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Article
Publication date: 1 June 2000

A. Savini

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community…

1146

Abstract

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 15 May 2009

Evgeny Shavelzon and Dan Givoli

The interaction of a global model (GM) and a local (regional) model (LM) of heat flow is considered under the framework of so‐called “one‐way nesting”. In this framework, the GM…

Abstract

Purpose

The interaction of a global model (GM) and a local (regional) model (LM) of heat flow is considered under the framework of so‐called “one‐way nesting”. In this framework, the GM is constructed in a large domain with coarse discretization in space and time, while the LM is set in a small subdomain with fine discretization.

Design/methodology/approach

The GM is solved first, and its results are then used via some boundary transfer operator (BTO) on the GM–LM interface in order to solve the LM. Past experience in various fields of application has shown that one has to be careful in the choice of BTO to be used on the GM–LM interface, since this choice affects both the stability and accuracy of the computational scheme. Here the problem is first theoretically analyzed for the linear heat equation, and stable BTOs are identified. Then numerical experiments are performed with one‐way nesting in a two‐dimensional channel for heat flow with and without radiation emission and linear reaction, using four different BTOs.

Findings

Among other conclusions, it is shown that the “negative Robin” BTO is unstable, whereas the Dirichlet, Neumann and “positive Robin” BTO are all stable. It is also shown that in terms of accuracy, the Neumann and “positive Robin” BTOs should be preferred over the Dirichlet BTO.

Originality/value

This study may be the first step in analyzing BTO accuracy and stability for more general atmospheric systems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 10 April 2009

C.C. Tsai

The purpose of this paper is to develop a meshless numerical method for three‐dimensional isotropic thermoelastic problems with arbitrary body forces.

Abstract

Purpose

The purpose of this paper is to develop a meshless numerical method for three‐dimensional isotropic thermoelastic problems with arbitrary body forces.

Design/methodology/approach

This paper combines the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method (MFS‐DRM) to solve three‐dimensional isotropic thermoelastic problems with arbitrary body forces. In the DRM, the arbitrarily distributed temperature and body force are approximated by polyharmonic splines with augmented polynomial basis, whose particular solutions and the corresponding tractions are reviewed and given explicitly. The MFS is then applied to solve the complementary solution. Numerical experiments of Dirchlet, Robin, and peanut‐shaped‐domain problems are carried out to validate the method.

Findings

In literature, it is commented that the Gaussian elimination can be used reliably to solve the MFS equations for non‐noisy boundary conditions. For noisy boundary conditions, the truncated singular value decomposition (TSVD) is more accurate than the Gaussian elimination. In this paper, it was found that the particular solutions obtained by the DRM act like noises and the use of TSVD improves the accuracy.

Originality/value

It is the first time that the MFS‐DRM is derived to solve three‐dimensional isotropic thermoelastic problems with arbitrary body forces.

Details

Engineering Computations, vol. 26 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 July 2006

Daniel Ioan, Gabriela Ciuprina and Marius Radulescu

The paper has the purpose of proposing a new open boundary condition to be used in conjunction with the finite integration technique (FIT) for the modelling of passive on‐chip…

Abstract

Purpose

The paper has the purpose of proposing a new open boundary condition to be used in conjunction with the finite integration technique (FIT) for the modelling of passive on‐chip components.

Design/methodology/approach

This boundary condition is ensured by using a virtual layer that surrounds the computational domain.

Findings

The paper proves which are the optimal material properties of the equivalent layer of open boundary.

Practical implications

When modelling passive on‐chip components with FIT, the method proposed is more efficient than the strategic dual image technique.

Originality/value

The paper shows the advantage of this approach – that the analysis algorithm remains unchanged, while saving the field‐circuit compatibility properties, such as current conservation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 5 May 2015

Martin Joseph Guillot and Steve C McCool

The purpose of this paper is to investigate the effect of numerical boundary condition implementation on local error and convergence in L2-norm of a finite volume discretization…

Abstract

Purpose

The purpose of this paper is to investigate the effect of numerical boundary condition implementation on local error and convergence in L2-norm of a finite volume discretization of the transient heat conduction equation subject to several boundary conditions, and for cases with volumetric heat generation, using both fully implicit and Crank-Nicolson time discretizations. The goal is to determine which combination of numerical boundary condition implementation and time discretization produces the most accurate solutions with the least computational effort.

Design/methodology/approach

The paper studies several benchmark cases including constant temperature, convective heating, constant heat flux, time-varying heat flux, and volumetric heating, and compares the convergence rates and local to analytical or semi-analytical solutions.

Findings

The Crank-Nicolson method coupled with second-order expression for the boundary derivatives produces the most accurate solutions on the coarsest meshes with the least computation times. The Crank-Nicolson method allows up to 16X larger time step for similar accuracy, with nearly negligible additional computational effort compared with the implicit method.

Practical implications

The findings can be used by researchers writing similar codes for quantitative guidance concerning the effect of various numerical boundary condition approximations for a large class of boundary condition types for two common time discretization methods.

