ABSTRACT
A moving least squares (MLS) approximation scheme, using curvilinear coordinates on the 1-D bounding surface of a 2-D body, or on the 2-D bounding surface of a 3-D body, is suitable for the BNM. The 2-D problem, which uses the curvilinear coordinate s on the boundary of a body, is discussed in detail in Mukherjee and Mukherjee [107] (potential theory) and in Kothnur et al. [72] (elasticity) (see, also, [108, 52, 77]). The 3-D problem requires the curvilinear surface coordinate s with components (s1, s2). (Chati and Mukherjee [26], potential theory; Chati et al. [25], elasticity). This procedure is described below. A brief discussion, of ongoing work on the BNM with Cartesian coordinates [79, 80, 163, 164], is presented as well.
