MURPHY -- A scalable multiresolution framework for scientific computing on 3D block-structured collocated grids
Thomas Gillis, Wim M. van Rees
TL;DR
Murphy tackles scalable high-order PDE simulations on 3D block-structured collocated grids by marrying a wavelet-based multiresolution framework with an octree data structure. It delivers explicit error control and moment-conserving refinement via lifted interpolating wavelets, enabling high-order accuracy across resolution jumps while compressing the grid where details are negligible. The paper validates error bounds, moment conservation for lifted waves, and convergence of finite-difference operators, and demonstrates robust weak scalability up to $16{,}384$ cores using MPI-RMA with PSCW synchronization. The resulting software, released under BSD-3, offers a practical, scalable tool for simulating advection and related PDEs on massively parallel architectures, with potential extensions to non-linear and elliptic problems and multiphysics couplings.
Abstract
We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on octree-based 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, combined 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, and show that lifting wavelets increase the grid compression rate while conserving discrete moments across levels. Further, we demonstrate that high-order PDE discretization schemes combined with sufficiently high order wavelets retain the expected convergence order even at resolution jumps. We then simulate the advection of a scalar to analyze convergence for the temporal evolution of a PDE. The results 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 a block-structured grid data structure for efficient multi-level operations, combined with a parallelization strategy that relies on a one-sided MPI-RMA communication approach with active PSCW synchronization. Using performance tests up to 16,384 cores, we demonstrate that this leads to a highly scalable performance. The associated code is available under a BSD-3 license at https://github.com/vanreeslab/murphy.