BEM-based second-order imperfect interface modeling of potential problems with thin layers

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. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a boundary-element-based approach for modeling and solving potential problems involving thin layers of varying curvature. Two imperfect interface models are considered, replacing perfectly bonded thin layers with zero-thickness imperfect interfaces, and accuracy is quantified using boundary element techniques. The techniques are detailed with a focus on evaluating nearly singular integrals and comparing the two interface models using a layer problem benchmark.