The isogeometric analysis boundary element method (IGABEM) has great potential in the simulation of heat conduction problems due to its exact geometric representation and good approximation properties. In this paper, the radial integration IGABEM (RI-IGABEM) is proposed to solve isotropic heat conduction problems in inhomogeneous media with heat source. Similar to traditional BEM, the domain integrals cannot be avoided since the foundational solution for the Laplace equation is used to derive integral equation. In order to preserve the advantage of IGABEM, i.e. only boundary is discretized, the radial integration method (RIM) is applied to transform the domain integral into an equivalent boundary integral. In addition, using a simple transformation method, the uniform potential method is successfully applied to solve the strongly singular integrals, and the Telles scheme and the element sub-division method are used to solve the weakly singular integrals in RI-IGABEM respectively. In order to validate the accuracy and convergence of the RI-IGABEM in the analysis of the single or multiple boundary heat conduction problems, several 2D and 3D numerical examples are used to discuss the influence of some factors, such as the number of applied points, the order of basis functions, and the position of internal applied points.

等几何分析边界元方法（IGABEM）由于其精确的几何表示和良好的逼近特性，在模拟导热问题方面具有巨大的潜力。本文提出了径向积分IGABEM（RI-IGABEM）来解决热源不均匀介质中的各向同性导热问题。与传统的BEM相似，由于使用Laplace方程的基础解来导出积分方程，因此无法避免域积分。为了保留IGABEM的优势，即仅离散边界，应用径向积分方法（RIM）将域积分转换为等效边界积分。此外，使用简单的转换方法，成功地采用了均匀势法求解强奇异积分，并分别采用Telles方案和单元细分法求解RI-IGABEM中的弱奇异积分。为了验证RI-IGABEM在单边界或多边界热传导问题分析中的准确性和收敛性，使用了几个2D和3D数值示例来讨论某些因素的影响，例如施加点的数量，基函数的顺序以及内部应用点的位置。