Robust modelling of implicit interfaces by the scaled boundary finite element method. (1st March 2021)

• Record Type: Journal Article
• Authors: Dsouza, Shaima M.; Pramod, A.L.N.; Ooi, Ean Tat; Song, Chongmin; Natarajan, Sundararajan
• Is Part Of: Engineering analysis with boundary elements. Volume 124(2021)
• Page Start: 266
• Page End: 286
• Publication Date: 2021-03-01
• Subjects: Bi-material interfaces -- Dirichlet boundary conditions on interfaces -- Material inclusions -- Scaled boundary finite element method -- Weak discontinuity; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2020.12.025
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper, we propose a robust framework based on the scaled boundary finite element method to model implicit interfaces in two-dimensional differential equations in nonhomegeneous media. The salient features of the proposed work are: (a) interfaces can be implicitly defined and need not conform to the background mesh; (b) Dirichlet boundary conditions can be imposed directly along the interface; (c) does not require special numerical integration technique to compute the bilinear and the linear forms and (d) can work with an efficient local mesh refinement using hierarchical background meshes. Numerical examples involving straight interface, circular interface and moving interface problems are solved to validate the proposed technique. Further, the presented technique is compared with conforming finite element method in terms of accuracy and convergence. From the numerical studies, it is seen that the proposed framework yields solutions whose error is O ( h 2 ) in L 2 norm and O ( h ) in the H 1 semi-norm. Further the condition number increases with the mesh size similar to the FEM.