This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics.
Preface.- Acknowledgements.- Preliminaries: Introduction; Overview of book; Mathematical preliminaries; Conclusions; References.- Programming: Strategies; FORTAN 90/95/2000 features; Charts and pseudo code; Parallel programming; BLAS libraries; Pre- and Postprocessing; Conclusions; Exercises; References.- Discretisation and Interpolation: Introduction; One-dimensional boundary elements; Two-dimesional elements; Three-dimensional cells; Elements of infinite extent; Subroutines for shape functions; Interpolation; Coordinate transformation; Differential geometry; Integration over elements; PROGRAM 3.1: Calculation of surface area; Concluding remarks; Exercises; References.- Material Modelling and Fundamental Solutions: Introduction; Steady state potential problems; Static elasticity problems; Conclusions; References.- Boundary Integral Equations: Introduction; Trefftz method; PROGRAM 5.1: Flow around cylinder, Trefftz method; Direct method; Computation of results inside the domain; PROGRAM 5.2: Flow around cylinder, direct method; Conclusions; Exercises; References.- Boundary Element Methods - Numerical Implementation: Introduction; Discretisation with isoparametric elements; Integration of kernel shape function products; Conclusions; Exercises; References.- Assembly and Solution: Introduction; Assembly of system of equations; Solution of system of equations; PROGRAM 7.1: general purpose program, direct method, one region; Conclusions; Exercises; References.- Element-by-element techniques and Parallel Programming: Introduction; The Element by Element Concept; PROGRAM 8.1 : Replacing direct by iterative solution; PROGRAM 8.2 : Replacing assembly by element-by-element procedure; PROGRAM 8.3 : Parallelising the element-by-element procedure; Conclusions; References.- Postprocessing : Introduction; Computation of boundaryresults; Computation of internal results; PROGRAM 9.1: Postprocessor; Graphical display of results; Conclusions; Exercises; References.- Test Examples : Introduction; Cantilever beam; Circular excavation in infinite domain; Square excavation in infinite elastic space; Spherical excavation; Conclusions; References.- Multiple regions: Introduction; Stiffness matrix assembly; Computer implementation; Program 11.1: General purpose program, direct method, multiple regions; Conclusions; Exercises; References.- Dealing with corners and changing geometry: Introduction; Corners and edges; Dealing with changing geometry; Alternative Strategy; Conclusions; References.- Body Forces: Introduction; Gravity; Internal concentrated forces; Internal distributed line forces; Initial strains; Initial stresses; Numerical integration over cells; Implementation; Sample input file and results; Conclusions; Exercises; References.- Dynamic Analysis: Introduction; Scalar wave equation, frequency domain; Scalar wave equation, time domain; Elastodynamics; Multiple regions; Examples; References.- Nonlinear Problems: Introduction; General solution procedure; Plasticity; Contact problems; Conclusions; References.- Coupled Boundary Element/ Finite Element Analysis: Introduction; Coupling theory; Example; Dynamics; Conclusion; References.- Industrial Applications: Introduction; Mechanical engineering; Geotechnical Engineering; Geological engineering; Civil engineering; Reservoir engineering; Conclusions; References.- Advanced topics: Introduction; Heterogeneous Domains; Linear inclusions; Piezo-electricity; Conclusions; References.- Appendix.
Engineering, Engineering, Engineering mathematics, Maths for engineers, Maths for scientists