An efficient forward propagation of multiple random fields using a stochastic Galerkin scaled boundary finite element method
- Authors: Mathew, Tittu , Pramod, A. L. N. , Ooi, Ean Tat , Natarajan, Sundararajan
- Date: 2020
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 367, no. (2020), p.
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- Description: This paper serves to extend the existing literature on the Stochastic Galerkin Scaled Boundary Finite Element Method (SGSBFEM) in two ways. The first part of this work deals with the formulation of multiple non-correlated Gaussian random fields using the conventional Karhunen–Loéve expansion technique and its forward propagation through the Spectral Stochastic Scaled Boundary Finite Element setting using the polynomial surface fit method in terms of the scaled boundary coordinates. The advantages in adopting such a forward propagation technique in capturing the statistical moments of Quantities of Interest (QoI) across the domain, are highlighted using carefully chosen linear elastic problems having large to least correlated random fields as inputs. The second contribution is the extension of the proposed forward Uncertainty Quantification (UQ) to take into account multiple independent random fields, followed by Polynomial Chaos Expansion (PCE) based sensitivity analysis. Both the computational efficiency and the accuracy of the proposed framework under different input random field correlation settings are elaborated upon by comparing their results against that obtained using the current existing SGSBFEM in the literature. Moreover, the stochastic results are validated for all the numerical examples using the Monte Carlo method. © 2020 Elsevier B.V.
Robust modelling of implicit interfaces by the scaled boundary finite element method
- Authors: Dsouza, Shaima , Pramod, A. L. N. , Ooi, Ean Tat , Song, Chongming , Natarajan, Sundararajan
- Date: 2021
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 124, no. (2021), p. 266-286
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- 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