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.
Bibliographical noteFunding Information:
The first author (Z.H.) gratefully acknowledges support from the National Natural Science Foundation of China through NSFC No. 12002084 and the Fundamental Research Funds for the Central Universities No. 20D110913. The second author (S.G.M.) gratefully acknowledges the support provided by the Theodore W. Bennett Chair, University of Minnesota. The third author (S.B.) gratefully acknowledges the Hsiao Shaw-Lundquist Fellowship granted by the University of Minnesota China Center. The fourth author (D.S.) gratefully acknowledges funding from the German Research Foundation through the DFG Emmy Noether Award SCH 1249/2–1.
© 2021 Elsevier Ltd
- Boundary Element Method
- Nearly singular integrals
- Potential problems
- Second-order imperfect interface models
- Thin layers