Authored Books


Cruse, T.A.
Mathematical Foundation of the Boundary-Integral Equation Method in
Solid Mechanics


Jaswon, M.A. and Symm, G.T.
Integral Equation Methods in Potential Theory and Elastostatics
Academic Press
278 pp
ISBN: 0 12 381050 7
Integral equations, as the authors of this book demonstrate, provide
distinctive formulations of the fundamental boundary-value problems of
potential theory and elastostatics. These formulations often yield
effective solutions which fall beyond the scope of other approaches.
This monograph on the subject brings together theory and practice and
includes much previously unpublished material. The first part of the
volume gives a very clear description of the theory of integral
equations in potential theory and elastostatics, provinding, as one of
its features, the first unifying account of scalar and vector potential
theory using a common formalism. In the second part, the authors
discuss numerical methods for solving the integral equation
formulations of practical problems, using their own extensive research
as a basis. The theory is illustrated by a wealth of numerical
solutions drawn from a variety of fields, including electrostatics,
potential fluid flow, heat conduction, and the stretching and bending
of thin plates. An extensive list of references is provided, which also
covers recent interesting numerical solutions of problems in
three-dimensional elastostatics.
The book should be of direct use to engineers interested in a new
approach to and of the fields mentioned, and it would also be suitable
for postgraduates requiring a guide to this rapidly evolving subject.


Brebbia, C.A.
The Boundary Element Method for Engineers
Pentech Press
189 pp
ISBN: 0 931215 00 5
The book is aimed to introduce the reader to the fundamentals of
boundary elements, and to the application of the method to potential
problems and 2-D elasticity respectively. The book consists of six
chapters: Introduction, Weighted residuals method, Potential problems,
Elasticity problems, 2-D elasticity, and Final remarks. Appendix 1
presents the numerical integration formulae. The Index completes the book.

Cruse, T.A. and Wilson, R.B.
Boundary-Integral Equation Methods for Elastic Fracture
Mechanics Analysis



Brebbia, C.A. and Walker, S.
Boundary Element Techniques in Engineering
ISBN: 0 408 00340 5
The mathematics of the boundary element technique in a simplified form
as well as applications of the BEM as presented. The book contains
seven chapters which cover: boundary element method and weighted
residuals method, direct and indirect formulations, flow of fluid
around a cylinder between parallel plates, linear, quadrilateral and
higher-order elements for 2-D potential problems, boundary elements for
3-D problems, boundary element method and solution of boundary value
problems, 2-D problems of the theory of elasticity, time-dependent and
non-linear problems, problem solutions in connection with the
irregularity or nonhomogeneity (several regions).


Banerjee, P.K. and Butterfield, R.
Boundary Element Methods in Engineering Science
McGraw-Hill Book Company
New York
452 pp
ISBN: 0 07 084120 9
The book provides an introduction to the fundamentals of BEM, and
demonstrates the power and versatility of the method in different areas
of application. The book contains 15 chapters with the following
topics: an introdcution to BEM, some 1-D problems, 2-D problems of
steady state potential flow, 2-D problems of elastostatics, 3-D
problems of steady state potential flow, 3-D problems in elasticity,
problems of edges and corners, parametric representation of functions
and geometry, transient potential flow (diffusion) problems, transient
problems in elasticity, plate-bending problems, elastoplasticity,
examples in fluid mechanics, combination of BEM with other numerical
methods, and computer implementation of BEM (the program listing is
included). Three appendices and an Index complete the book. 



Mukherjee, S.
Boundary Element Methods in Creep and Fracture
Elsevier Applied Science Publishers
210 pp
ISBN: 0 85334 163
This book presents the development of BEm for non-linear problems in
solid mechanics together with some fracture mechanics applications. The
book contains ten chapters. These cover topics such as: brief
historical account of the BEM development, state variable models for
time-dependent inelastic deformation of metals, numerical integration
strategy for the time domain, 2-D, 3-D and axisymmetric
elastoplasticity and viscoplasticity, viscoplastic torsion and bending
of plates, 2-D problems in fracture mechanics. The index compl;etes the


Crouch, S.L. and Starfield, A.M.
Boundary Element Methods in Solid Mechanics
Allen and Unwin
322 pp
ISBN: 0 04 620010 X
The book can serve as a basic reading on the subject. Useful to the
reader primarily interested in solving problems by these methods. The
book contains eight chapters which cover: comparison of finite element
method with boundary element method, linear elasticity theory, singular
solution, indirect boundary element methods, direct boundary element
method, application to plane classical elasticity, a higher-order
formulation for elements, applications in rock mechanics and geological
engineering. Three appendices contain listings of three programs based
on the text.

Liggett, J.A. and Liu, P.L.F.
Boundary Integral Equation Method for Porous Media Flow
Allen and Unwin
272 pp
ISBN: 0 04 62001 8
The book provides an introduction to the mathematics and applications
of the subject.

Telles, J.C.F.
The Boundary Element Method Applied to Inelastic Problems
Lecture Notes in Engineering - Vol 1
243 pp
ISBN: 0 387 12387 3
The book can serve as basic reading on the subject. The inelastic 2-D
problems are handled (the current state-of-the-art). A complete review
of the elasticity problems is included. A set of numerical applications
is given. Subjects covered in seven chapters. The book contains: review
of the work up-to-date, basic theory of elasticity, BEM formulation for
elastic problems, BEM formulation for inelastic problems, initial
stress/strain methods and elastoplastic analysis, viscoplasticity and
creep, mathematical aspects for BEM inelastic analysis. Appendices give
some ideas on code developments.

Venturini, W.S.
Boundary Element Methods in Geomechanics
Lecture Notes in Engineering - Vol 4
246 pp
ISBN: 3 540 17497 4
The book can serve as a basic reading on the subject. Topics on the
application of BEM in geomechanics are given in eleven chapters. These
cover: material models associated with geomechanical stress analysis,
formulation for linear problems, initial stress/strain formulations for
2-D continuum analysis, 3-D formulation to the generalized plane strain
problems, reduction of boundary-integral equations to algebraic form,
BEM application to no-tension materials, alternative formulations for
directionally oriented material weakness and slip or separation along
discontinuities types of behaviour for rocks, elasto-plasticity analysis
as applied to soils, elasto-viscoplasticity, viscoplastic analysis
applied to a variety of geomechanics problems (strip footing, slope
stability, tunnels), practical numerical analysis.


Brebbia, C.A., Telles, J.C.F. and Wrobel, L.C.
Boundary Element Techniques - Theory and Applications in Engineering
464 pp
ISBN: 3 540 12484 5
The book presents up-to-date treatment of the boundary element method.
Chapters included in the book cover: a generalized mathematical
formulation, elastostatics, elastoplasticity, viscoplasticity,
vibration, plate bending, wave propagation, fluid mechanics, coupling
FE method with the BE method. A comprehensive bibliography and listing
of a program complete the book.

Hromadka II, T.V.
The Complex Variable Boundary Element Method
Lecture Notes in Engineering - Vol 9

243 pp
ISBN: 0 387 13743 2
This book presents the detailed mathematics associated with the CVBEM
(Complex Variable Boundary Element Method). The simplifications which
allow the interpretation of the CVBEM approximation error are
discussed. Computer programs which allow the solution of 2-D problems
are included. Several application problems are solved.

