A strategy for modeling 3D piecewise homogeneous regions and solving boundary value problems by generalized PIES

摘要

The purpose of this paper is to generalize the parametric integral equation system (PIES) to three-dimensional piecewise homogeneous regions. Generalization is at the level of numerical solving of PIES as a results of combining properly modeled subregions with different parameters. The effectiveness of solving problems with homogeneous areas modeled using various differential equations was studied in previous works. To model the geometry of subregions we have used flat and curved surfaces. In order to check the reliability and effectiveness of the proposed method several examples were solved. These examples refer to 3D boundary problems modeled by Laplace's and Navier-Lame differential equations.