Dual reciprocity boundary element formulation for potential problems with arbitrarily distributed sources

The boundary element method is applied to analyze the three-dimensional diffusion equation for the eddy current problems. The diffusion equation is known as the governing equation of the heat conduction problems. The boundary element method using scalar variables and the time-dependent fundamental solution have been applied to solve these scalar potential problems and similar problems with one component of vector variables. This paper deals with the boundary element method using vector variables for mangetic field analysis. The formulation of this method is based on the vector Green's theorem and the time-dependent fundamental solution. For the analysis of the three-dimensional eddy current distribution, the magnetic vector potential, the current vector potential and the magnetic flux density are used as an unknown vector variable, respectively. The methods for each of the above unknown vector variables are applied to the permeation problem on the magnetic field. It is indicated that our method is available in transient magnetic field analysis. We also point out the necessity of a consistent choice of time step and spatial discretization.

A dual reciprocity boundary element solution method for the free vibration analysis of fluid-coupled Kirchhoff plates

Preface. Solving heat transfer problems by the dual reciprocity BEM. Transient problems using time-dependent fundamental solutions. Solving linear heat conduction problems by the multiple reciprocity method. Solving nonlinear heat transfer problems using the boundary element method. Coupled conduction-convection problems. Solving coupled problems involving conduction, convection and thermal radiation. Advanced thermoelastic analysis. Integral equation analyses of natural convection problems in fluid flow. Improperly posed problems in heat transfer. Acknowledgments. References.

The boundary element method (BEM) can be effectively used to solve mixed boundary value problems, as well as fluid-structure interaction problems. Among the advantages of BEM are the reduction of the problem dimension by one, high accuracy and the efficient treatment of problems with infinite domains. The direct BEM leads to a system of equations with dense and unsymmetric matrices. Thus, coupling with symmetric domain discretization techniques, such as finite element methods, is numerically inefficient. For this reason, alternative approaches are use herein derived from variational principles leading to symmetry by construction. By relaxing continuity between the fields on the boundary and those in the domain two multi-field variational principles have been formulated. Emerging from these variational principles, two Hybrid Boundary Element Methods (HBEM) were developed, the Hybrid Displacement Method and the Hybrid Stress Method, respectively. The choice of weighted fundamental solutions as domain approximations selected independently from polynomial approximations of boundary variables allow to map domain integrals in boundary integrals. Symmetric sytems of equations for frequency and time domain are obtained.

Higher-order boundary element methods (BEM) are presented for time-dependent convective diffusion problems. The time-dependent convective diffusion free-space fundamental solutions originally proposed by Carslaw and Jaeger are used to obtain the boundary integral formulation. For the linear, quadratic and quartic time interpolation functions considered in this paper, a complete set of closed form time integrals for the one-dimensional formulation are developed. Boundary element method solutions are obtained for four problems of unsteady convection-diffusion, including shock wave propagation. It is shown that the BEM solutions are extremely accurate in contrast to finite-difference and finite-element methods. Moreover, no upwinding is needed for the boundary element methods, even for high Peclet number flows. Finally, the conventional BEM formulation is extended to a problem involving singular flux arising due to a sudden rise of temperature on the boundary. This infinite flux BEM formulation provides significantly more accurate numerical results than the conventional approach.

The dual reciprocity method (DRM) and the radial integration method (RIM) are techniques used in BEM to transform domain integrals into boundary integrals. They are suitable for boundary element formulations where a complete fundamental solution is either unavailable or very complex, because in these cases one or more terms can remain as domain integrals in order to use a simpler fundamental solution. Thus, a large number of problems can be solved with the knowledge of a few number of fundamental solutions and additional terms as inertia or non-linear effects, can be treated as body forces and taken to the boundary. In both methods, the remaining terms are approximated through a finite series expansion involving proposed approximating functions and coefficients to be determined. This expansion is substituted in the generated domain integrals that are, subsequently, tr ansformed into boundary integrals. In this paper, a boundary element formulation for thin shallow shells with no domain discretization is presented. The domain integrals due to the curvature of the shells are tran sformed into boundary integrals using the radial integration method. Two approximation functions are used in this work. The first is the radial ba sis function that has been used extensively in the DRM given by:

Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells. Topics in Engineering, Vol 43

The authors consider a boundary-element method (BEM) for 3-D transient eddy current problems formulated in terms of the second-order vector potential (SOVP). Indirect boundary integral equations are derived using the time-dependent fundamental solution and fictitious source densities. In the numerical implementation, a time-stepping convolution approach is adopted to eliminate the need for volume discretization and domain integration. Numerical results of a benchmark problem demonstrate the validity and accuracy of the technique. The proposed scheme, compared with an alternative volume-based recurring initial condition approach, not only provides considerable reduction in the manpower requirements for modeling, but also permits a more precise solution, especially for 3-D problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The article presents two elements associated with the practice of application of the boundary element method. The first is associated with BEM ability to analyze an open boundary objects and application of infinite boundary elements in the area of mammography. The second element is associated with the damped wall investigations. Wall humidity and moisture represents heterogeneous environment (Functionally Graded Materials) which has to be treated in a special way.

Finite element method (FEM) is widely used in the modeling of electromagnetic systems and as a reliable method to verify analytical modeling of electromagnetic devices in design step. As the method is based on discretization of domains, the electromagnetic continuity conditions at the boundaries of elements should be confirmed. Electromagnetic continuity conditions in FEM modeling were investigated in this article. It was shown that the continuity of tangential component of magnetic field intensity is not guaranteed at the boundaries of elements. The inability of FEM to establish the continuity condition leads to some virtual surface current densities at the boundaries of adjacent elements which does not exist in reality. The existence of virtual surface currents is proved in an example. Then, with the help of a complicated example, it is shown that large number of elements and, consequently, the large number of boundaries between elements may cause great errors in FEM postprocess results, especially in calculating magnetic stored energy and electromagnetic forces acting on moving parts. It has been shown that it is very important to take into account the impact of these virtual current densities in energy conversion analysis by FEM.

Boundary element method in nonlinear transient heat transfer of reactor solids with convection and radiation on surfaces

This work describes a time-domain 2-D BEM formulation, which employs the fundamental solution corresponding to a time constant concentrated source. All steps concerning the development of the fundamental solution are presented in details. The numerical solution procedure employs linear boundary elements and linear triangular cells, respectively, for the boundary and domain discretizations. The potential and its normal derivative are assumed to have linear variation in time and space, and, as usual in BEM time-dependent formulations, the time integration is carried out analytically. Another aspect to be mentioned is related to the time-stepping procedure: here, the so-called linear θ-method is adopted and the answer at the time tn+1 is computed from the response at the time tn+θ. In order to assess the accuracy of the formulation, two numerical examples are analysed. Copyright © 2002 John Wiley & Sons, Ltd.

