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In this work, we introduce a new algorithm for N-to-M checkpointing in finite element simulations. This new algorithm allows efficient saving/loading of functions representing physical quantities associated with the mesh representing the physical domain. Specifically, the algorithm allows for using different numbers of parallel processes for saving and loading, allowing for restarting and post-processing on the process count appropriate to the given phase of the simulation and other conditions. For demonstration, we implemented this algorithm in PETSc, the Portable, Extensible Toolkit for Scientific Computation, and added a convenient high-level interface into Firedrake, a system for solving partial differential equations using finite element methods. We evaluated our new implementation by saving and loading data involving 8.2 billion finite element degrees of freedom using 8,192 parallel processes on ARCHER2, the UK National Supercomputing Service.

Quantum computing has attracted considerable attention in recent years because it promises speed-ups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers are, in most cases, still too small to solve significant problems, their future impact on domain sciences is already being explored now. Within this context, we present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media with two components: a theoretical formulation and an implementation on a real quantum computer. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schr\"{o}dinger equation, which can be simulated directly on a gate-based quantum computer. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on the real quantum computer IBM Brisbane. The latter produce simulation results that qualitatively agree with the error-free version but are contaminated by quantum decoherence and noise effects. Complementing the discrete transformation to the Schr\"{o}dinger equation by a continuous version allows the replacement of finite differences by other spatial discretisation schemes, such as the spectral-element method. Anticipating the emergence of error-corrected quantum chips, an analogy between our method and analyses of coupled mass-spring systems suggests that our quantum computing approach may lead to wave field simulations that run exponentially faster than simulations on classical computers., Comment: 16 pages, 4 figures

Large-scale PDE simulations using high-order finite-element methods on unstructured meshes are an indispensable tool in science and engineering. The widely used open-source PETSc library offers an efficient representation of generic unstructured meshes within its DMPlex module. This paper details our recent implementation of parallel mesh reading and topological interpolation (computation of edges and faces from a cell-vertex mesh) into DMPlex. We apply these developments to seismic wave propagation scenarios on Mars as an example application. The principal motivation is to overcome single-node memory limits and reach mesh sizes which were impossible before. Moreover, we demonstrate that scalability of I/O and topological interpolation goes beyond 12'000 cores, and memory-imposed limits on mesh size vanish., Comment: 23 pages, 11 figures