Ingham, D.B. and Kelmanson, M.A.
Boundary Integral Equation Analysis of Singular Potential and
Biharmonic Problems

Lecture Notes in Engineering - Vol 7
173 pp
ISBN: 0 387 13646 0
The book provides an introduction to the mathematics and applications
of BIE to singular, potential, and biharmonic problems. Topics covered:
biharmonic equation for fluid flow problems involving stick-slip
boundary conditions, problems of flow around sharp corners, non-linear
heat transfer, viscous flow with free surfaces, slow flow in bearings
with arbitrary geometries.

Manzoor Madassar, I.
Heat Flow Through Extended Surface Heat Exchangers
Lecture Notes in Engineering - Vol 5
286 pp
ISBN: 0 387 13047 0
The book deals with the application of boundary elements to heat
transfer problems encountered on surface heat exchangers. The book
has six chapters dealing with introduction to heat exchangers and their
design, the one and two dimensional analysis of fin assembly heat
transfer including the numerical solution of the problem using boundary
integral equations, the analysis of fin reduction, the effect of
surface roughness and interfacial bending and conclusions related to
the design of heat exchangers and the applicability of boundary
elements to solve these problems.


Kitahara, M.
Boundary Integral Equation Methods in Eigenvalue Problems of
Elastodynamics and Thin Plates

Studies in Applied Mechanics - Vol 10
Elsevier Science Publishers
282 pp
ISBN: 0 444 42447 4
This book contains two parts. The first one handles the analytical
formulation and numerical solution for 2-D problems of vibration and
scattering. The second part considers the application of BIE methods to
the vibration and buckling characteristics of thin plates. The first
part of the book consists of seven chapters, the second one of three
chapters. Some topics treated: the basis of the application of integral
equation methods to eigenvalue problems, the integral equation
formulation in terms of the various boundary value problems, eigenvalue
problems for 2-D boundary integral equation formulation, analytical
treatment of the BIE for circular and annular domains, numerical
eigenvalue solution for the integral equation formulation, eigenvalue
problems of antiplane elastodynamics, review of numerical analysis
results for 2-D eigenvalue problems, integral equation fundamentals for
thin plate problems, numerical analysis of eigenvalue problems for plates.


Gipson, G.S.
Boundary Element Fundamentals: Basic Concepts of Recent Developments in
the Poisson Equation

Topics in Engineering - Vol 2
Computational Mechanics Publications
288 pp
ISBN: 0 905451 80 5
The book contains seven chapters, one of them contains a listing of a
boundary element program. It is devoted to discussion of the
fundamentals and the Poisson equation. The presented chapters cover:
integral equations and Green's functions, approximation methods with
emphasis on the weighted residual method, boundary element methods and
Laplace and Poisson types of differential equations, examples of
Laplace problems, solution of the Poisson equation, Monte Carlo method
and boundary elements, examples of the Poisson problem, description and
listing of a FORTRAN code for Laplace and Poisson equations.

Gravert, P.
Numerical Simulation of Extreme Gravity Waves in Time Domain with the
Direct BEM and a Time Stepping Procedure

ISBN: 3 18 143207 5
A Lagrangian formulation is given for the boundary and initial value
problem of gravity waves. This formulation is solved numerically by the
direct boundary element method (BEM) and a multistep time integration
procedure (Adams-Bashforth-Moulton). For singular integrals suitable
numerical integration formulas are derived from analytical
integrations. The discretization of the boundaries uses higher order
isoparametric elements and, especially for the free and moving surface,
cubic spline elements. The boundary integral equation is solved by a
modified least squares method instead of a collocation or Galerkin
approach. The proposed BEM satisfies in the weighted Gaussian normal
equation constraints exactly by means of a static condensation
algorithm. Steep unsteady and even breaking water waves are calculated
for deep and shallow water conditions. The accuracy and reliability of
the method are shown by comparison of numerical simulations of a wave
channel with experimental results.

Hartmann, F.
Introduction to Boundary Elements

378 pp
ISBN: 0 387 17336 6
This book consists of an introduction, nine chapters, a list of
references, a bibliography and a description of available computer
programs. The bibliography contains 300 references. In addition to the
text, three computer programs for the solution of the membrane, plane
elasticity, and plate flexure problems are included. These programs are
written in TURBO-PASCAL for the IBM PC and compatible computers. The
book deals with the subjects as: fundamentals of the BEM, 1-D problems,
plane problems of the theory of elasticity, problems with non-linear
materials, plate bending, coupling of FEM and BEM, and dynamic problems.

Hromadka II, T.V.
Complex Variable Boundary Elements
Software Package Series
Computational Mechanics Publications
226 pp plus diskette
ISBN: 0 905451 62 7
The book describes the Complex Variable Boundary Element Method (CVBEM)
for the solution of two dimensional Laplace equation problems. The book
part of the software package contains sufficient detail to enable the
reader to comprehend the numerical technique without extensive
prerequisite study. Computer listings in FORTRAN are included for five
different CVBEM programs. A general purpose code is provided on the
floppy disk for use with IBM-PC compatible hardware.

Hromadka, T.V. and Chintu, Lai
Complex Variable Boundary Element Method in Engineering Analysis
389 pp
ISBN: 0 387 96400 2
The authors introduce the complex variable boundary element method as a
new modelling method in computational mechanics and hydraulics. This
book presents the detailed mathematics associated with the CVBEM. The
CVBEM is a generalization of the Cauchy integral formula into a
boundary integral equation method. There are eight chapters in this
book. Partial contents: fundamentals, the development of a computer
algorithm, error analyses, modelling techniques and actual
applications, procedures for the basic potential problems. A number of
numerical programs are included.

Telles, J.C.F.
Two Dimensional Analysis using Boundary Elements
Software Package Series
Computational Mechanics Publications
208 pp plus diskette
ISBN: 0 905451 63 5
This software package has been developed for engineers and applied
mathematicians who would like an introduction to the boundary element
technique particularly applied to elasticity problems. The numerical
aspects of the method are discussed in detail and a fully operational 2-D
FORTRAN code listing is presented. A preprocessor is a part of the
code. A copy of the code on floppy disk running on IBM PC compatible
machines is included.

Wrobel, L.C.
Two Dimensional Potential Analysis using Boundary Elements
Software Package Series
Computational Mechanics Publications
186 pp plus diskette
ISBN: 0 905451 64 3
The book starts by discussing the basic theory of the method and the
formulation of the problem in terms of integral equations and boundary
elements. The development is focused on the solution of Laplace's
equation which can be used to solve steady state heat conduction,
groundwater flow problems, flow of ideal fluids, electrostatics and other
engineering problems. This part is followed by a description of an
efficient code written in FORTRAN, running on IBM PC compatible
hardware. The program runs interactively and has a preprocessor which
simplifies the input. The program, preprocessor and data files are all
provided on the floppy disk. Several applications of the code are


Brebbia, C.A. and Dominguez, J.
Boundary Elements - An Introductory Course
Computational Mechanics Publications
300 pp
ISBN: 0 905451 76 7
ISBN: 0 931215 668 (US, Canada, Mexico)
The theory of boundary elements is presented in a form that can be
readily understood and applied by engineering students. The book
stresses the practical uses of the Boundary Element Method and includes
computer codes presented in standard FORTRAN 77 for ease of
comprehension and which can be implemented on an IBM PC. Each copy of
the book includes a diskette with the complete listing in FORTRAN. The
book covers topics such as: formulation of boundary integral equations,
potential problems, elastostatics, treatment of body forces, coupling
with finite elements, anisotropy, curvilinear coordinates and others.
It also includes a special section on numerical integration. The
computer codes listed in the book and included in the diskette are,
constant and linear codes for potential problems and constant and
quadratic codes for elastostatics.

