Edited Advances, Progress, Special Topic Books


Banerjee, P.K. and Butterfield, R. (Eds)
Developments in Boundary Element Methods - 1
Elsevier Applied Science Publishers
292 pp
ISBN: 0 85334 845 6
The book is intended to demonstrate the versatility and power of BEM.
It covers the applications to a wide range of complex practical
problems. Many subjects are covered in ten chapters, including new
concepts of BEM, non-linear problems of potential flow, implementation
of BEM for 2-D and 3-D elastostatics, 2-D and 3-D problems of
elastoplasticity, 2-D and 3-D problems of fracture mechanics, analysis
of wave problems, BEM in thermoelasticity, analysis of plates and
shells, applications in electrical engineering, and coupling with other
numerical methods. List of contributors, with addresses, and Index
complete the book.


Brebbia, C.A. (Ed.)
Progress in Boundary Element Methods
Vol 1
Pentech Press
315 pp
ISBN: 0 7273 1610 9
The book presents the fundamentals of the BEM, and applications to
different areas of engineering. Nine chapters of the book present the
following topics: basis of boundary elements, fundamental solutions,
potential theory, elastostatics, plasticity, time-dependent potential
problems, elastodynamics, combined boundary element and finite element
methods, and mathematical aspects on asymptotic accuracy and
convergence. A list of contributors and Index complete the book.


Banerjee, P.K. and Shaw, R.P. (Eds)
Developments in Boundary Element Methods - 2
Elsevier Applied Science Publishers
288 pp
ISBN: 0 85334 112 5
The book aims to demonstrate the versatility and power of the BEM. It
covers the applications to a wide range of complex practical problems.
Many subjects are covered in nine chapters. This volume has been
restricted to time-dependent problems in engineering. Topics included
are: BE formulation for melting and solidification, transient flow
through porous elastic media, applications to water wave problems,
general viscous flow, time-dependent inelastic deformation of metals,
determination of eigenvalues, transient stress analysis of tunnels and
caverns, analysis of hydrodynamic loads, and acoustic emissions from
submerged structures. List of contributors, with addresses, and Index
complete the book.


Brebbia, C.A. (Ed.)
Progress in Boundary Element Methods
Vol 2
Pentech Press
217 pp
ISBN: 0 7273 1611 7
The book presents the recent developments in BEM. This volume contains
eight chapters representing new developments on the subject or reviews
of recent literature in a particular area. Subjects covered are as
follows: inhomogeneous heat conduction problems, pressure waves in
liquid sodium in a pressure vessel, fracture mechanics and bibliography
review, 2-D and 3-D body force loading problems, BEM application to 2-D
contact problems with and without friction, bending of thin plates,
fluid-shell interaction and fluid-solid impact problems, viscosity and
creep problems.


Banerjee, P.K. and Mukherjee, S. (Eds)
Developments in Boundary Element Methods - 3
313 pp
ISBN: 0 85334 253 9
The book aims to demonstrate the versatility and power of the BEM. It
covers applications to a wide range of complex practical problems. This
volume is designed to describe the developments in non-linear problems
of solid and fluid mechanics. Subjects covered in ten chapters are as
follows: application of BEM for 3-D problems of elastoplasticity and
viscoplasticity, formulations for large strain - large deformation
problems of plasticity and viscoplasticity elastoplastic analysis by
indirect methods, non-linear problems of fracture mechanics, large
deflection analysis of thin elastic plates, time-dependent
Navier-Stokes flow, non-linear water wave problems, non-linear sloshing
problems, integration schemes for 2-D and 3-D non-linear analysis, and
linear and non-linear problems in aero- and hydrodynamics. List of
contributors, with addresses, and Index complete the book.

Brebbia, C.A. (Ed.)
Progress in Engineering Series
Vol V
Computational Mechanics Publications
100 pp
ISBN: 0 905451 27 9
The book contains a series of papers on boundary elements published in
the Engineering Analysis, Applied Ocean Research and Advances in
Engineeering Software journals. The papers are extracted and edited
versions of those published in the journals. They deal with fluid flow
applications, thermoelastic problems, hydrodynamics, seepage,
structural vibrations and microcomputer applications.

