MURPHY -- A scalable multiresolution framework for scientific computing on 3D block-structured collocated grids

TL;DR

This paper introduces MURPHY, a scalable multiresolution framework for 3D scientific computing that uses wavelets on octree-based grids, enabling efficient adaptive simulations with explicit error control and high scalability.

Contribution

The paper presents a novel multiresolution adaptive grid framework combining high-order wavelets with finite-difference schemes, validated for error control, grid compression, and high-performance parallel computing.

Findings

Wavelet family provides strict error control during grid coarsening.

Lifting wavelets increase grid compression while conserving moments.

High-order schemes retain convergence order at resolution jumps.

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.