Use of the multigrid methods for heat radiation problem

[摘要] We consider the integral equation arising as a result of heatradiation exchange in both convex and nonconvex enclosures ofdiffuse grey surfaces. For nonconvex geometries, the visibilityfunction must be taken into consideration. Therefore, ageometrical algorithm has been developed to provide an efficientdetection of the shadow zones. For the numerical realization ofthe Fredholm integral equation, a boundary element method based onGalerkin-Bubnov discretization scheme is implemented.Consequently, multigrid iteration methods, which are closelyrelated to two-grid methods, are used to solve the system oflinear equations. To demonstrate the high efficiency of theseiterations, we construct some numerical experiments for differentenclosure geometries.

[学科分类] 应用数学