Brebbia, C.A. (Ed.)
Topics in Boundary Element Research
Vol 1 - Basic Principles and Applications
260 pp
ISBN: 0 387 13097 7
The book is aimed at the state-of-the-art in current research activity
in the boundary element method. Chapters included in the book cover:
review of formulations of BEM, transient heat conduction problems,
thermoelastic fracture mechanics, fluid mechanics problems, water wave
analysis, interelement continuity in BEM, applications in geomechanics,
applications to mining problems, combined BEM/FEM methods, and finite
deflection of plates.


Brebbia, C.A. (Ed.)
Topics in Boundary Element Research
Vol 2 - Time-Dependent and Vibration Problems
260 pp
ISBN: 0 387 13993 1
The book is aimed at the state-of-the-art in the solution of
time-dependent and vibration problems. Chapters included in the book
cover: boundary integral equation methods in elastodynamics, elastic
potentials in BIE formulations, time-dependent non-linear potential
problems, transient scalar waves, boundary integral formulation of mass
matrices for dynamic analysis, and asymptotic accuracy and convergence
for point collocation methods.


Banerjee, P.K. and Watson, J.O. (Eds)
Development in Boundary Element Methods - 4
Elsevier Science Publishers
346 pp
ISBN: 0 85334 376 4
The book aims to demonstrate the versatility and power of the BEM. It
covers the applications to a wide range of complex practical problems.
Different subjects not covered in previous volumes are presented in eight
chapters, namely: Hermitian cubic boundary elements, 3-D transient
(hyperbolic) dynamic analysis, stress analysis of axisymmetric bodies
subjected to asymmetric loading, new plate bending formulation,
non-linear deformation analysis of sandwich plates and shallow shells,
transient non-linear heat transfer analysis, non-linear analysis of
geomechanics problems (BEM/FEM), review of modelling of fluid flow
problems in the aircraft industry. List of contributors, with
addresses, and Index complete the book


Beskos, D.E. (Ed.)
Boundary Element Methods in Mechanics
Computational Methods in Mechanics - Vol 3
Computational Mechanics Publications
598 pp
ISBN: 0 444 87990 0
The book presents a collection of 12 chapters on different BEM topics
written by some of the best researchers. It contains the following
chapters: introduction, potential theory, elastostatics, two chapters
on elastodynamics, non-linear problems, fracture mechanics, fluid
mechanics, acoustics, heat conduction problems and thermoelasticity,
dynamics of soil-structure interaction and fluid-structure interaction.

Brebbia, C.A. (Ed.)
Applications in Geomechanics
Topics in Boundary Element Research - Vol 4
172 pp
ISBN: 0 387 17497 4
This volume studies the applications of the method to a wide variety of
geomechanics problems, most of which are ideally suited for boundary
elements. The eight chapters in this volume bring together a series of
recent advances made in the applications of BEM for soil mechanics,
soil-structure interaction, consolidation, foundations, saltwater
intrusion and groundwater flow problems.

Brebbia, C.A. (Ed.)
Computational Aspects
Topics in Boundary Element Research - Vol 3
288 pp
ISBN: 0 387 16113 9
This book deals with the computational aspects of boundary elements and
includes fully operational codes for potential and elastostatics. It
consists of nine chapters: numerical convergence for transient heat
conduction, viscoelastic problems, numerical integration, computational
aspects of boundary elements, the Edge Function method, multigrid
methods, complex variable boundary elements, software for potential
problems and software for elastostatics. A subject index completes the


Mackerle, J. and Brebbia, C.A. (Eds)
The Boundary Element Reference Book
Computational Mechanics Publications
382 pp
ISBN:0 905451 74 0
This handbook is intended to provide boundary element practitioners
with a reference book dealing with the most important boundary element
publications and the most up to date codes. The book is divided into
four sections: development of the BEM, the BE books written up to now
with a brief description of their contents, BE codes description
(general purpose and special purpose programs), and Who's Who of
Boundary Elements with details of the best known practitioners in
industry and academia.