Developments in the connected fields of optics, optoelectronics and photonics have had a profound effect on the emergence of modern technologies and their influence on our lives. In all of these fields, understanding and improving the basic underlying materials is of crucial importance for the development of systems and applications. The International Conference on Optical, Optoelectronic and Photonic Materials and Applications (ICOOPMA) has successfully married these fields and become a regular feature in the conference calendar. The 6th conference in the series, held at the University of Leeds from 27th July – 1st August, 2014, continued the ICOOPMA tradition and attracted 220 international delegates with a diverse range of disciplines and interests. The 59 papers in this Proceedings provide an excellent overview of the topics presented. The conference consisted of four thematic areas in the fields of inorganic semiconductors, carbon and polymeric materials, inorganic glasses and crystalline materials, and metamaterials and plasmonics where each theme area included research on basic materials through to device applications. The conference began with a Workshop organised by Professor Dan Hewak (University of Southampton) with speakers covering Organic Optoelectronic Complexes (Dr Richard Curry, University of Surrey), Metamaterials (Dr Vassili Fedotov, University of Southampton), Graphene (Dr Monica Craciun, University of Exeter) and Amorphous Semiconductors (Dr Jiri Orava, University of Cambridge and Tohoku University). This provided an excellent overview of a representative range of the important topics that were discussed further at the conference. The conference included a banquet which successfully combined excellent food with a relaxing opportunity for the conference delegates to socialise and network. The pinnacle of the evening was the after dinner speech given by our distinguished guest, Professor Sir David Payne (University of Southampton), who gave a highly informative and humorous history of the development of photonics and the important role played by optical fibres, of which he was one of the key pioneers. Emerging scientific talent was also given a platform, with a particular feature of the conference being the Young Scientists Forum, organised by Dr Senthil Ganapathy (University of Southampton), consisting of a series of themed sessions providing up-and-coming researchers a opportunity to present and discuss their work.Each technical theme of the conference was introduced with Plenary lectures delivered by leading international figures in their respective fields. Professor Jim Harris (Stanford University) discussed the development of epitaxially grown dilute-nitride semiconductors and the important role that they play in high efficiency solar cells. This theme was continued by Professor Wolfgang Stolz (Philipps University, Marburg) who described the use of novel III-V semiconductors for the development of lasers on silicon. Dr Jerry Meyer (Naval Research Laboratories) and Dr Kumar Patel (Pranalytica) discussed the important field of mid-infrared devices highlighting the significant developments that have been made in inter-band cascade and quantum cascade based devices, respectively and which have wide-ranging applications in sensing. Professor Neil Greenham (University of Cambridge) discussed solution-based semiconductors based on conjugated polymers and nanocrystals offering low cost routes to the wide-scale deployment of photonics. Professor Ortwin Hess (Imperial College) gave an overview of the physics and fascinating technological potential of negative refractive index materials. Professor Stephen Elliott (University of Cambridge) discussed the optoelectronic properties of phase change materials for memories. These areas were expanded upon in over 70 invited talks from international speakers highlighting recent developments in each of these areas. Further detailed discussions were presented in many parallel Oral and Poster sessions. This Proceedings provides an exciting and wide-ranging discussion of the topics presented at ICOOPMA 2014. We are very grateful to the many people who helped with the organisation of the conference, with particular thanks to Alison Whiteley and her team who enabled the smooth running of the conference, Dr Senthil Ganapathy for his many and wide ranging contributions to the conference and finally Professor Safa Kasap for his wisdom, advice and strong support. The conference could not have happened without the commitment of the Local Organising Committee, who helped in many ways to assemble and run the conference, and for the International Programme, Advisory and Steering committees who guided the technical direction of the conference and assisted with the conference programme and proceedings. We are also extremely pleased to have received generous sponsorship from a large number of organisations and companies. Finally, we are also very grateful to Sarah Toms and the Editorial staff at the Institute of Physics, and the many contributors and reviewers for helping us to put-together this proceedings.Stephen Sweeney, Guildford, UK Animesh Jha, Leeds, UK

Boundary element method (BEM) is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expanding the geometry quantities at the field point as Taylor series. New analytical formulas are derived for geometry quantities defined on the curved line/plane, and unified expressions are obtained for both two-dimensional and three-dimensional problems. For the two-dimensional boundary integrals, analytical expressions for the third-order derivatives are derived and are employed to verify the complex-variable-differentiation method (CVDM) which is used to evaluate the high order derivatives for three-dimensional problems. A few numerical examples are given to show the effectiveness and the accuracy of the present method.

This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE) applications in different fields of biomechanics between 1976 and 1991. The aim of this paper is to help the users of FE and BE techniques to get better value from a large collection of papers on the subjects. Categories in biomechanics included in this survey are: orthopaedic mechanics, dental mechanics, cardiovascular mechanics, soft tissue mechanics, biological flow, impact injury, and other fields of applications. More than 900 references are listed.