Numerical Integration for Interactive Terms in Mesh Superposition Method by Auto-Mesh Generation
Atsushi Sando · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A · 2011
The interactive terms in the mesh superposition method are calculated approximately because the integrand has a discontinuity along the mesh lines in a superimposed global mesh. In this paper, the accurate numerical integration technique for a discontinuous integrand by the Delaunay triangulation is proposed. Integral ranges including discontinuous integrands are divided into triangles only with a continuum integrand. The exact solution is sum of the integral values calculated in all triangles. Appropriate triangle edges can be regenerated by the swapping algorithm even though generated triangles contain the inappropriate boundary lines which bring about a discontinuity. A comparison of the accuracy of numerical integration between the proposed technique and conventional approximate means and an application to a sensitivity calculation are investigated in the first example. The second example illustrates the swapping algorithm for the adjustment of generated triangles.