Stein, E. and Wendland, W.L. (Eds)
Finite Element and Boundary Element Techniques from Mathematical and
Engineering Point of View

No 301
CISM International Centre for Mechanical Sciences
Courses and Lecture
333 pp
ISBN: 3 211 82103 1
Traditional FEM and the more recent BEM are underlying many engineering
computational methods and corresponding software. Both methods have
their merits and their restrictions. Therefore, the combination of both
methods will provide an improved numerical tool in the future.
The aim of this book is to present significant basic formulations
of FEM and BEM and to show their common practical and mathematical
foundations, their differences as well as possibilities for their
combination. These include variational foundations, FEM and BEM for
linear and nonlinear elasticity and potential problems, the combination
of FEM-BEM asymptotic error analysis, modifications due to corner and
crack singularities and corresponding improvement of convergence,
plastic analysis, numerical algorithms and engineering applications.


Brebbia, C.A. (Ed.)
Viscous Flow Applications
Topics in Boundary Element Research - Vol 5
181 pp
ISBN: 0 387 50609 8
This book presents the state-of-the-arts 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 comprehensive 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 and Massachusetts Institute of
Technology researchers. Chapter 3 describes the generalized formulation
for unsteady viscous flow problems developed over many years at Georgia
Institute of Technology. This formulation has been extensively applied
to solve aerodynamic problems. The approach followed in Chapter 4 is
the velocity-vorticity formulation plus the inclusion of special
integral expressions for the energy equation and the computation of
pressure fields. The approach has been validated by numerical
experiments and represents the work carried out at Computational
Mechanics Institute, University of Maribor and University of Nuremberg.
The procedure proposed in Chapter 5 for the solution of steady state
Navier-Stokes type problems is different from that in Chapters 2 and 3
as it is based on a pseudo-body force formulation employing the penalty
function approach. This technique has been developed at Toshiba in
collaboration with Computational Mechanics Institute.
Chapter 6 discusses how the boundary layer effect can be introduced in
potential flow. It deals with the coupling of FDM and BEM. The authors
at DFVLR Gottingen proposed solving the boundary layer flow using
infinite difference and then combining that solution with boundary
elements for the outer flow.
Chapter 7 is based on the research carried out at Western Australia
University for the solution of non-Newtonian fluid also using a concept
of `pseudo forces' related to that described in Chapter 4. The last
chapter of the book deals with the solution of Stokes flow as a
particular type of viscous fluid.

Brebbia, C.A. (Ed.)
Electromagnetic Applications
Topics in Boundary Element Research - Vol 6
234 pp
ISBN: 0 387 50607 1
Chapter 1 of this volume reviews the different formulations of
Maxwell's equations used in electrical engineering and the resulting
boundary integral statements. It discusses indirect as well as direct
approaches and applies them to a series of interesting practical cases.
Chapter 2 concentrates on the boundary element solution of three
dimensional electromagnetic fields in terms of the magnetic flux or the
vector potential. The next contribution - Chapter 3 - discusses the case
of magnetic fields of power devices under constant voltage sources. A
new approach is proposed which can take into account the external power
source voltage as input data and permits a direct rather than iterative
analysis to be carried out. Chapter 4 analyses eddy current problems
with particular reference to three dimensional cases.
In some cases it is more advantageous to couple boundary elements
with classical finite elements. The author of Chapter 5 recommends the
use of finite elements for saturation phenomena and boundary elements
for the nonsaturable region. The technique is applied to the case of
electric motors and electromagnetics. Chapter 6 also studies the
coupling of the two methods for electromagnetic problems reviewing the
advantages of both techniques and their field of applications.
Examples are presented for electrostatics, magnetostatics and field
analysis, including the non-linear case. The last contribution
- Chapter 7 - deals with applications of boundary elements for the
analysis and design of electrical machines considering two and three
dimensional cases.


Ciskowski, R.D. and Brebbia, C.A. (Eds)
Boundary Element Methods in Acoustics
Computational Mechanics Publications
292 pp
ISBN: 1 85312 104 5
ISBN: 0 945824 87 4 (US, Canada, Mexico)
This book is the first to focus on research and applications involving
the use of boundary elements in acoustics. Acoustics is an ideal
application area for the boundary element method (BEM) because of the
presence in many cases of infinite domains extending to infinity, the
need to obtain accurate solutions and as a BEM requires only the
discretization of the boundary.
Chapter 2 provides an historical perspective of BEM in acoustics
with a valuable list of key references. Chapter 2 addresses basic
formulations and fundamental concepts. Chapter 3 deals with radiation
and scattering from elastic solids and shells. Chapter 4 provides
formulations to determine the sensitivity of the acoustic field to
material or shape parameters and frequency. Chapter 6 discusses the use
of BEM for acoustic modeling coupled to FEM for structural modeling.
Chapter 7 addresses boundary element applications in automobile
interior and exterior acoustics. Chapter 8 presents applications in
biological and biomedical engineering, and bioacoustics. Chapter 9
introduces the use of the BEM for the study and prediction of noise in
the environment.
The intended audience for this book consists of engineers and
scientists in research and practice, and postgraduate students who want
to understand the BEM and its many applications in acoustics.


