The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries

[摘要] This paper gives very significant and up-to-date analytical andnumerical results to the three-dimensional heat radiation problemgoverned by a boundary integral equation. There are two types ofenclosure geometries to be considered: convex and nonconvexgeometries. The properties of the integral operator of theradiosity equation have been thoroughly investigated andpresented. The application of the Banach fixed point theoremproves the existence and the uniqueness of the solution of theradiosity equation. For a nonconvex enclosure geometries, thevisibility function must be taken into account. For the numericaltreatment of the radiosity equation, we use the boundary elementmethod based on the Galerkin discretization scheme. As a numericalexample, we implement the conjugate gradient algorithm withpreconditioning to compute the outgoing flux for athree-dimensional nonconvex geometry. This has turned out to bethe most efficient method to solve this type of problems.

[学科分类] 应用数学