The Schwartz Alternating Algorithm for Solving 3D Exterior Helmholtz Problems

Based on the natural boundary reduction, an overlapping domain decomposition method is discussed for solving exterior Helmholtz problem over a three-dimensional (3D) domain. By introducing two different artificial boundaries, the original unbounded domain is divided into a bounded subdomain and a typical unbounded region, and a Schwartz alternating method is presented. The finite element method and natural boundary element method are alternately applied to solve the problems in the bounded subdomain and the typical unbounded subdomain. Moreover, the convergence of the Schwartz alternating algorithm is studied. Finally, some numerical experiments are presented to show the performance of this method.

Temperature field distribution of coal seam in heat injection

In this article, we present a natural boundary element method (NBEM) to solve the steady heat flow problem with heat sources in a coal seam. The boundary integral equation is derived to obtain the temperature filed distribution of the coal seam under the different injecting conditions.