Beskos, D.E. (Ed.)
Boundary Element Analysis of Plates and Shells
Computational Mechanics Publications
VIII+368 pp
ISBN: 3 540 54464 X
This is the first book to deal specifically with the analysis of plates
and shells by the BEM and to cover all aspects of their behaviour, and
combines tutorial and state-of-the-art articles on the BEM as applied
to plates and shells.


Aliabadi, M.H. and Brebbia, C.A. (Eds)
Computational Methods in Contact Mechanics

Computational Mechanics Publications
ISBN: 1 85312 184 3
ISBN: 1 56252 113 6 (US, Canada, Mexico)
Modern engineering design leads to the realization of the importance of
contact problems in many technological fields. Contact problems are
complex and inherently non-linear due to their moving boundaries and
the existence of friction along contact surfaces. Until a few years ago,
researchers were engaged only in the fundamental concepts of contact
problems. Today, due to the great improvement in computer technology
and computational methods, it is possible to solve many complex
practical contact problems accurately and efficiently.
This book is the first which presents a comprehensive review of the
contact mechanics with particular emphasis on computational methods.
Much attention is devoted to the physical interpretation of the contact
properties as well as the numerical methodologies necessary to solve
complex engineering problems. As such, the book covers formulations
based on load incremental and mathematical programming approaches
using both finite and boundary element methods. The mathematical
modelling techniques described include the constraint method, the
flexibility approach, the penalty method and the Lagrange multiplier
In Chapter One, the applications of boundary element method to
frictional contact problems are presented using a fully load incremental
technique together with a constraint approach. Its application to fracture
mechanics is also described. Chapter Two deals with the boundary
element flexibility formulation for the analysis of frictionless and
frictional contact problems. The formulation is described in detail and
several examples are presented to demonstrate the accuracy of the
In Chapter Three, the Lagrange multiplier formulation for the finite
element method is presented. General algorithms are described for the
detection of overlapping meshes and the evaluation of contact forces.
An example problem of contact stress analysis in an orthopaedic knee
is presented.
Chapters Four and Five concentrate on the application of the penalty
method in contact problems using the finite and boundary element
methods respectively. Particular attention is paid to the numerical
implementation of the method and several examples are presented to
demonstrate the accuracy of the methods.
In Chapter Six, the application of the boundary element method to
three-dimensional contact problem is described. The authors present a
detailed formulation of the problem before proceeding to solve some
classical problems.
The remaining three chapters of the book deal with mathematical
programming approaches. Chapter Seven presents a formulation to deal
with both small and large displacement contact problems. The chapter
provides a review of the mathematical programming methods as well
as giving recommendations for future development of the method. In
Chapter Eight, a general solution method for three dimensional quasistatic
contact problems is presented. The formulation is based on the boundary
element method and mathematical programming approaches.
Finally, in Chapter Nine, the application of the finite element method
to elastic-plastic contact problems is presented employing a parametric
quadratic programming approach. The authors describe the numerical
implementation of the method in detail and present several examples to
demonstrate the accuracy of their technique.

