Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
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In this work, smoothed meshfree methods are firstly applied to numerically analyze two-dimensional electromagnetic wave propagation models. A weakened weak formulation based on the edges of triangular cells obtained by a Delaunay triangulation is considered here, framing the so-called edge-based smoothed domains. The meshfree shape functions are computed by the Radial Point Interpolation Method (RPIM) considering two schemes for the shape function support domains, namely the T3- and the T6-scheme. These schemes are based on the above mentioned triangular cells and they consider fixed numbers of nodes for the support domains. A new procedure to compute the transient related matrices is discussed here, aiming to be more consistent with the edge-based smoothed point interpolation method. In this new procedure, finer local integration techniques are managed to be considered at lower computational costs, rendering more accurate and efficient techniques. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the proposed methodologies.