MURPHY – A scalable multiresolution framework for scientific computing on 3D block-structured collocated grids
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We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on 3D block-structured collocated grids with distributed computational architectures. Our approach provides a consistent handling of non-lifted and lifted interpolating wavelets of arbitrary order demonstrated using second, fourth, and sixth order wavelets, and combines that with standard finite-difference based discretization operators. We first validate that the wavelet family used provides strict and explicit error control when coarsening the grid, that lifting wavelets increase the grid compression rate while conserving discrete moments across levels, and that high-order PDE discretization schemes retain their convergence order even at resolution jumps when combined with sufficiently high order wavelets. We then use a test case of the advection of a scalar to analyze convergence for the temporal evolution of a PDE, which shows that our wavelet-based refinement criterion is successful at controlling the overall error while the coarsening criterion is effective at retaining the relevant information on a compressed grid. Our software exploits the block-structured grid data structure for efficient multi-level operations, and the parallelization strategy relies on a one-sided MPI-RMA communication approach with active PSCW synchronization leading to highly scalable performance on more than 7,000 cores.
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