The
Herein, we discuss algorithms that are necessary for a comprehensive and generic implementation of
We provide a reference implementation of our algorithms as part of the open source library
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hp -adaptive finite element method—where one independently chooses the mesh size (h ) and polynomial degree (p ) to be used on each cell—has long been known to have better theoretical convergence properties than eitherh - orp -adaptive methods alone. However, it is not widely used, owing at least in part to the difficulty of the underlying algorithms and the lack of widely usable implementations. This is particularly true when used with continuous finite elements.hp -adaptive finite element methods on distributed-memory, parallel machines. In particular, we will present a multistage algorithm for the unique enumeration of degrees of freedom suitable for continuous finite element spaces, describe considerations for weighted load balancing, and discuss the transfer of variable size data between processes. We illustrate the performance of our algorithms with numerical examples and demonstrate that they scale reasonably up to at least 16,384 message passage interface processes.deal.II .Free, publicly-accessible full text available September 30, 2024