Originality/value

The paper provides a comprehensive study of accuracy and convergence of the finite volume discretization for a wide range of benchmark cases and common time discretization methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 April 2018

Omar Abu Arqub

The purpose of this study is to introduce the reproducing kernel algorithm for treating classes of time-fractional partial differential equations subject to Robin boundary

442

Abstract

Purpose

The purpose of this study is to introduce the reproducing kernel algorithm for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of energy, heat conduction and electric circuit.

Design/methodology/approach

The method provides appropriate representation of the solutions in convergent series formula with accurately computable components. This representation is given in the W(Ω) and H(Ω) inner product spaces, while the computation of the required grid points relies on the R(y,s) (x, t) and r(y,s) (x, t) reproducing kernel functions.

Findings

Numerical simulation with different order derivatives degree is done including linear and nonlinear terms that are acquired by interrupting the n-term of the exact solutions. Computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found and is very valid for solving such time-fractional models.

Research limitations/implications

Future work includes the application of the reproducing kernel algorithm to highly nonlinear time-fractional partial differential equations such as those arising in single and multiphase flows. The results will be published in forthcoming papers.

Practical implications

The study included a description of fundamental reproducing kernel algorithm and the concepts of convergence, and error behavior for the reproducing kernel algorithm solvers. Results obtained by the proposed algorithm are found to outperform in terms of accuracy, generality and applicability.

Social implications

Developing analytical and numerical methods for the solutions of time-fractional partial differential equations is a very important task owing to their practical interest.

Originality/value

This study, for the first time, presents reproducing kernel algorithm for obtaining the numerical solutions of some certain classes of Robin time-fractional partial differential equations. An efficient construction is provided to obtain the numerical solutions for the equations, along with an existence proof of the exact solutions based upon the reproducing kernel theory.

Article
Publication date: 12 August 2020

Manki Cho

This paper aims to present a meshless technique to find the Green’s functions for solutions of Laplacian boundary value problems on rectangular domains. This paper also…

Abstract

Purpose

This paper aims to present a meshless technique to find the Green’s functions for solutions of Laplacian boundary value problems on rectangular domains. This paper also investigates a theoretical basis for the Steklov series expansion methods to reduce and estimate the error of numerical approaches for the boundary correction kernel of the Laplace operator.

Design/methodology/approach

The main interest is how the Green's functions differ from the fundamental solution of the Laplace operator. Steklov expansion methods for finding the correction term are supported by the analysis that bases of the class of all finite harmonic functions can be formed using harmonic Steklov eigenfunctions. These functions construct a basis of the space of solutions of harmonic boundary value problems and their boundary traces generate an orthogonal basis of the trace space of solutions on the boundary.

Findings

The main conclusion is that the boundary correction term for the Green's functions is well-approximated by Steklov expansions with a few Steklov eigenfunctions. The error estimates for the Steklov approximations of the boundary correction term involved in Dirichlet or Robin boundary value problems are found. They appear to provide very good approximations in the interior of the region and become quite oscillatory close to the boundary.

Originality/value

This paper concentrates to document the first attempt to find the Green's function for various harmonic boundary value problems with the explicit Steklov eigenfunctions without concerns regarding discretizations when the region is a rectangle.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 9 September 2013

Istvan Bardi, Kezhong Zhao, Rickard Petersson, John Silvestro and Nancy Lambert

– This paper aims to present a domain decomposition method to overcome the challenges posed by multi-domain, multi-scale high frequency problems.

Abstract

Purpose

This paper aims to present a domain decomposition method to overcome the challenges posed by multi-domain, multi-scale high frequency problems.

Design/methodology/approach

A hybrid finite element and boundary integral procedure is also presented that allows for domains to employ different solution methods in different subdomains.

Findings

By decomposing large electromagnetic regions into smaller domains, the finite element method can cope with the simulation of electrically large problems.

Practical implications

Real life examples demonstrate the accuracy and efficiency of the new method.

Originality/value

The Robin transmission condition (RTC) is applied to link the domains and preserve field continuity on interfaces.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 32 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 20 August 2021

Salam Adel Al-Bayati and Luiz C. Wrobel

The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one…

Abstract

Purpose

The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction.

Design/methodology/approach

The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence.

Findings

The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency.

Originality/value

Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 21 April 2020

Sebastian Böhmelt, Nils Kielian, Michael Hagel, Marcus Stiemer, Marvin-Lucas Henkel and Markus Clemens

The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS) systems in…

Abstract

Purpose

The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS) systems in biology. The numerical scheme is analyzed and first applications are discussed.

Design/methodology/approach

The scheme is based on a finite element discretization of the individual domains obtained by decomposition and a physically consistent inter-domain coupling realized via Robin boundary conditions. The proposed algorithms can efficiently be implemented on a highly parallelized computing grid.

Findings

The feasibility and applicability of the method is proven. Further, a couple of technical details are found that increase the efficiency of the method.

Originality/value

The presented method offers an enhanced geometrical flexibility and extensibility to simulate larger cell systems with higher model resolution compared to other methods presented in the literature. The presented analysis provides an understanding of the balanced coupling scheme for large EQS systems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

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