Aliabadi, M.H. and Brebbia, C.A. (Eds)
Advances in Boundary Element Methods for Fracture Mechanics
Computational Mechanics Publications
ISBN: 1 85312102 9
ISBN: 1 94582 485 8 (US, Canada, Mexico)
The boundary element method (BEM) has emerged over the past few years
as the most powerful numerical technique for the solution of linear
elastic crack problems in fracture mechanics. While much progress has
been made, there are still many new frontiers to be explored with this
method. The aim of this book is to present the state-of-the-art in
applications of the boundary element method to crack problems. As such,
it includes chapters written by some of the leading researchers in the
field describing the recent advances of the method, as well as
presenting new ideas for further development.
It is well-known that the straightforward application of BEM to
crack problems leads to a mathematical degeneration in the numerical
formulation, if the two cracks are co-planar. The first two chapters of
the book deal with methods of removing this difficulty. In Chapter 1, a
dual boundary element formulation is presented where the displacement
integral equation and the traction equation are used independently on
crack surfaces. In Chapter 2, a boundary element displacement
discontinuity method is presented for elastodynamic problems.
Formulation for bodies containing interior, surface breaking and near
surface cracks are presented. Also discussed are problems associated
with interface cracks for which multidomain analysis is used.
In Chapter 3, the applications of BEM to analyse delamination
of composite laminates is described. The numerical treatment of
delaminated structures is carried out by using special crack-tip
elements and the energy method. In Chapter 4, an indirect boundary
element formulation known as the body force method is described.
The remaining chapters of the book concentrate on the
application of BEM to three-dimensional crack problems. Chapter 5
describes different crack-front elements, including the quarter-point
element which can be used to model the displacement and stress fields
in the vicinity of the crack front. Chapter 6 presents an application
of BEM to the analysis of three-dimensional stress intensity factor
weight functions. A weight function formulation based on the notion of
fundamental fields is derived. The fundamental displacements and stress
fields for rectilinear and penny-shaped crack fronts are given.
The final chapter describes the application of the boundary
element method to anisotropic crack problems. A detailed discussion
on the numerical implementation of the anisotropic fundamental solution
is described.

Aliabadi, M.H. and Brebbia, C.A. (Eds)
Advanced Formulations in Boundary Element Methods
Computational Mechanics Publications
ISBN: 1 85312 182 7
ISBN: 1 56252 111 X (US, Canada, Mexico)
The boundary element method is now being increasingly applied to new
topics in engineering. This has led researchers to investigate and
develop new formulations of the method which lend themselves better to
problems such as fracture mechanics, coupling with finite elements,
moving boundary applications and nonlinear problems. This book
presents new boundary element formulations which are now emerging as
viable alternatives for a wide range of complex problems.
In Chapter 1, a new formulation entitled dual boundary element
method (DBEM) is presented for crack problems in fracture mechanics.
This new formulation removes the difficulties associated with the
modelling of co-planar crack surface using the standard boundary
element method. Chapters 2 and 3 address the problem of domain
integrals which can occur in the boundary element method for problems
involving body forces or nonlinearities. In Chapter 2, the dual
reciprocity method (DRM) is presented to solve these difficulties for a
wide range of problems such as time dependent convection diffusion and
elastodynamics. In Chapter 3, the so-called multiple reciprocity method
(MRM) is presented for applications involving body forces as well as
transient heat conduction problems.
A new hybrid boundary element formulation is presented in Chapter
4, which enables the simple coupling with finite elements. The authors
also briefly describe the hybrid-stress formulation before proceeding
with the detailed description of the hybrid-displacement approach.
Several examples are presented to demonstrate the accuracy of the
method. Chapter 5, concentrates on a new formulation for obtaining
higher-order interelement continuity using B-splines. Chapter 6, deals
with the hypersingular approach (HIBEM) for two-dimensional potential
problems. The formulation is presented in detail and several examples
are included to demonstrate its accuracy. In Chapter 7, the
non-singular computation of field derivatives is described. It is
demonstrated that by using the proposed formulation the field
derivatives such as temperature gradients can be evaluated more
accurately than has been possible using conventional approaches.
Finally, the application of the complex variable boundary element
method (CVBEM) to heat conduction problems is presented in Chapter 8.
Formulations are presented for simply and multiply connected domains
and several examples are given to demonstrate the versatility of the
method for two-dimensional problems.

Brebbia, C.A. and Aliabadi, M.H. (Eds)
Adaptive Finite and Boundary Element Methods

