Carlos A. Brebbia – författare

This book contains chapters written by eminent scientists on the latest de- velopment in computer technology and applications in Japan. The material contained in this book is an edited version of the presenta- tion at a seminar arranged by the Computational Mechanics Institute of the Wessex Institute of Technology at Southampton during 1989. The objective of the Seminar was to provide an awareness of the considerable advances being made by Japanese scientists in the general area of information tech- nology and in the so-called Fifth Generation Computer Systems. In the first chapter, Watanabe of the NEC Corporation, describes advanced architecture and technology of supercomputing systems. This theme is fol- lowed by Nakamura of Tohoku University in the next chapter. Another type of supercomputer for vector processing, the FACOM VP 2000 Series is then described by Uchida of Fujitsu Ltd in Chapter Three. Expert systems are presented in the next two chapters by Ueno and Oomari of Tokyo Denki University and by Koseki and Goto of the NEC Corpora- tion. Important applications in computer graphics are described in Chapter Six by Ishii and Murakami of Fujitsu Laboratories.Hayashi from the same Laboratory then discusses neurocomputers in Japan. The final chapter by Noguchi of Tohoku University illustrates an important application in com- munications. The Editors acknowledge the help of Computational Mechanics Publica- tions in the preparation and sub-editing of the manuscript and are grateful for the high standards of presentation.

The application of BEM in all fields of engineering and science has progressed at an accelerate rate since the first book on the method appeared in the late seventies. In particular the advantages of BEM for potential problems are essential to solve a whole range of electrical engineering problems. Previous volumes in this series have focussed on the state of the art in other fields while this volume discusses only problems related to electrical engineering. The book reviews a series of important applications such as the design of semiconductor devices and their thermal analysis. The following two chapters concentrate on the study of galvanic corrosion and cathodic protection. Chapter 4 deals with the design of capacitance transducers. The next three chapters concentrate on the applications of the method to simulate electrochemical problems with special reference to Plating Process. The last chapter in the book discusses the case of inverse problems in electrical engineering and presents some applications including their use in tomography.

The application of BEM in all fields of engineering and science has progressed at an accelerate rate since the first book on the method appeared in the late seventies. In particular the advantages of BEM for potential problems are essential to solve a whole range of electrical engineering problems. Previous volumes in this series have focussed on the state of the art in other fields while this volume discusses only problems related to electrical engineering. The book reviews a series of important applications such as the design of semiconductor devices and their thermal analysis. The following two chapters concentrate on the study of galvanic corrosion and cathodic protection. Chapter 4 deals with the design of capacitance transducers. The next three chapters concentrate on the applications of the method to simulate electrochemical problems with special reference to Plating Process. The last chapter in the book discusses the case of inverse problems in electrical engineering and presents some applications including their use in tomography.

This series has been developed in response to the interest shown in boundary ele­ ments by scientists and engineers. Whilst Volume 1 was dedicated to basic principles and applications, this book is concerned with the state of the art in the solution of time-dependent problems. Since papers have recently been published on this im­ portant topic it is time to produce a work of a more permanent nature. The volume begins with a chapter on the Fundamentals of Boundary Integral Equation Methods in Elastodynamics. After reviewing the basic equations of elasto­ dynamics, the wave equation and dynamic reciprocal theorems are stated and the direct and indirect boundary element formulations are presented. Eigenvalue problems are discussed together with the case of the Fourier transformations. Several applications illustrate the effectiveness of the technique for engineering. Chapter 2 examines some of the various boundary integral equation formulations available for elastodynamic problems. In particular the displacement-traction for­ mulation is compared with the displacement-potential case. The special character­ istics of the elastodynamics fundamental solutions are discussed in detail and a criti­ cal comparison with the elastostatics case is presented. While the chapter is not meant to be a complete review of the work in the field, the original presentation of the problem and the suggestions for further work make an important contribu­ tion to the development of the method.

This series has been developed in response to the interest shown in boundary ele­ ments by scientists and engineers. Whilst Volume 1 was dedicated to basic principles and applications, this book is concerned with the state of the art in the solution of time-dependent problems. Since papers have recently been published on this im­ portant topic it is time to produce a work of a more permanent nature. The volume begins with a chapter on the Fundamentals of Boundary Integral Equation Methods in Elastodynamics. After reviewing the basic equations of elasto­ dynamics, the wave equation and dynamic reciprocal theorems are stated and the direct and indirect boundary element formulations are presented. Eigenvalue problems are discussed together with the case of the Fourier transformations. Several applications illustrate the effectiveness of the technique for engineering. Chapter 2 examines some of the various boundary integral equation formulations available for elastodynamic problems. In particular the displacement-traction for­ mulation is compared with the displacement-potential case. The special character­ istics of the elastodynamics fundamental solutions are discussed in detail and a criti­ cal comparison with the elastostatics case is presented. While the chapter is not meant to be a complete review of the work in the field, the original presentation of the problem and the suggestions for further work make an important contribu­ tion to the development of the method.

