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Robust modelling of implicit interfaces by the scaled boundary finite element method

- Dsouza, Shaima, Pramod, A. L. N., Ooi, Ean Tat, Song, Chongming, Natarajan, Sundarajan

  • Authors: Dsouza, Shaima , Pramod, A. L. N. , Ooi, Ean Tat , Song, Chongming , Natarajan, Sundarajan
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Engineering Analysis with Boundary Elements Vol. 124, no. (2021), p. 266-286
  • Full Text: false
  • Reviewed:
  • Description: 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(h2) in L2 norm and O(h) in the H1 semi-norm. Further the condition number increases with the mesh size similar to the FEM. © 2021 Elsevier Ltd

Treatment of multiple input uncertainties using the scaled boundary finite element method

- Dsouza, Shaima, Varghese, Tittu, Ooi, Ean Tat, Natarajan, Sundararajan, Bordas, Stephane

  • Authors: Dsouza, Shaima , Varghese, Tittu , Ooi, Ean Tat , Natarajan, Sundararajan , Bordas, Stephane
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Applied Mathematical Modelling Vol. 99, no. (2021), p. 538-554
  • Full Text: false
  • Reviewed:
  • Description: This paper presents a non-intrusive scaled boundary finite element method to consider multiple input uncertainties, viz., material and geometry. The types of geometric uncertainties considered include the shape and size of inclusions. The inclusions are implicitly defined, and a robust framework is presented to treat the interfaces, which does not require explicit generation of a conforming mesh or special enrichment techniques. A polynomial chaos expansion is used to represent the input and the output uncertainties. The efficiency and the accuracy of the proposed framework are elucidated in detail with a few problems by comparing the results with the conventional Monte Carlo method. A sensitivity analysis based on Sobol’ indices using the developed framework is presented to identify the critical input parameter that has a higher influence on the output response. © 2021 Elsevier Inc.
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