Cruse, T.A.
Boundary Element Analysis in Computational Fracture Mechanics
162 pp
ISBN: 90 247 3614 5
The book provides exposition of the BEM to fracture mechanics. The book
contains eight chapters giving critical insight into; key historical
developments, review of fracture mechanics, mathematical foundations of
BEM, modelling of elastic cracks by BEM, demonstration of the power of
the integral equation formulations, BEM applications to inelastic
fracture mechanics, applications of BEM to several 2-D and 3-D fracture
mechanics problems.

Manolis, G.D. and Beskos, D.E.
Boundary Element Methods in Elastodynamics
Unwin Hyman
282 pp
ISBN: 004 6200193
The book gives a brief summary of classical elastodynamics and proceeds
with the integral formulation and numerical treatment of both
steady-state and general transient problems. Other chapters include:
wave propagation problems, soil-structure interaction and fracture
mechanics. Other boundary methods related to the BEM are briefly
described, as well as effects of inhomogeneity, anisotropy, porosity,
viscosity and temperature.

Tang, W.
Transformation Domain into Boundary Integrals in BEM: Generalized

Lecture Notes in Engineering
209 pp
ISBN: 0 387 19217 4
The purpose of this set of notes on the boundary element method is to
apply a Fourier series representation as a means for reducing certain
domain integrals to equivalent boundary integrals. The author handles
both potential problems and the vector problem for elastostatics.
Numerous numerical evaluations of resulting Fourier coefficients are given.

Umetani, S.J.
Adaptive Boundary Element Methods in Elastostatics
Topics in Engineering - Vol 5
Computational Mechanics Publications
107 pp
ISBN: 0 905451 81 3
This book examines the adaptive Boundary Element Method (BEM) for
applications in 2-dimensional elastostatics. The author first examines
several problems using a commercial BEM package to compare it with the
Finite Element Method. Next the adaptive BEM is developed to obtain
accurate and reliable solutions. The new approach employs the Galerkin
technique to solve integral equations, the Legendre polynomials
(p-version) and an iterative scheme solves the resulting system of
linear equations. The process is controlled by error estimators which
are used to further refine the model (b-version). Finally all adaptive
strategy using p- and h-versions is proposed. The feasibility of the
adaptive method is shown through solving problems in 2-D elastostatics
including cracks.


Balaš, J. , Sládek, J. and  Sládek, V.
Stress Analysis by Boundary Element Methods (Studies in Applied Mechanics 23)
Veda, Publishing House of the
Slovak Academy of sciences
ISBN: 0-444-98830-0 (Vol. 23) (Elsevier)
ISBN: 0-444-41758-3 (Series) 
ISBN: 80-224-0004-1 (Veda)

   The boundary element method is an extremely versatile and powerful tool of computational mechanics. The purpose of this book is to present a comprehensive and up-to-date treatment of the boundary element method in applications to various fields of continuum mechanics:

  • Elastostatics
  • Elastodynamics
  • Thermoelasticity
  • Micropolar thermoelasticity
  • Elastoplasticity
  • Viscoelasticity
  • Theory of plates and stress analysis by hybrid methods

   In this book, the fundamental solutions of governing differential equations, integral representations of the displacement and temperature fields, regularized integral representations of the stress field and heat flux, boundary integral equations and boundary integro-differential equations are derived, too.

   Besides the mathematical foundations of the boundary integral method, the book deals with practical applications of this method. Most applications are devoted to linear fracture mechanics. The method has been found to be very efficient in stressintensity factor computations.

   Also included are developments made by the authors in the boundary integral formulation of the thermoelasticity, micropolar elasticity, viscoelasticity, plate theory, hybrid method in elasticity and solution of crack problems. The solution of boundary-value problems of thermoelasticity and micropolar thermoelasticity is for the first time formulated as the solution of pure boundary problems. A new unified formulation of general crack problems is presented by integro-diferential equations.

Jiang, Y.S.
Slope Analysis using Boundary Elements
Lecture Notes in Engineering - Vol 52

176 pp
ISBN: 0 387 51625 5

Karami, G.
A Boundary Element Method for Two-Dimensional Contact Problems
Lecture Notes in Engineering - Vol 51

ISBN: 3 540 51562 3
The boundary element method (BEM) has been established as a powerful
numerical tool for the analysis of continua in recent years. The method
is based on an attempt to transfer the governing differential equations
into integral equations over the boundary. Thus, the discretization
scheme or the introduction of any approximations must be done over the
boundary. This book presents a BEM for two-dimensional elastic,
thermo-elastic and body-force contact problems. The formulation is
implemented for the general case of contact with various frictional
conditions. The analysis is limited to linear elastostatics and small
strain theory. Following a review of the basic nature of contact
problems, the analytical basis of the direct formulation of the BEM
method is described. The numerical implementation employs three-noded
isoparametric line elements for the representation of the boundary of
the bodies in contact. Opposite nodal points in equi-length
element-pairs are defined on the two surfaces in the area which is
expected to come into contact under an increasing load. The use of
appropriate contact conditions enables the integral equations for the
two bodies to be coupled together. To find the proper contact
dimensions and the contact load a combined incremental and iterative
approach is utilised. With this approach, the loads are applied
progressively, and the sliding and adhering portion of the contact
region is established for each load increment using an iterative
procedure. A coulomb type of friction law is assumed. The results of
the numerical formulation show excellent agreement with the well known
Hertzian contact solution. Several problems involving more complicated
and non-Hertzian contact are also solved. The BEM solutions agree well
with existing experimental and finite element results. The analytical
and numerical treatment of the boundary integral equations for problems
with body forces and temperature changes is described. In particular,
the pseudo-body force approach which treats the temperature gradients
as a kind of body force, is employed for the thermoelastic analysis. It
is shown that the domain integrals containing the body force and
pseudo-body force terms can be transformed to integrals over the
boundary. Several examples of contact with body forces and temperature
changes are presented.

Lefeber, D.
Solving Problems with Singularities using Boundary Elements
Topics in Engineering - Vol 4
Computational Mechanics Publications
183 pp
ISBN: 0 905451 96 1
This book has considerable bearing on the use of the Boundary Element
Method and other numerical techniques on the all-important area of
finding engineering solutions near singularities. When a linear partial
differential equation has singularities in the boundary conditions, it
is generally impossible to obtain accurate approximations in the
neighbourhood of those points using standard numerical methods. In
practical engineering problems, quantities involving derivatives such
as stresses, bending moments, shear forces, etc., play an important
role in the design process, so that an accurate knowledge of the
behaviour of these quantities, especially near the singular points, is
necessary. In this text, a method is outlined to obtain an accurate
approximation in the domain and on the boundary, especially near the
singularities. In particular, any derived quantity of the proposed
approximate solution can be obtained with sufficient precision, by
analytical derivation. The method is based on a set of singular
functions satisfying the partial differential equation and part of the
boundary conditions. The method is developed in detail in the case of
potential problems with mixed boundary conditions, and for thin plate
problems with any combination of simply-supported, clamped or free
boundary conditions. Special attention is given to skew plates.


