This paper introduces the Scaled Coordinate Transformation Boundary Element Method (SCTBEM), a novel boundary-type method for solving 3D potential problems. To address the challenges of applying the Boundary Element Method (BEM) to complex problems, it is common practice to use the fundamental solution corresponding to the partial governing equation operator to establish the integral equation. However, this approach introduces domain integral, which may jeopardize the dimensionality reduction advantages of BEM. To preserve the benefits of dimensionality reduction, this paper proposes a novel domain integral transformation method known as the Scaled Coordinate Transformation (SCT). The SCT is purely a mathematical operation that does not rely on particular solution of operators, which requires only discretization on the structure's surface while remaining analytical in the radial direction. An even better novelty is that the lower-order singularity can be eliminated by coordinate translation technique. To facilitate the wider adoption of BEM, the authors present 99-line MATLAB code. Numerical results confirm that the SCTBEM exhibits high numerical accuracy even when dealing with complex model.

翻译：本文提出了一种新型边界类方法——缩放坐标变换边界元法（SCTBEM），用于求解三维势问题。为应对边界元法（BEM）在复杂问题中的应用挑战，通常采用偏控制方程算子对应的基本解建立积分方程。然而，该方法会引入域积分，可能削弱BEM的降维优势。为保留降维特性，本文提出一种新颖的域积分变换方法——缩放坐标变换（SCT）。SCT纯属数学运算，不依赖于算子的特解，仅需在结构表面进行离散化，而在径向方向保持解析性。更具创新性的是，通过坐标平移技术可消除低阶奇异性。为促进BEM的广泛采用，作者提供了99行MATLAB代码。数值结果表明，即使处理复杂模型，SCTBEM仍具有高数值精度。