Past volumes of this series have concentrated on the theoretical and the more formal aspects of the boundary element method. The present book instead stresses the computational aspects of the technique and its applications with the objective of facilitating the implementation of BEM in the engineering industry and its better understanding in the teaching and research environments. The book starts by discussing the topics of convergence of solutions, application to nonlinear problems and numerical integration. This is followed by a long chapter on the computational aspects of the method, discussing the different numerical schemes and the way in which influence functions can be computed. Three separate chapters deal with important techniques which are related to classical boundary elements, namely the edge method, multigrid schemes and the complex variable boundary element approach. The last two chapters are of special interest as they present and explain in detail two FORTRAN codes which have numerous applications in engineering, i.e. a code for the solution of potential problems and another for elastostatics. Each sub­ routine in the programs is listed and explained. The codes follow the same format as the ones in the classical book "The Boundary Element Method for Engineers" (by C. A. Brebbia, Computational Mechanics Publications, first published in 1978) but are more advanced in terms of elements and capabilities. In particular the new listings deal with symmetry, linear elements for the two dimensional elasticity, some mixed type of boundary conditions and the treatment of infinite regions.

Past volumes of this series have concentrated on the theoretical and the more formal aspects of the boundary element method. The present book instead stresses the computational aspects of the technique and its applications with the objective of facilitating the implementation of BEM in the engineering industry and its better understanding in the teaching and research environments. The book starts by discussing the topics of convergence of solutions, application to nonlinear problems and numerical integration. This is followed by a long chapter on the computational aspects of the method, discussing the different numerical schemes and the way in which influence functions can be computed. Three separate chapters deal with important techniques which are related to classical boundary elements, namely the edge method, multigrid schemes and the complex variable boundary element approach. The last two chapters are of special interest as they present and explain in detail two FORTRAN codes which have numerous applications in engineering, i.e. a code for the solution of potential problems and another for elastostatics. Each sub­ routine in the programs is listed and explained. The codes follow the same format as the ones in the classical book "The Boundary Element Method for Engineers" (by C. A. Brebbia, Computational Mechanics Publications, first published in 1978) but are more advanced in terms of elements and capabilities. In particular the new listings deal with symmetry, linear elements for the two dimensional elasticity, some mixed type of boundary conditions and the treatment of infinite regions.

The first volume of this series dealt with the Basic Principles of Boundary Elements, while the second concentrated on time dependent problems and Volume three on the Computational Aspects of the method. This volume studies the applications of the method to a wide variety of geomechanics problems, most of which are ideally suited for boundary elements demonstrating the potentiality of the technique. Chapter 1 deals with the application of BEM to three dimensional elastody­ namics soil-structure interaction problems. It presents detailed formulations for rigid, massless foundations of arbitrary shape both in the frequency and time domains. The foundations are assumed to be resting on a linearly elastic, homogeneous, isotropic half-space and be subjected to externally applied loads on obliquely incident body. The chapter reviews the major advances in soil foundation interaction presents a series of numerical results and stresses the practical application of BEM, pointing out the high accuracy and efficiency of the technique, even when using coarse mesh discretizations.

The first volume of this series dealt with the Basic Principles of Boundary Elements, while the second concentrated on time dependent problems and Volume three on the Computational Aspects of the method. This volume studies the applications of the method to a wide variety of geomechanics problems, most of which are ideally suited for boundary elements demonstrating the potentiality of the technique. Chapter 1 deals with the application of BEM to three dimensional elastody­ namics soil-structure interaction problems. It presents detailed formulations for rigid, massless foundations of arbitrary shape both in the frequency and time domains. The foundations are assumed to be resting on a linearly elastic, homogeneous, isotropic half-space and be subjected to externally applied loads on obliquely incident body. The chapter reviews the major advances in soil foundation interaction presents a series of numerical results and stresses the practical application of BEM, pointing out the high accuracy and efficiency of the technique, even when using coarse mesh discretizations.

General Applications of BEM to electromagnetic problems are comparatively new although the method is ideally suited to solve these problems, which usually involve unbounded domains. The present volume comprises contributions by eminent researchers working on applications of boundary elements in electromagnetic problems. The volume deals with the solutions of Maxwell''s equation for three-dimensional as well as two-dimensional cases. It also discusses combination of BEM with FEM particularly in the case of saturated media. Some chapters specifically deal with the design of electromagnetic devices. The book is essential reading to those engineers and scientists, who are interested in the state of the art for electrical and electromagnetic application of boundary elements. It is also an important reference for those engineers who are working on the design of electromagnetic components many of which can be advantageously carried out using BEM.

General Applications of BEM to electromagnetic problems are comparatively new although the method is ideally suited to solve these problems, which usually involve unbounded domains. The present volume comprises contributions by eminent researchers working on applications of boundary elements in electromagnetic problems. The volume deals with the solutions of Maxwell's equation for three-dimensional as well as two-dimensional cases. It also discusses combination of BEM with FEM particularly in the case of saturated media. Some chapters specifically deal with the design of electromagnetic devices. The book is essential reading to those engineers and scientists, who are interested in the state of the art for electrical and electromagnetic application of boundary elements. It is also an important reference for those engineers who are working on the design of electromagnetic components many of which can be advantageously carried out using BEM.