Beasy Self-Teaching Guide
Computational Mechanics Publications
ISBN: 1 85312 040 5
ISBN: 1 945824 23 8 (US, Canada, Mexico)
This guide is designed to give a training course in the use of BEASY
and its pre and postprocessor BEASY-IMS. The course is arranged in a
series of sessions which should be followed while sitting at a
terminal. The sessions contain examples of increasing complexity, and
each introduces more modeling features and concepts. While the examples
have been chosen to resemble real engineering applications, they are
necessarily small, because the aim of the book is to teach you how to
use BEASY.

Kitagawa, K.
Boundary Element Method Analysis of Viscous Flow
Lecture Notes in Engineering - Vol 55
136 pp
ISBN: 0 387 51930 0
In this book, applications of the BEM to viscous flow and thermal
convection problems are investigated. The proposed formulation is
based on an analogy between Navier's equations in elastostatics and
Navier-Stokes equations expressed by using a penalty function. After
briefly reviewing the previous research on viscous flow problems and
BEM in the first chapter, the second chapter deals with the proposed
formulation in detail. Chapter 3 presents the numerical
implementation, in particular, the numerical computation methods for
evaluating quasi-singular boundary integrations and domain
integrations. Some two-dimensional results are compared with previous
results in Chapter 4, and finally, three-dimensional results are also

Pande, G.N., Beer, G. and Williams, J.R.
Numerical Methods in Rock Mechanics
ISBN: 0471 92021 5
Numerical methods are applied to rock mechanics problems in tunnelling,
mining, construction of dams and other areas. The important
developments in the field during the past decade are reflected here,
and the authors describe the most important methods in numerical
modelling of rocks and rock masses: the finite element method, the
boundary element method and the discrete element method.
Numerical Methods in Rock Mechanics highlights the
essential features of the behaviour of rocks, assuming a knowledge of
soil mechanics, and deals with the theory of elasto-plasticity and
elasto-viscoplasticity, which is essential for modelling of the
constitutive behaviour of jointed rock masses.
Mechanical behaviour of intact rocks, rock joints and
jointed masses is covered; simple analytical and numerical models are
discussed and later used as `building blocks' for a comprehensive,
constitutive model of the behaviour of jointed rock masses. Joint
elements and infinite elements are introduced with emphasis on
modelling of discrete major discontinuities such as fault and shear
zones. Various models of behaviour of jointed rock masses of varying
complexities are given and multi-laminate models are described.
Examples of the practical applications for each of the
methods are given and comprehensive reference lists direct the reader
to a more detailed study.


Aliabadi, M.H. and Rooke, D.P.
Numerical Fracture Mechanics
Computational Mechanics Publications
276 pp
ISBN:1 85312 057 X
ISBN: 0 945824 39 4 (US, Canada, Mexico)
The purpose of this book is to demonstrate the use of numerical methods
in solving crack problems in fracture mechanics. The text concentrates,
to a large extent, on the application of the Boundary Element Method
(BEM) to fracture mechanics, although an up-to-date account of recent
advances in other numerical methods such as the Finite Element Method
is also presented. The book is an integrated presentation of modern
numerical fracture mechanics, and contains a compilation of the work of
many researchers as well as accounting for some of the authors' most
recent work on the subject. It is hoped that this book will bridge the
gap that exists between specialist books on theoretical fracture
mechanics on the one hand, and texts on numerical methods on the other.
Although most of the methods presented are the latest developments in
the field of numerical mechanics, the authors have also included some
simple techniques which are essential for understanding the physical
principles that govern crack problems in general. Different numerical
techniques are described in detail and where possible simple examples
are included, as well as test results for more complicated

Bruch, E.K.
The Boundary Element Method for Groundwater Flow
Lecture Notes in Engineering
ISBN: 3 540 54407 0
ISBN: 0387 54407 0
During the last few years rapid progress has been made on the solution
of partial differential equations, which are now routinely solved using
computers. Their implementation is based numerically in three methods
which in chronological order are the finite difference method, the
finite element method and the boundary element method. In comparison
to the other two methods, the latter presents some important advantages
which have motivated its rapid development in the last decade or so.
In this book the application of the boundary element method to the
solution of the Laplace equation is examined. This equation is of
fundamental importance in engineering and science as it describes
different types of phenomena, including the groundwater flow
applications highlighted in this book. Special subjects such as
numerical integration, subdivision of the domain into regions and other
computational aspects are discussed in detail in the first chapters. To
demonstrate the accuracy and efficiency of the boundary element method,
results obtained when solving the Laplace equation have been compared
against known analytical solutions. Other chapters deal with problems
such as steady state and unsteady flow in addition to infiltration
problems. The applications demonstrate that the boundary element method
provides a powerful solution technique which can be effectively applied
to solve this type of problem.

DeFigueiredo, T.G.B.
A New Boundary Element Formulation in Engineering
Lecture Notes in Engineering

ISBN: 3 540 54030 X
ISBN: 0 387 54030 X

Elzein, A.
Plate Stability by Boundary Element Method
Lecture Notes in Engineering

ISBN: 3 540 53710 4
ISBN: 0 387 53710 4

Partridge, P.W., Brebbia, C.A. and Wrobel, L.C.
The Dual Reciprocity Boundary Element Method
Computational Mechanics Publications
ISBN: 1 85312098 7
ISBN: 0 945824 82 3(US, Canada, Mexico)
The boundary element method (BEM) is now a well-established numerical
technique which provides an efficient alternative to finite difference
and finite element methods for the solution of a wide range of
engineering problems. The main advantage of the BEM is its unique
ability to provide a complete problem solution in terms of boundary
values only, with substantial savings in computer time and data
preparation effort.
An initial restriction of the BEM was that the fundamental solution
to the original partial differential equation was required in order to
obtain an equivalent boundary integral equation. Another was that
non-homogeneous terms accounting for effects such as distributed loads
were included in the formulation by means of domain integrals, thus
making the technique lose the attraction of its `boundary-only' character.
Many different approaches have been developed to overcome these
problems. The most successful so far is the dual reciprocity method
(DRM), which is the subject matter of this book. The basic idea behind
this approach is to employ a fundamental solution corresponding to a
simpler equation and to treat the remaining terms, as well as other
non-homogeneous terms in the original equation, through a procedure
which involves a series expansion using global approximating functions
and the application of reciprocity principles.
The dual reciprocity procedure is completely general and
conceptually simple. In this book, the method is applied to both two-
and three-dimensional problems, some of which include nonlinear and
transient effects.

