Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow
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The boundary element method (BEM) is an integral-equation-based numerical technique that in many cases offers several advantages over Finite Difference Methods (FDM), Finite Volume Methods (FVM), or Finite Element Methods (FEM). The BEM relies on the formulation of a boundary integral equation (BIE) for the field problem to be analyzed, and specifically, this is predicated on the availability of the Green’s free-space solution for the problem of interest. One of the most striking features of BEM is that, for many field problems of engineering, a boundary integral equation is discretized to solve the field problem of interest. Consequently, only the bounding surface of the domain is discretized, thereby reducing the dimension of the problem by one. For instance, in the analysis of linear and non-linear isotropic steady-state heat conduction without heat generation, a boundary discretization is only required to resolve the temperature field.