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