  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.
