3 research outputs found
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Hybrid Multigrid for Adaptive Fourth Order Cut Cells:
We present a hybrid geometric-algebraic multigrid approach for
solving Poisson's equation on domains with complex geometries.
The discretization uses a novel fourth-order finite
volume cut cell representation to discretize the
Laplacian operator on a Cartesian mesh.
This representation is based on a weighted least-squares fit to a
cell-averaged discretization,
which is used to provide a conservative and accurate framework for
the multi-resolution discretization, despite the presence of cut cells.
We use geometric multigrid coarsening with an algebraic multigrid
bottom solver, so that the memory overhead of algebraic coarsening
is avoided until the geometry becomes under-resolved.
With tuning, the hybrid approach has the simplicity
of geometric multigrid while still retaining the
robustness of algebraic multigrid.
We investigate at what coarse level the transition should occur,
and how the order of accuracy of the prolongation operator affects
multigrid convergence rates.
We also present some converged
solutions as examples of how the use of adaptivity and
a cell connectivity graph can affect performanc
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AMRZone: A Runtime AMR Data Sharing Framework For Scientific Applications:
Frameworks that facilitate runtime data sharing across multiple applications are of great importance for scientific data analytics. Although existing frameworks work well over uniform mesh data, they can not effectively handle adaptive mesh refinement (AMR) data. Among the challenges to construct an AMR-capable framework include: (1) designing an architecture that facilitates online AMR data management; (2) achieving a load-balanced AMR data distribution for the data staging space at runtime; and (3) building an effective online index to support the unique spatial data retrieval requirements for AMR data. Towards addressing these challenges to support runtime AMR data sharing across scientific applications, we present the AMRZone framework. Experiments over real-world AMR datasets demonstrate AMRZone's effectiveness at achieving a balanced workload distribution, reading/writing large-scale datasets with thousands of parallel processes, and satisfying queries with spatial constraints. Moreover, AMRZone's performance and scalability are even comparable with existing state-of-the-art work when tested over uniform mesh data with up to 16384 cores; in the best case, our framework achieves a 46% performance improvement