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Book Title : A Beginner's Course in Boundary Element Methods
eBook download format(s) : htm
Author(s) : Whye-Teong Ang
Section : Mathematics
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Book Description
During the last few decades, the boundary element method, also known as the boundary integral equation method or boundary integral method, has gradually evolved to become one of the few widely used numerical techniques for solving boundary value problems in engineering and physical sciences. In implementing the method, only the boundary of the solution domain has to be discretized into elements. In the case of a two-dimensional problem, this is really easy to do. Put N closely packed points on the boundary (a simple closed curve) and join up two consecutive neighboring points to form N straight line elements.

Some specific research areas using the boundary integral method include linear fracture mechanics (accurate computation of stress intensity factors using special Green's functions), analyses of nonhomogeneous media (such as functionally graded materials), diffusion with specification of mass, modeling of photonic crystal fibers, integral formulation of imperfect interfaces, and bioheat transfer.

The chapters were written with the task of introducing the method to beginners, mainly advanced undergraduate and research students. It is assumed that the readers have some prior basic knowledge of vector calculus (covering topics such as line, surface and volume integrals and the various integral theorems), ordinary and partial differential equations, complex variables, and computer programming.

FORTRAN 77 codes for the numerical procedures discussed are listed in the chapters. Some justifications (if any is needed at all) for using "good old FORTRAN 77" would be: (a) in spite its seniority, it still remains a powerful "number crunching tool", (b) its codes are relatively easy to decipher and would be of some use even to readers who are attempting to implement the numerical procedures using newer software tools (such as C and MATLAB), and (c) free FORTRAN 77 compilers (e.g. FTN77 from Salford Software and GNU Fortran) can be downloaded from the internet.

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