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We present a technical enhancement within the p4est software for paralleladaptive mesh refinement. In p4est primitives are stored as octants in threeand quadrants in two dimensions. While, classically, they are encoded by thenative approach using its spatial and refinement level, any othermathematically equivalent encoding might be used instead.  Recognizing this, we add two alternative representations to the classical,explicit version, based on a long monotonic index and 128-bit AVX quadintegers, respectively. The first one requires changes in logic for low-levelquadrant manipulating algorithms, while the other exploits data levelparallelism and requires algorithms to be adapted to SIMD instructions. Theresultant algorithms and data structures lead to higher performance and lessermemory usage in comparison with the standard baseline.  We benchmark selected algorithms on a cluster with two Intel(R) Xeon(R) Gold6130 Skylake family CPUs per node, which provides support for AVX2 extensions,192 GB RAM per node, and up to 512 computational cores in total.

Alternative quadrant representations with Morton index and AVX2 vectorization for AMR algorithms within the p4est software library