A novel efficient technique is presented for the evaluation of domain integrals that appear in the boundary element method (BEM). Herein, the source term is approximated with the use of radial basis functions, as in the dual reciprocity BEM. The proposed technique, called the Kriging Integration Method (KIM), comprises the use of the Simple Kriging Method in non-overlapping patches for obtaining the weights of the integration points located inside. As it is necessary to compute the integrals of the covariance function prior to obtaining these weights, this can be efficiently realized using the Cartesian Transformation Method. The domain integrals over all the generated partitions are then computed and added to obtain the value of the whole-domain integral. Using KIM, it is possible to evaluate approximately weakly singular domain integrals over simply or multiply connected domains without applying any transformation or regularization method to the singular integrand. The numerical results obtained in several 2D potential problems demonstrate that this integration scheme is as accurate as both the dual reciprocity method and RIM and less time consuming than the RIM.

提出了一种新颖有效的技术，用于评估边界元方法（BEM）中出现的域积分。在本文中，如在对等互惠BEM中一样，使用径向基函数来近似源项。所提出的技术称为Kriging积分方法（KIM），包括在非重叠面片中使用Simple Kriging方法来获得位于内部的积分点的权重。由于在获得这些权重之前必须计算协方差函数的积分，因此可以使用笛卡尔变换方法有效地实现这一点。然后计算所有生成分区上的域积分，并相加以获得整个域积分的值。使用KIM，可以在简单或多重连接域上评估近似弱奇异域积分，而无需对奇异被积数应用任何变换或正则化方法。在几个2D潜在问题中获得的数值结果表明，该集成方案与对等方法和RIM一样准确，并且比RIM耗时少。