The Boundary Element Method has now become a powerful tool of engineering analysis and is routinely applied for the solution of elastostatics and potential problems. More recently research has concentrated on solving a large variety of non-linear and time dependent applications and in particular the method has been developed for viscous fluid flow problems. This book presents the state of the art on the solution of viscous flow using boundary elements and discusses different current approaches which have been validated by numerical experiments. . Chapter 1 of the book presents a brief review of previous work on viscous flow simulation and in particular gives an up-to-date list of the most important BEM references in the field. Chapter 2 reviews the governing equations for general viscous flow, including compressibility. The authors present a compre­ hensive treatment of the different cases and their formulation in terms of boundary integral equations. This work has been the result of collaboration between Computational Mechanics Institute of Southampton and Massa­ chusetts Institute of Technology researchers. Chapter 3 describes the gen­ eralized formulation for unsteady viscous flow problems developed over many years at Georgia Institute of Technology. This formulation has been extensively applied to solve aer09ynamic problems.

The Boundary Element Method has now become a powerful tool of engineering analysis and is routinely applied for the solution of elastostatics and potential problems. More recently research has concentrated on solving a large variety of non-linear and time dependent applications and in particular the method has been developed for viscous fluid flow problems. This book presents the state of the art on the solution of viscous flow using boundary elements and discusses different current approaches which have been validated by numerical experiments. . Chapter 1 of the book presents a brief review of previous work on viscous flow simulation and in particular gives an up-to-date list of the most important BEM references in the field. Chapter 2 reviews the governing equations for general viscous flow, including compressibility. The authors present a compre­ hensive treatment of the different cases and their formulation in terms of boundary integral equations. This work has been the result of collaboration between Computational Mechanics Institute of Southampton and Massa­ chusetts Institute of Technology researchers. Chapter 3 describes the gen­ eralized formulation for unsteady viscous flow problems developed over many years at Georgia Institute of Technology. This formulation has been extensively applied to solve aer09ynamic problems.

This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.

This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.

The International Conference on Boundary Element Methods in Engineering was started in 1978 with the following objectives: i) To act as a focus for BE research at a time when the technique wasjust emerging as a powerful tool for engineering analysis. ii) To attract new as weIl as established researchers on Boundary Elements, in order to maintain its vitality and originality. iii) To try to relate the Boundary Element Method to other engineering techniques in an effort to help unify the field of engineering analysis, rather than to contribute to its fragmentation. These objectives were achieved during the last 7 conferences and this meeting - the eighth - has continued to be as innovative and dynamic as any ofthe previous conferences. Another important aim ofthe conference is to encourage the participation of researchers from as many different countries as possible and in this regard it is a policy of the organizers to hold the conference in different locations. It is easy to forget when working on scientific projects that in science as weIl as in other subjects, human relationships are as important as mathematical equations. Science progresses not only as a resuIt oflaboratory and computer experiments or abstract thinking but also by a process of personal interaction.

The International Conference on Boundary Element Methods in Engineering was started in 1978 with the following objectives: i) To act as a focus for BE research at a time when the technique wasjust emerging as a powerful tool for engineering analysis. ii) To attract new as weIl as established researchers on Boundary Elements, in order to maintain its vitality and originality. iii) To try to relate the Boundary Element Method to other engineering techniques in an effort to help unify the field of engineering analysis, rather than to contribute to its fragmentation. These objectives were achieved during the last 7 conferences and this meeting - the eighth - has continued to be as innovative and dynamic as any ofthe previous conferences. Another important aim ofthe conference is to encourage the participation of researchers from as many different countries as possible and in this regard it is a policy of the organizers to hold the conference in different locations. It is easy to forget when working on scientific projects that in science as weIl as in other subjects, human relationships are as important as mathematical equations. Science progresses not only as a resuIt oflaboratory and computer experiments or abstract thinking but also by a process of personal interaction.

This series has been developed in response to the interest shown in boundary ele- ments by scientists and engineers. Whilst Volume I was dedicated to basic principles and applications, this book is concerned with the state of the art in the solution of time-dependent problems. Since papers have recently been published on this im- portant topic it is time to produce a work ofa morepermanent nature. The volume begins with a chapter on the Fundamentals of Boundary Integral Equation Methods in Elastodynamics. After reviewing the basic equations of elasto- dynamics, the wave equation and dynamic reciprocal theorems are stated and the direct and indirect boundary element formulations are presented. Eigenvalue problems are discussed together with the case of the Fourier transformations. Several applications illustrate the etfectiveness ofthe technique for engineering. Chapter 2 examines some ofthe various boundary integral equation formulations available for elastodynamic problems. In particular the displacement-traction for- mulation is compared with the displacement-potential case.The special character- istics ofthe elastodynamics fundamental solutions are discussed in detail and a criti- cal comparison with the elastostatics case is presented. While the chapter is not meant to be a complete review of the work in the field, the original presentation of the problern and the suggestions for further work make an important contribu- tion to the development ofthe method.