Radial basis function generated finite difference (RBF-FD) methods for PDEs require a set of interpolation points which conform to the computational domain Ω. One of the requirements leading to approximation robustness is to place the interpolation points with a locally uniform distance around the boundary of Ω. However generating interpolation points with such properties is a cumbersome problem. Instead, the interpolation points can be extended over the boundary and as such completely decoupled from the shape of Ω. In this paper we present a modification to the least-squares RBF-FD method which allows the interpolation points to be placed in a box that encapsulates Ω. This way, the node placement over a complex domain in 2D and 3D is greatly simplified. Numerical experiments on solving an elliptic model PDE over complex 2D geometries show that our approach is robust. Furthermore it performs better in terms of the approximation error and the runtime vs. error compared with the classic RBF-FD methods. It is also possible to use our approach in 3D, which we indicate by providing convergence results of a solution over a thoracic diaphragm.

径向基函数生成的PDE的有限差分（RBF-FD）方法需要一组符合计算域Ω的插值点。导致近似鲁棒性的要求之一是将插值点放置在Ω的边界周围，具有局部均匀的距离。然而，产生具有这种特性的插值点是一个麻烦的问题。取而代之的是，插值点可以在边界上延伸，并因此完全与Ω形状分离。在本文中，我们提出了对最小二乘RBF-FD方法的修改，该方法允许将插值点放置在封装Ω的盒子中。这样，大大简化了2D和3D中复杂域上的节点放置。在复杂的2D几何上求解椭圆模型PDE的数值实验表明，我们的方法是可靠的。此外，与传统的RBF-FD方法相比，它在逼近误差和运行时间与误差方面的表现更好。也可以在3D中使用我们的方法，通过在胸膜上提供解的收敛结果来表明这一点。