Computational Mechanics Publications
ISBN: 1 85312 185 1
ISBN: 1 56252 114 4 (US, Canada, Mexico)
In recent years increasing attention has been paid to adaptive meshing
and analysis techniques in order to improve the reliability of numerical
analysis techniques such as the finite and boundary element method.
This book presents a comprehensive review of adaptive analysis in
engineering computation. As such the topics are wide ranging and
include algorithms for automatic meshing, adaptive improvements,
error analysis and adaptive solution procedures.
In Chapter 1, adaptive analysis methods such as h, p and h-p versions
are described in detail for the finite and boundary element methods. A
detailed description of a posteriori error estimates and subsequent mesh
refinements are presented. Chapter 2, deals with adaptive finite element
techniques for three-dimensional Navier Stokes equations and other
transient problems. A technique is described to control the mesh grading
by the estimate of errors. Several examples are presented for problems
involving viscous flow simulation and phase transitions. In Chapter 3,
adaptivity through mesh movements is considered rather than the usual
localized mesh refinement techniques. Application to aeronautical
problems such as inviscid flow around an aerofoil are presented to
demonstrate the versatility of the proposed method. Chapter 4, deals
with adaptive finite element method for transient compressible flow
problems. In this chapter the capability of an adaptive unstructured
mesh approach is described in which the mesh is automatically adapted
to account for the motion of the boundaries. The application of adaptive
finite element method for phase change problems is described in
Chapter 5. Here, an error estimation technique for adaptive finite
element analysis of heat conduction problems is presented. Two
examples of solidification of an aluminium casting with change of
phase are presented. In Chapter 6, adaptive solution strategies for
nonlinear finite element analysis are presented. Particular attention has
been paid to computationally intensive operations such as updating the
stiffness matrices, decomposition, bisection and line search algorithms.
Parallel computation and solution procedures for linear elliptic partial
differential systems are presented in Chapter 7, using the finite element
method based on automatically unstructured grids. Finally, the application
of boundary and finite element methods to three-dimensional problems
of acoustic scattering is presented in Chapter 8. This chapter concentrates
mainly on computational aspects such as geometric modelling,
hp-adaptivity and a posteriori error estimates.

Kane, J.H., Maier, G., Tosaka, N. and Atluri, S.N. (Eds)
Advances in Boundary Element Techniques
ISBN: 3 540 55921 3
ISBN: 0 387 55921 3
The book contains a collection of papers written by leading experts in
the field providing an overview of the state-of-the-art of boundary
element analysis.
With treatments of mechanical, thermal, fluid, and electromagnetic
phenomena, this book will be of great value to graduate students,
practitioners, and researchers in engineering, mathematics and the
physical sciences wishing to obtain a broader perspective or remain
current in these important areas of computational simulation. The
topics include mathematical, numerical, and computational aspects,
basic formulations, potential, thermal, fluid mechanics and
aerodynamics applications, elasticity and elastoplasticity,
elastodynamics, electromagnetics, and acoustics, and coupled problems.
Throughout this volume, many different boundary approaches are
described including the indirect and direct singular and hypersingular
collocation and symmetric Galerkin formulations.

Manolis, G.D. and Davies, T.G. (Eds)
Boundary Element Techniques in Geomechanics
Computational Mechanics Publications

Wrobel, L.C. and Brebbia, C.A. (Eds)
Computational Methods for Free and Moving Boundary Problems
in Heat Transfer and Fluid Flow