Zhao, Z.
Shape Design Sensitivity Analysis and Optimization using the Boundary
Element Method

Lecture Notes in Engineering - Vol 62
ISBN: 3 540 53518 7
ISBN: 0 387 53518 7
This book investigates the various aspects of shape optimization of
two-dimensional continuum structures, including shape design
sensitivity analysis, structural analysis using the boundary element
method (BEM), and shape optimization implementation.
The book begins by reviewing the developments of shape
optimization, followed by the presentation of the mathematical
programming methods for solving optimization problems. The basic theory
of the BEM is presented which will be employed later on as the
numerical tool to provide the structural responses and the shape design
The key issue of shape optimization, the shape design
sensitivity analysis, is fully investigated. A general formulation of
stress sensitivity using the continuum approach is presented. The
difficulty of the modelling of the adjoint problem is studied, and two
approaches are presented for the modelling of the adjoint problem. The
first approach uses distributed loads to smooth the concentrated
adjoint loads, and the second approach employs the singularity
subtraction method to remove the singular boundary displacements and
tractions from the BEM equation.
A novel finite difference based approach to shape and
design sensitivity is presented, which overcomes the two drawbacks of
the conventional finite difference method. This approach has the
advantage of being simple in concept, and easier in implementation.
A shape optimization program for two-dimensional
continuum structures is developed, including structural analysis using
the BEM, shape design sensitivity analysis, mathematical programming,
and the design boundary modelling. Some numerical examples are used to
demonstrate the proposed formulations for shape design sensitivity
analysis and shape optimization implementation.


Amini, S., Harris, P.J. and Wilton, D.T.
Coupled Boundary and Finite Element Methods for the Solution of the
Dynamic Fluid-Structure interaction Problem

Lecture Notes in Engineering - Vol 77
This text considers the problem of the dynamic fluid-structure
interaction between a finite elastic structure and the acoustic field
in an unbounded fluid-filled exterior domain.
The exterior acoustic field is modelled through a boundary
integral equation over the structure surface. However, the classical
boundary integral equation formulations of this problem either have no
solutions or do not have unique solutions at certain characteristic
frequencies (which depend on the surface geometry) and it is necessary
to employ modified boundary integral equation formulations which are
valid for all frequencies. The particular approach adopted here
involves an arbitrary coupling parameter and the effect that this
parameter has on the stability and accuracy of the numerical method
used to solve the integral equation is examined.
The boundary integral analysis of the exterior acoustic problem is
coupled with a finite element analysis of the elastic structure in
order to investigate the interaction between the dynamic behaviour of
the structure and the associated acoustic field. Recently there has
been some controversy over whether or not the coupled problem also
suffers from the non-uniqueness problem associated with the classical
integral equation formulations of the exterior acoustic problem. This
question is resolved by demonstrating that the solution to the coupled
problem is not unique at the characteristic frequencies and that it is
necessary to employ an integral equation formulation valid for all
Numerical results are presented and discussed for both the
uncoupled acoustic problem and the coupled fluid-structure interaction
problem for a number of axisymmetric and fully three-dimensional
problems. In particular, the method is applied to the coupled problem
of a piezoelastic ring sonar transducer transmitting an acoustic signal
in water for which reasonable agreement between the theoretical
predictions and some experimental results is observed.

Antes, H. and Panagiotopoulos, P.D.
The Boundary Integral Approach to Static and Dynamic Contact Problems
Birkhauser Verlag
ISBN: 3 7643 25925
ISBN: 0 8176 2592 5
The aim of the present book is the formulation and study of boundary
integral equation methods for static and dynamic contact problems. The
cases of equality and inequality constraints are both examined. The
former lead to classical boundary integral equations, whereas the
inequality constraints lead to multivalued boundary integral equations.
In parallel to the formulation and the mathematical study, numerical
examples help to illustrate the theories presented.
This book is the first one to deal with multivalued boundary integral
equations in the theory of elasticity, with cracks involving unilateral
contact and friction interface conditions, with boundary integral equations
formulated on interfaces and boundaries of fractal geometry, and finally
with the neural network approach to multivalued boundary integral
equations resulting in inequality contact problems.

Becker, A.A.
The Boundary Element Method in Engineering-A Complete Course
McGraw-Hill Book Company
ISBN: 0 07 707415 7,  335 p. ,   £21.95

This textbook provides a complete course on the Boundary Element (BE)
method aimed specifically at engineers and engineering students. No
prior knowledge of advanced mathematics or numerical techniques is
assumed. This self-contained book provides an introduction to the BE
method as well as a foundation for further research.

Special features include :
. The mathematical principles are contained in one chapter - this
chapter can either be referred to occasionally or omitted altogether
without affecting the understanding of the BE formulation.
. A step-by-step approach is used to derive the numerical implementation
of the BE method.
. The final chapter fully describes a FORTRAN
computer program using isoparametric quadratic elements for
two-dimensional and axisymmetric elastostatic problems.
. Full listing of the program, a description of the main variables, as well as a
separate user's manual are provided in appendices.

CONTENTS : Introduction. Mathematical Background. Two-Dimensional
Potential Problems. Two-Dimensional  Elastostatic Problems.
Three-Dimensional Potential and Elastostatic Problems. Axisymmetric
Potential and Elastostatic Problems. Thermoelastic Problems.
Multi-Domain and Contact Problems. Fracture Mechanics Problems. Review
of Non-Linear Problems. Further Applications : coupling BE and FE
techniques, centrifugal loading, axisymmetric geometries with
arbitrary boundary conditions, infinite boundary elements,
time-dependent potential problems. BE Computer Program (BEACON).
User's Manual. List of Main Variables. Full Listing of BEACON.

Beer, G. and Watson, J.O.
Introduction to Finite and Boundary Element Methods for Engineers
ISBN: 0 471 92813 5
This book is a readable yet accurate introduction to the theory and
practice of two computational techniques: the well established and
versatile finite element method (FEM) and the less widely accepted but
very promising boundary element method (BEM). The text is introductory
in the sense that a relatively narrow range of problems is considered, but
advanced in its treatment of the theoretical and practical aspects of that
range of problems.
Where possible, a unified presentation of the numerical
implementations of the two methods is given. By means of examples of
applications it is demonstrated which problems may best be solved by
each method, or by a combination of the methods. Two computer
programs written in FORTRAN are included to show programming
techniques used to implement both methods and to allow readers to
become familiar with their use. The book will appeal to undergraduate
and postgraduate students, practising engineers and developers of
numerical modelling software.

Camp, C.V. and Gipson, G.S.
Boundary Element Analysis of Nonhomogeneous Biharmonic Phenomena
Lecture Notes in Engineering - Vol 74

260 pp
ISBN: 3 540 55020 8

Chen, G. and Zhou, J.
Boundary Element Methods
Academic Press
ISBN: 0 12 170840 X

Chen, J.T. and Hong, H.K.
Boundary Element Method (Second Editon)
Taipei Publ
This book gives a compact and unified potential theory of boundary
element methods in selected analysis, Laplace equation and crack
problem. The hypersingular integral formulation is emphasized to treat
the degenerate boundary value problems, eg. Darcy flow around a cutoff
wall and crack problem in elasticity. The dual integral equations are
derived amd the dual boundary element method (DBEM) is implemented. It
consists of nine chapters. Chapter 0 gives a literature review and
introduction. Chapter 1 is concerned with the associated
preliminaries. Chapter 2 is devoted to the computational algorithm
of discretization of integral equations. The applications of the dual
integral formulation in Laplace equation and crack problem are
presented in chapters 3 and 4, respectively. The integral
representations of J2 flow elastoplasticity is derived from the rate
equation model in chapter 5. Chapter 6 discusses the mechanism of the
fictitious eigenvalues of the integral formulation of Helmholtz
equation. Chapter 7 derives a unified integral solution of the time
dependent boundary condition problems and applied to the earthquake
engineering. Chapter 8 contains the comparison of BEM and FEM and
discusses the coupling use. Chapter 9 summarizes a short conclusion.
The references contain three parts, thesis in Taiwan, papers and textbooks.

