutions. Originality/value: Since psi-Caputo fractional differential equation is a new and emerging field, many engineers can utilize the present technique for the numerical simulations of their linear/non-linear psi-Caputo fractional differential models. To the best of the authors' knowledge, the present work has never been introduced and implemented for psi-Caputo fractional differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
13. Unified solution of some problems of rectangular plates with four free edges based on symplectic superposition method.
- Author
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Su, Xin, Bai, Eburilitu, and Hai, Guojun
- Subjects
SEPARATION of variables ,BOUNDARY value problems ,PARTIAL differential equations ,FREE vibration ,ANALYTICAL solutions ,EIGENVECTORS ,HAMILTONIAN systems - Abstract
Purpose: A unified framework for solving the bending, buckling and vibration problems of rectangular thin plates (RTPs) with four free edges (FFFF), including isotropic RTPs, orthotropic rectangular thin plates (ORTPs) and nano-rectangular plates, is established by using the symplectic superposition method (SSM). Design/methodology/approach: The original fourth-order partial differential equation is first rewritten into Hamiltonian system. The class of boundary value problems of the original equation is decomposed into three subproblems, and each subproblem is given the corresponding symplectic eigenvalues and symplectic eigenvectors by using the separation variable method in Hamiltonian system. The symplectic orthogonality and completeness of symplectic eigen-vectors are proved. Then, the symplectic eigenvector expansion method is applied to solve the each subproblem. Then, the symplectic superposition solution of the boundary value problem of the original fourth-order partial differential equation is given through superposing analytical solutions of three foundation plates. Findings: The bending, vibration and buckling problems of the rectangular nano-plate/isotropic rectangular thin plate/orthotropic rectangular thin plate with FFFF can be solved by the unified symplectic superposition solution respectively. Originality/value: The symplectic superposition solution obtained is a reference solution to verify the feasibility of other methods. At the same time, it can be used for parameter analysis to deeply understand the mechanical behavior of related RTPs. The advantages of this method are as follows: (1) It provides a systematic framework for solving the boundary value problem of a class of fourth-order partial differential equations. It is expected to solve more complicated boundary value problems of partial differential equations. (2) SSM uses series expansion of symplectic eigenvectors to accurately describe the solution. Moreover, symplectic eigenvectors are orthogonal and directly reflect the orthogonal relationship of vibration modes. (3) The SSM can be carried to bending, buckling and free vibration problems of the same plate with other boundary conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
14. A numerical algorithm to find optimum parameters of a flexible-link manipulator arm for performing payload launching.
- Author
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Alipour, Khalil and Tarvirdizadeh, Bahram
- Subjects
MANIPULATORS (Machinery) ,BOUNDARY value problems ,NONLINEAR equations ,ALGORITHMS - Abstract
Purpose: The aim of the current study is proposing a novel framework to attain the optimum value of a flexible arm manipulator parameters for payload launching missions. Design/methodology/approach: The proposed scheme is based on optimal control approach and combines direct and indirect search methods while considering the actuator capacity. Findings: Three nonlinear parameter-optimization problems will be solved to illustrate how the proposed algorithm can be exploited. Employing variational based nonlinear optimal control within the suggested framework, the answer of these problems is highly intertwined to the solution of a set of differential equations with split boundary values. To solve the obtained boundary value problem (BVP), the related solver of MATLAB® software, bvp6c, will be employed. The achieved simulation results support the worth of the developed procedure. Originality/value: For the first time, the optimal parameters of a flexible link robot for object launching are found in the current research. In addition, the actuator saturation limits are considered which enhances the applicability of the suggested method in the real world applications. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
15. A wavelet method for solving Caputo–Hadamard fractional differential equation.
- Author
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Saeed, Umer
- Subjects
FRACTIONAL differential equations ,NONLINEAR boundary value problems ,QUASILINEARIZATION ,BOUNDARY value problems ,INITIAL value problems ,HADAMARD matrices ,WAVELET transforms - Abstract
Purpose: The purpose of the present work is to propose a wavelet method for the numerical solutions of Caputo–Hadamard fractional differential equations on any arbitrary interval. Design/methodology/approach: The author has modified the CAS wavelets (mCAS) and utilized it for the solution of Caputo–Hadamard fractional linear/nonlinear initial and boundary value problems. The author has derived and constructed the new operational matrices for the mCAS wavelets. Furthermore, The author has also proposed a method which is the combination of mCAS wavelets and quasilinearization technique for the solution of nonlinear Caputo–Hadamard fractional differential equations. Findings: The author has proved the orthonormality of the mCAS wavelets. The author has constructed the mCAS wavelets matrix, mCAS wavelets operational matrix of Hadamard fractional integration of arbitrary order and mCAS wavelets operational matrix of Hadamard fractional integration for Caputo–Hadamard fractional boundary value problems. These operational matrices are used to make the calculations fast. Furthermore, the author works out on the error analysis for the method. The author presented the procedure of implementation for both Caputo–Hadamard fractional initial and boundary value problems. Numerical simulation is provided to illustrate the reliability and accuracy of the method. Originality/value: Many scientist, physician and engineers can take the benefit of the presented method for the simulation of their linear/nonlinear Caputo–Hadamard fractional differential models. To the best of the author's knowledge, the present work has never been proposed and implemented for linear/nonlinear Caputo–Hadamard fractional differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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