Computational Mechanics
ISBN: 1 85312 221 1
ISBN:1 56252 145 4 (US, Canada, Mexico)
The mathematical modelling of free and moving boundary problems is
characterized by the presence of one or more surfaces which are
initially unknown or move throughout the analysis. The determination of
the location of these surfaces is an important part of the solution
procedure, generally involving the use of iterative or time-marching
algorithms. Examples of practical engineering problems are numerous,
e.g. nonlinear wave motion, cavitating flows, solidification and
melting, metal casting, to name but a few. The present volume
concentrates on computational methods of solution of such problems with
emphasis on boundary and finite elements.
Chapter 1 discusses direct iteration and optimization
techniques used in conjunction with the boundary element method (BEM)
for solution of gravity and pressure-driven free surface flow problems.
Chapter 2 uses Baiocchi's integral transformation in a fixed domain
method for free surface flow in porous media. Chapters 3 and 4 deal
with nonlinear wave motion. The former describes a wave model based on
the fully nonlinear potential flow equation to study wave motion in
shallow water, including wave overturning induced by the ocean bottom
or by coastal engineering structures.
The flow about submerged partially or supercavitating
axisymmetric bodies both at zero and non-zero angle of attack is
considered in Chapter 5. Chapter 6 discuss two implementations of the
BEM to solve the slow viscous flow of a fluid moving between two
parallel plates which are in relative motion. The situations in which
petroleum reservoir models generate shocks are considered in Chapter 7.
When rain runs down a window pane in a stream, it normally
meanders instead of going straight. This interesting problem is
analysed in Chapter 8, which presents the condition of stable
meandering of water rivulets on an inclined smooth plate, derived by the
bend theory including the effect of surface tension. A series of heat
flow problems are considered in Chapters 9 to 11. Chapter 9, on
solidification problems, presents a macroscopic model for the treatment
of the macrosegregation process in a binary material, and a microscopic
model for the freezing processes in foodstuffs. Modelling of the
mathematical behaviour of an aluminium electrolytic cell is presented
in Chapter 11. This model predicts and assesses fundamental variables
in cell operation: form and thickness of the frozen bath, heat flows,
position of isotherms, electric potentials, etc. Chapter 12 presents a
resume of work involving the Isotherm Migration Method. Applications
include implicit moving boundaries (oxygen diffusion through absorbing
tissues) and melting ranges (mushy problems). The modelling of the
filling stage of casting processes is the subject of Chapter 13 where a
two-dimensional FEM to treat non-steady flows of Newtonian fluids,
coupled with heat transfer and turbulence is described.
Chapter 14 discusses the steady state, irrotational, ideal
fluid flow produced by a submerged source, or sink, from a region
containing three homogeneous layers of fluids at different densities
with gravity as the restoring force. In Chapter 15, the motion and
deformation of viscous drops and gas bubbles which occur in many
industrial and biological systems, are studied through a completed
double layer boundary integral equation method. Finally Chapter 16
reviews the historical development and state-of-the-art in Green's
function structured discrete approximation methods for modelling
microscopic and macroscopic transport phenomena in solid-liquid
phase-change systems.


Power, H. (Ed.)
BE Applications in Fluid Mechanics
Advances in Fluid Mechanics - Vol 4
Computational Mechanics Publications
ISBN: 1 85312288 2
ISBN: 1 56252 212 4 (US, Canada, Mexico)
ISSN: 1353 808X
The boundary element method (BEM) is now a well established numerical
technique for the analysis of engineering problems, particularly those
involving linear analysis. One of its main advantages is the
considerable reduction in data preparation in relation to domain
methods, as only surface elements are necessary. The basis of the
method is that a fundamental solution is used to take some or all of
the terms in the governing equation to the boundary.
In the past, further increases in the number of applications of
BEM were hampered by the need to operate with relatively complex
fundamental solutions or the difficulties encountered when trying to
extend the BEM to non-linear and time dependent problems. Recent
developments in the boundary element method have been very successful
in dealing with those complex problems.
Fluid dynamics is traditionally one of the most challenging areas
of computational mechanics; the simulation of fluid motion is always a
serious test for any numerical method. The book is a compilation of
some advanced topics on the application of BEM in fluid mechanics. The
eleven chapters in the book have been contributed by leading authors in
the field. This book accordingly provides an important addition to the
literature in fluid mechanics.

Nowak, A.J. and Neves, A.C. (Eds)
The Multiple Reciprocity Boundary Element Method
Computational Mechanics Publications
ISBN: 1 85312277 7
ISBN: 1 56252 201 9 (US, Canada, Mexico)
The boundary element method (BEM) is a numerical technique which is now
emerging as a viable alternative to finite difference and finite
element methods for solving a wide range of engineering problems. The
main advantage of the BEM over domain-type methods is its unique
ability to confine the dependence of the problem solution to the
boundary values only. This reduces the data preparation effort and
saves computer time since the system of equations to be solved is
smaller than those resulting from domain techniques. However, the main
drawback of the BEM occurs in problems such as those with body forces,
time-dependent effects or non-linearities. In these cases, the domain
integrals that appear in the integral equation are usually evaluated by
using cell integration. Although this technique is effective and
general, it affects the overall efficiency of the BEM and detracts from
its elegance due to the additional internal discretization.
In an effort to avoid the internal discretization, many different
approaches have been developed. The most recent one is the multiple
reciprocity method (MRM) which is the main subject of this book. The
basic idea behind the MRM is to employ a sequence of higher order
fundamental solutions which permit the application of the reciprocity
theorem recurrently. The success of the method is reflected in the
works carried out by several active groups around the world and
presented here in the chapters of the book.