# PHYSICS-BASED BALANCING DOMAIN DECOMPOSITION BY CONSTRAINTS FOR MULTI-MATERIAL PROBLEMS

Abstract : In this work, we present a novel balancing domain decomposition by constraints preconditioner that is robust for multi-material problems. We start with a well-balanced subdomain partition, and based on an aggregation of elements according to their physical coefficients, we end up with a finer physics-based (PB) subdomain partition. Next, we define geometrical objects (corners, edges and faces) for this PB partition, and select some of them to enforce subdomain continuity (primal objects). When the physical coefficient in each PB subdomain is constant and the set of selected primal objects satisfy a mild condition on the existence of acceptable paths, we can show both theoretically and numerically that the condition number does not depend on the contrast of the coefficient. An extensive set of numerical experiments for 2D and 3D Poisson's and linear elasticity problems is provided to support our findings. In particular, we show robustness and weak scalability of the new preconditioner up to 8232 cores when applied to 3D multi-material problems with the contrast of the physical coefficient up to $10^8$ and more than half a billion degrees of freedom. For the scalability analysis, we have exploited a highly scalable advanced inter-level overlapped implementation of the preconditioner that deals very efficiently with the coarse problem computation. The proposed preconditioner is compared against a state-of-the-art implementation of an adaptive BDDC method in PETSc for thermal and mechanical multi-material problems.
Keywords :
Type de document :
Pré-publication, Document de travail
2018
Domaine :

Littérature citée [43 références]

https://hal.archives-ouvertes.fr/hal-01337968
Contributeur : Hieu Nguyen <>
Soumis le : mercredi 23 mai 2018 - 04:58:47
Dernière modification le : vendredi 25 mai 2018 - 01:03:56

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• HAL Id : hal-01337968, version 4

### Citation

Santiago Badia, Alberto Martín, Hieu Nguyen. PHYSICS-BASED BALANCING DOMAIN DECOMPOSITION BY CONSTRAINTS FOR MULTI-MATERIAL PROBLEMS. 2018. 〈hal-01337968v4〉

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