Hayami, K.
A Projection Transformation Method for Nearly Singular Surface Boundary
Element Integrals


VIII+456 pp
ISBN: 3 540 55000 3

Pozrikidis, C.
Boundary Integral and Singularity Methods for Linearized Viscous Flow
Cambridge University Press
ISBN: 0 521 40502 5(hardback)
ISBN: 0 521 40693 5 (paperback)
Over the last two decades, boundary integral and singularity methods
have enjoyed increasing popularity, and have become a viable alternative
to traditional theoretical and computational methods of mathematical
engineering and physics. Their development continues to be a topic of
active research, especially in the areas of potential theory, solid
mechanics, and fluid mechanics.
The aim of this book is to bring together classical and recent
developments in the particular field of Newtonian flow at low Reynolds
numbers. The methods are developed from first principles, alternative
formulations are compared, and a variety of configurations are addressed.
The proper mathematical framework is discussed in the context of
functional analysis and integral-equation theory, and procedures of
numerical solutions in the context of the boundary element method are
introduced. The text contains original material pertaining to the properties
and explicit form of the Green's functions, and the theory of the integral
equations that arise from boundary integral representations.
The targeted audience includes graduate students and academic or
industrial researchers in engineering, computer science, and applied
mathematics. The only prerequisites are fundamental knowledge of
fluid mechanics, functional analysis, and numerical methods.

Wrobel, L.C. and Brebbia, C.A.
Boundary Element Methods in Heat Transfer
Computational Mechanics Publications
ISBN: 1 85312103 7
ISBN: 0 945824 86 6 (US, Canada, Mexico)
Heat transfer problems in industry are usually of a very complex
nature, simultaneously involing different transfer modes such as
conduction, convection, radiation and others. Beacause of this, very
few problems can be solved analytically and one generally has to resort
to numerical analysis.
The boundary element method is a numerical technique which has
been receiving growing attention for solving heat transfer problems
because of its unique abiltiy to confine the discretization process to
the boundaries of the problem region. This allows major reductions in
the data preparation and computer effort necessary to solve complex
industrial problems.
The purpose of this book is to present efficient algorithms used
in conjunction with the boundary element method for the solution of
steady and transient, linear and non-linear heat transfer problems. It
represents the state-of-the-art of boundary element application in the
field of heat transfer, and constitutes essential reading for
researchers and practising engineers involved with the important topic.


Dominguez, J.
Boundary Elements in Dynamics
Computational Mechanics Publications
ISBN: 1 85312 258 0
ISBN: 1 56252 182 9 (US, Canada, Mexico)
The main emphasis of this book is on the development of the different
boundary element formulations for time-dependent problems and the
necessary mathematical transformations to produce computer codes which
are able to solve scalar, elastic and poroelastic wave propagation
problems. There is also a substantial part of the book which covers the
application of the boundary element method to important engineering
problems in dynamics. The book is a result of the author's involvement
over a period of sixteen years in the field of boundary elements, and
of boundary elements in dynamics in particular. The mathematics
developed in the book is at a level to make it as self-contained as
possible. Readers with almost no background in boundary elements or in
dynamics should be able to follow the text.
The purpose of this book is two-fold. It is intended to provide a
reference book for researchers and engineers, and at the same time
provide a text from which scientists can learn in detail the
formulation, implementation and practical applications of the boundary
element method in dynamics. The book could serve as an advanced level
text to a course on boundary elements in dynamics or as a supplement to
other books in a more general course.

El-Zafrany, A.
Techniques of the Boundary Element Method
Ellis Horwood
ISBN: 0 13 898511 1
This is one of the first books on the boundary element method to be
specifically aimed at students. Written in such a way as to prove
acceptable to engineering students, mathematicians and practising
engineers, the book outlines the basic steps necessary for a full
understanding of the direct boundary element method.
Intended as a `stand alone' text this book's no-nonsense approach
to this complex subject will make it a welcome addition to the

Nachbin, A.
Modelling of Water Waves in Shallow Channels
Topics in Engineering - Vol 13
Computational Mechanics Publications
ISBN: 1 85312 135 5
ISBN: 1 56252 062 8 (US, Canada, Mexico)
ISSN: 0952 5300 (series)
This book constitutes an invaluable tool in the numerical study of
a wide range of linear water wave problems. It is expected that the material
presented will appeal to scientists and engineers, from both the theoretical
and computational point of view.
Chapter 1 presents an introduction to the theory and the partial
differential equations governing water wave propagation. For the reader
inclined towards computations, Chapters 2, 3 and 4 contain a very
detailed presentation of each method, a careful study of their numerical
stability, (i.e. numerical dispersion relation) and a series of numerical
experiments showing that the boundary element method performs very
well. Not only is this method accurate over a long time interval, but the
method is sensitive to small scale components of the topography. This
is a useful property because it allows the modelling of a more complete
and detailed bottom surface. Chapter 5 includes new results which
account for the quantitative agreement between theory and computations.

Portela, A.
Dual Boundary Element Analysis of Crack Growth
Topics in Engineering - Vol 14
Computational Mechanics Publications
ISBN: 1 85312 187 8
ISBN: 1 56252 116 0 (US, Canada, Mexico)
ISBN: 0952 5300 (series)
This book describes the dual boundary element method and its application
to the analysis of fatigue crack-growth problems, in the context of the
damage tolerance analysis with linear elastic fracture mechanics.
The dual boundary element method which incorporates two
independent boundary integral equations, uses the displacement equation
to model one of the crack boundaries and the traction equation to model
the other. As a consequence, the analysis of general crack problems can
be performed effectively in a single-region formulation. The dual
boundary integral equations, derived from the work theorem, are
defined in terms of Cauchy and Hadamard principal value integrals that
are computed directly over discontinuous boundary elements by means
of finite-part integrals.
The stress intensity factors are evaluated by the techniques of the
singularity subtraction and the J-integral. The basic formulation of the
singularity subtraction technique is first extended for the single-region
analysis of non-symmetrical problems. A general formulation of this
technique is then presented for the solution of problems of piece-wise
straight cracks, through an automatic partition of the problem domain.
The J-integral is the most efficient technique used in the dual boundary
element method to solve general crack problems. The decomposition
method, used to decouple the stress intensity factors in mixed-mode
problems, is implemented automatically by considering a small circular
contour path around each crack tip.
Fatigue crack growth is simulated with an incremental crack-
extension analysis. Each crack-path increment is first predicted by the
maximum principal stress criterion and then corrected to account for the
discreteness of the analysis. For each increment of the crack extension.
the dual boundary element method is applied to perform a stress analysis
of the structure and the J-integral technique is applied to compute the
stress intensity factors. When the crack extension is discretized with
new boundary elements, remeshing is not required by virtue of the
single-region analysis, an intrinsic feature of the dual boundary element
method. As a consequence, the solution of the system of algebraic
equations that is usually the most time-consuming stage, can be
performed quite efficiently by an incremental LU decomposition
The accuracy and efficiency of the dual boundary element method
are both demonstrated with the solution of several crack problems.
Finally, an engineering application of the dual boundary element
incremental analysis of fatigue crack growth is presented for a pin-
loaded lug problem.


