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Wolfgang Bangerth,
Carsten Burstedde,
Timo Heister,
Martin Kronbichler

**Algorithms and data structures for massively parallel generic
adaptive finite element codes**

ACM Transactions on Mathematical Software, vol. 38 (2011), pp. 14/1-28.

Today's largest supercomputers have 100,000s of processor cores and
offer the potential to solve partial differential equations
discretized by billions of unknowns. However, the complexity of
scaling to such large machines and problem sizes has so far prevented
the emergence of generic software libraries that support such
computations, although these would lower the threshold of entry and
enable many more applications to benefit from large-scale computing.

We are concerned with providing this functionality for mesh-adaptive
finite element computations. We assume the existence of an "oracle"
that implements the generation and modification of an adaptive mesh
distributed across many processors, and that responds to queries about
its structure. Based on querying the oracle, we develop scalable
algorithms and data structures for generic finite element methods.
Specifically, we consider the parallel distribution of mesh data,
global enumeration of degrees of freedom, constraints, and
postprocessing. Our algorithms remove the bottlenecks that typically
limit large-scale adaptive finite element analyses.

We demonstrate scalability of complete finite element workflows on up to
16,384 processors. An implementation of the proposed algorithms, based on
the open source software `p4est`

as mesh oracle, is provided under an open
source license through the widely used `deal.II`

finite element
software library.

*Wolfgang Bangerth*

* Mon Feb 19 10:30:46 MST 2018 *