Performance analysis of the MHM simulator in a petascale machine

Gomes, Antônio Tadeu A.; Paredes, Diego; Pereira, Weslley da Silva; Souto, Roberto Pinto; Valentin, Frédéric

doi:10.20906/cps/cilamce2017-0381

Cited by 1 publication

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“…A study on this direction demands expertise on the implementation of parallel algorithms, which is out of the scope of the present manuscript. We refer to [25,36] as some seminal works considering the performance of the MHM-H 1 method for elasticity. • The construction of a two-scale MHM-WS characterization for three-dimension MFEM-WS methods is feasible using a similar methodology, as in the 2D case presented in Theorem 4.2.…”

Section: Discussionmentioning

confidence: 99%

“…It is defined rowisely in the spirit of standard projection-based interpolants π D γ : H s (Ω, R 2 ) → V γ adopted for twoscale Poisson-compatible pairs {V γ , P γin }, with enhanced bubble flux components (see[19,20]). Recalling the definition of π D γ for the single-scale case (23)-(25), the two-scale version becomesπ D γ η = π D,∂ γ η+π D γin (η−π D,∂ γ η), where only the internal interpolantπ D γin has to be updated. A uniform bound for ||Π σ 1,γ τ || H(div,Ω,M) , independent of γ, follows from the same property valid for ||π D γ || H(div,Ω,R 2 ) .…”

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confidence: 99%

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NewH(div)-conforming multiscale hybrid-mixed methods for the elasticity problem on polygonal meshes

et al. 2021

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This work proposes a family of multiscale hybrid-mixed methods for the two-dimensional linear elasticity problem on general polygonal meshes. The new methods approximate displacement, stress, and rotation using two-scale discretizations. The first scale level setting consists of approximating the traction variable (Lagrange multiplier) in discontinuous polynomial spaces, and of computing elementwise rigid body modes. In the second level, the methods are made effective by solving completely independent local boundary Neumann elasticity problems written in a mixed form with weak symmetry enforced via the rotation multiplier. Since the finite-dimensional space for the traction variable constraints the local stress approximations, the discrete stress field lies in the H (div) space globally and stays in local equilibrium with external forces. We propose different choices to approximate local problems based on pairs of finite element spaces defined on affine second-level meshes. Those choices generate the family of multiscale finite element methods for which stability and convergence are proved in a unified framework. Notably, we prove that the methods are optimal and high-order convergent in the natural norms. Also, it emerges that the approximate displacement and stress divergence are super-convergent in the L 2 -norm. Numerical verifications assess theoretical results and highlight the high precision of the new methods on coarse meshes for multilayered heterogeneous material problems.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%