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An eXtended Stochastic Finite Element Method for solving stochastic partial differential equations on random domains

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Fig. 5. Level-set φ(·, θ) whose iso zero on e ∂Ω(θ) represents the boundary of hyper–
Fig. 7. For a given outcome φ(·, ξ) of the level-set, subdivision of a 3-nodes triangle K and of its edges for the numerical integration on K ∩ Ω(ξ), ∂K ∩ Γ 2 (ξ) and K ∩ Γ 2 (ξ).
Fig. 8. Function λ(K ∩ Ω(ξ)) as a function of ξ. Level-set φ(x, ξ) = x · a − ξ In fact, the above partition of Θ can be completely characterized by the values of the random level-set
Fig. 11. Comparison between isotropic and anisotropic split of a 3D cell. ¤ and △ denote two different states of the vertices.
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