Banerjee, P.K.
The Boundary Element Methods in Engineering
ISBN: 0 07 707769 5
The last two decades have seen the emergence of a versatile and
powerful method of computational engineering mechanics, namely the
boundary element method.
The Boundary Element Methods in Engineering looks at the massive
development of this technology and describes its formulation for almost
all applications. For ease of use, a simple utilitarian and tutorial
approach is adopted in the initial chapters, introducing the basic
background necessary to learn the method. Simple, but detailed
instructions for its application to heat transfer (potential flow) and
stress analyses are offered, before the book moves on to a
progressively advanced level in later chapters. Numerous case studies
are employed for a large number of applications in dynamics, vibration,
fluid flow and nonlinear mechanics, making this a comprehensive guide
for all engineers interested in the use of these methods in a wide
range of engineering problems.
Special features include:
* Accessible design, with numerous examples
* Detailed discussion of computer applications
* A new approach to the analysis of solids with holes and

do Rego Silva, J.J.
Acoustic and Elastic Wave Scattering using Boundary Elements
Topics in Engineering - Vol 18
Computational Mechanics Publications
ISBN: 1 85312293 9
ISBN: 1 56252 217 5 (US, Canada, Mexico)
ISSN: 0952 5300
The present work deals with the propagation of acoustic and elastic
harmonic waves in three-dimesional regions. The problems are formulated
using integral equations, and their numerical solution obtained through
the boundary element method. The book contains both the theoretical
support to the integral equation theory and extensive discussions on
the numerical aspects involved in the computational implementation.
The main focus of the book is on formulations involving
hypersingular integrals. The smoothness conditions for the existence of
these integrals are examined in detail, forming the basis for the
mathematical justification of the algorithms employed. Their numerical
implementation is discussed in a coherent manner, especially regarding
the use of isoparametric continuous elements.
An important aspect of the present work is a formulation for
exterior acoustic problems which is valid for any value of frequency.
This formulation, originally suggested by Panich, is implemented and
compared to the more popular formulation of Burton and Miller.
Finally, a new integral formulation is presented for elastic wave
propagation problems. A rigorous proof of uniqueness of solution and
the requirement condition for the existence of the hypersingular
integral is included, showing that this new technique is numerically
reliable for any value of frequency.

Hall, W.S.
The Boundary Element Method
Kluwer Academic Publishers
ISBN: 0 7923 2580 X
The Boundary Element Method sets out a simple, efficient and cost
effective computational technique which provides numerical solutions -
for objects of any shape - for a wide range of scientific and
engineering problems.
The Boundary Element Method provides a complete approach to
formulating boundary integral equations for scientific and engineering
problems and solving them numerically using an element approximation.
Only a knowledge of elementary calculus is required, since the text
begins by relating familiar differential equations to integral
equations and then moves on to the simple solution of integral
equations. From this starting point, the mathematics of formulation and
numerical approximation are developed progressively with every
mathematical step being provided. Particular attention is paid to the
problem of accurate evaluation of singular integrands and to the use of
increasing levels of accuracy provided by constant, linear and
quadratic approximations. This enables a full solution to be given for
both two dimensional and three dimensional potential problems and
finally, for the two dimensional elastostatics problem.
The Boundary Element Method develops the mathematics of the text
progressively both within chapters and from chapter to chapter. It is
a self-contained, step by step, exposition of the Boundary Element
Method leading to its application to the key problem of elastostatics.
The Boundary Element Method serves as a standard introductory
reference text for the mathematics of this method and is ideal for
final year undergraduate study as well as for postgraduates, scientists
and engineers new to the subject. Worked examples and exercises are
provided throughout the text.

Ingham, D.B. and Yuan, Y.
The Boundary Element Method for Solving Improperly Posed Problems
Topics in Engineering - Vol 19
Computational Mechanics Publications
ISBN: 1 85312291 2
ISBN: 1 56252 215 9 (US, Canada, Mexico)
ISSN: 0952 5300
In recent years an increasing amount of research work has been carried
out on the application of the Boundary Element Method (BEM) to a
growing variety of problems. The purpose of this book is to extend the
range of applications of the BEM, with a view to establishing a sound
basis on which to build new solution procedures with particular
attention being paid to problems which arise in inverse heat conduction.
The minimal energy technique has been introduced to modify the BEM
for solving inverse heat conduction problems which are improperly posed
and the results indicate that excellent convergent and stable numerical
approximate solutions may be obtained for various inverse heat
conduction problems, which may be linear or nonlinear, steady or
unsteady. Examples show that the agreement between the numerical
results and the analytical solutions, where available, is excellent.

Kane, J.H.
Boundary Element Analysis in Engineering Continuum Mechanics
Prentice Hall
ISBN: 0 13 086927 9

Leitao, V.M.A.
Boundary Elements in Fracture Mechanics
Topics in Engineering - Vol 21
Computational Mechanics Publications
ISBN: 1 85312335 8
ISBN: 1 56252 259 0 (US, Canada, Mexico)
ISSN: 0952 5300
This book provides a new elastoplastic formulation for the analysis of
problems in nonlinear fracture mechanics. The method relies on the use
of two independent boundary integral equations, thus `the elastoplastic
dual boundary element method' (EPDBEM). The two equations of the method
are the displacement equation on one face of the crack and the traction
equation on the opposite face. This feature allows for the analysis of
general mixed-mode crack problems within a single-region formulation.
The EPDBEM formulation was applied to the problem of cracks
growing in ductile materials in the presence of residual stresses. In
particular, the formulation is used to investigate the effect of
prestressing on the behaviour of fatigue cracks. Special emphasis is
given to the redistribution (relaxation) of the residual stresses due
to the presence and growth of the cracks. This application is
complemented by another, based on linear elastic fracture mechanics
concepts, in which the superposition of the residual stress and fatigue
stress fields is used. Superposition is also used to investigate the
effect of cold-working open holes on the behaviour of fatigue cracks.
An elastic boundary element formulation incorporating weight functions
is used for the calculation of stress intensity factors. Crack growth
rates are predicted and compared to experimental results.

Man, K.W.
Contact Mechanics using Boundary Elements
Topics in Engineering - Vol 22
Computational Mechanics Publications
ISBN: 1 85312334 X
ISBN: 1 56252 258 2 (US, Canada, Mexico)
In this book, a Boundary Element formulation for solving structural
problems associated with frictional contact is presented; it develops
and uses an efficient iterative and fully loaded-incremental technique.
Problems with any number of two-dimensional bodies in contact can be
analysed using this technique; the bodies may be conforming or
non-conforming, of similar or dissimilar materials. The interface may
be frictionless or frictional and may undergo slip or partial slip.
Both symmetrical and non-symmetrical progressive contact problems in
the presence of friction are solved. Numerical solutions of both normal
and tangential traction distributions can be obtained automatically for
successive load increments.
The problem of ensuring that stress intensity factor solutions for
cracked bodies are accurately calculated continues to be a major
consideration in design, particularly in the presence of fretting
forces. In this book, the technique for solving problems in cracked
structures is presented for configurations which require a non-linear
analysis of the contact conditions. Stress intensity factors are
evaluated at the end of each load step using the J-integral method.

