This paper describes a boundary-element-based approach for the modeling and solution of potential problems that involve thin layers of varying curvature. On the modeling side, we consider two types of imperfect interface models that replace a perfectly bonded thin layer by a zero-thickness imperfect interface across which the field variables undergo jumps. The corresponding jump conditions are expressed via second-order surface differential operators. To quantify their accuracy with respect to the fully resolved thin layer, we use boundary element techniques, which we develop for both the imperfect interface models and the fully resolved thin layer model. Our techniques are based on the use of Green’s representation formulae and isoparametric approximations that allow for accurate representation of curvilinear geometry and second order derivatives in the jump conditions. We discuss details of the techniques with special emphasis on the evaluation of nearly singular integrals, validating them via available analytical solutions. We finally compare the two interface models using the layer problem as a benchmark.

本文介绍了一种基于边界元的方法，用于建模和解决涉及不同曲率薄层​​的潜在问题。在建模方面，我们考虑了两种类型的不完美界面模型，它们用零厚度不完美界面替换了完美粘合的薄层，场变量在该界面上发生跳跃。相应的跳跃条件通过二阶表面微分算子表示。为了量化它们相对于完全解析薄层的准确性，我们使用边界元技术，我们为不完美的界面模型和完全解析的薄层模型开发了这种技术。我们的技术基于格林的表示公式和等参近似的使用，允许在跳跃条件下准确表示曲线几何和二阶导数。我们讨论了这些技术的细节，特别强调了对近似奇异积分的评估，并通过可用的解析解来验证它们。我们最终以层问题为基准比较了两种接口模型。