Power, H. and Wrobel, L.C.
Boundary Integral Methods in Fluid Mechanics
Computational Mechanics Publications
ISBN: 1 85312252 1
ISBN: 1 56252 176 4 (US, Canada, Mexico)
Physical phenomena are usually described methematically in terms of
partial differential equations. In many cases, an alternative (and
equivalent) mathematical representation of the problem can be found in
terms of integral equations. The theory of integral equations was
originally developed in mathematics as a tool for proving uniqueness
and existance of solutions of related partial differential equations.
Since the beginning of the century, the integral equations theory has
been an important subject in applied mathematics. Nowadays, due to
advances in numerical methods and computer facilities, this approach
can be used in the actual simulation of physical phenomena. One of the
most effective numerical techniques to solve integral equations is the
boundary element method.
Fluid mechanics is one of the main topics of applied mathematics
and physics. Some of the most relevant theories of these sciences have
been found during the study of fluid flow problems. Fluid dynamics is
also one of the most challenging areas of computational mechanics, the
simulation of fluid motion being a series test for any numerical
method, particularly for nonlinear problems. Integral equation
techniques offer an attractive alternative for the numerical solution
of a wide variety of problems in fluid dynamics.
The majority of mathematical books on integral equations are
purely theoretical, while the majority of engineering books give
emphasis on numerical solutions using boundary elements, with very
little theoretical background. This book intends to provide a bridge
between the engineering and mathematics literature on integral equation
techniques, particularly in the field of fluid dynamics. The main
subject of this book is the integral equation modelling of the flow of
incompressible viscous fluids.
The book is divided into seven chapters. The first three are
introductory, presnting an in-depth review of basic concepts of fluid
mechanics, integral equations, and potential theory, respectively.
Chapter 4 describes numerical techniques for solution of selected
potential problems with particular features like moving boundaries.
Chapters 5 to 7 cover the mathematical formulation and numerical
solution of creeping flow problems described by the Stokes equations,
and includes a thorough description of the completed double-layer
integral equation method originally developed by one of the authors.
Finally, Chapter 8 presents several numerical algorithms for solution
of the Navier-Stokes equations.

Schclar, N.A.
Anisotropic Analysis using Boundary Elements
Topics in Engineering - Vol 20
Computational Mechanics Publications
ISBN: 1 85312333 1
ISBN: 1 56252 257 4 (US, Canada, Mexico)
This book investigates the use of the Boundary Element Method to solve
three dimensional anisotropic potential and elastic problems.
Anisotropic analysis has been one of the major stumbling blocks for the
application of boundary elements in solving practical engineering
problems. This work comprises the numerical implementation of the well
known anisotropic fundamental solution and a new formulation based on
more recent work on the Dual Reciprocity Method. In both cases the
objective of the research is to produce a boundary only formulation
which retains the main advantage of the technique.
The new Dual Reciprocity Boundary Element formulation presented
here uses the fundamental solution for isotropic elasticity. The Dual
Reciprocity Method is used to model the anisotropy by expressing the
elastic constants as the sum of average isotropic values plus a
deviation and taking the resulting domain integrals to the boundary in
the usual manner. The technique is also extended to deal with any type
of body force.
A series of representative numerical examples are presented and
discussed to demonstrate the accuracy of the two methods used by the
author. Comparisons are carried out with analytical and other numerical
Finally, a new adaptive technique is developed for the automatic
definition of the number and position of the internal points in the
Dual Reciprocity Boundary Element and error estimators are presented.
This book constitutes the most up to date work on the use of
boundary elements for anisotropic problems. It is addressed to
engineers involved in the development of boundary element computer
codes as well as researchers in academia and industry.

Trevelyan, J.
Boundary Elements for Engineers: Theory and Applications
Computational Mechanics Publications
ISBN: 1 85312279 3
ISBN: 1 56252 203 5 (US,
Canada, Mexico)
The book is designed to make BEM more accessible to students and
engineers looking for a concise overview of the method and the
mathematics behind it. The book also contains many examples of
realistic engineering analysis problems, describing how the BEM can be
applied most effectively.
The problem with the boundary element method is that, although the
end-user BEM software appears refreshingly simple, the theory behind it
is rarely described with anything approaching that simplicity. Text
books are widely available for the academic engineer, but not so for
the practising engineer. This book addresses the engineer's
requirements of a technical book including: the need to see an overview
of the theoretical formulation written in terms of engineering instead
of pure mathematics; and enough theory to feel comfortable with the use
of BEM software in production analysis, but not in a level of detail
which overcomplicates and clouds the main issues. The book provides
example application areas, and most importantly some indications of how
to use BEM software effectively in practice for real engineering problems.
This book results from several years of experience in working with
a commercial boundary element software package, BEASY, in a training
and support environment to industrial corporations using this code. In
this way, the book provides a combination of theory and practice in the
application of boundary elements to real world engineering.





Kirkup, S.
The Boundary Element Method in Acoustics
Integrated Sound Software, UK

Sládek, V. and Sládek J.
Singular Integrals in Boundary Element Methods
Computational Mechanics Publications
ISBN: 1 85312 533 4
ISSN: 1460-1419

   Boundary Element Methods (BEM) use singular solutions, in contrast to other discretization methods, such as finite element or finite difference methods. The presence of the mathematical singularity gives rise to the need for accurate computation of singular integrals. The appearance of singular integrals in BEM formulations is often considered a handicap in computation. However, they can be a source of effectiveness and stability in numerical solutions, if they are properly treated.

   This book provides a theoretical and numerical treatment for singular integrals in BEMs. Both the boundary and domain integrals are considered in two and three dimensional boundary value problems, while the use of symbolic computation and the formulation using complex arithmetic in the case of plane problems are outlines. The formulations given deal with potential problems, elasticity, plate and crack problems.

   Describing techniques which are universal in character and can be applied to a wide variety of engineering problems, this book will enable readers to understand the nature and treatment of singular integrals in BEMs.


M. Bonnet
Boundary Integral Equation Methods for Fluids and Solids
J. Wiley and Sons
ISBN 0471 97184 7
Going far beyond the standard texts, this book extensively covers boundary integral equation (BIE) formulations and the boundary element method (BEM). The first section introduces BIE formulations for potential and elasticity problems, following the modern regularization approach- the fundamental starting point for research in this field. Secondly, a clear description of BIE formulations for wave and elastodynamics problems, in both time and frequency domains is presented. Finally, recent research in the field, related to variational integral formulations, use of geometrical symmetry, shape sensitivity and fracture mechanics is summarised. Within the text a broad range of application areas, industrial as well as research related, are examined. These include:

  • elasticity and small-strain elastoplasticity;
  • time-domain and frequency-domain scalar and elastic waves
  • fracture mechanics

Including an extensive bibliography, this text will be of considerable value and interest to graduate students, researchers and lecturers in engineering mechanics, applied maths and physics, as well as industrial practitioners working within these areas.


Books published in year 2000 and onward are listed in New Books section