arXiv subjects

Marcel Ferrari

Publications and source records attributed to Marcel Ferrari.

4 recordsLinked to original sources

arXiv2026

Pyroclast: A Modular High-Performance Python Solver for Geodynamics

This monograph presents the design, implementation, and evaluation of Pyroclast, a modular high-performance Python framework for large-scale geodynamic simulations. Pyroclast addresses limitations of legacy geodynamics solvers, often implemented in monolithic Fortran, C++, or C codebases with limited GPU support and extensibility, by combining modern numerical methods, hardware-accelerated execution, and a flexible object-oriented architecture. Designed for distributed and GPU-accelerated environments, Pyroclast provides an accessible and efficient platform for simulating mantle convection and lithospheric deformation using the marker-in-cell method and a matrix-free finite difference discretization. The work focuses on a scalable two-dimensional viscous mechanical solver that forms the computational core for future visco-elasto-plastic models. The solver includes a stress-conservative staggered grid discretization of the incompressible Stokes equations, a matrix-free geometric multigrid solver, Krylov and quasi-Newton methods, and MPI-based domain decomposition for distributed execution. Benchmarks evaluate performance and scalability. Shared-memory tests show strong scaling of the Stokes solver and demonstrate a 5-10x speedup on NVIDIA A100 GPUs compared to a multi-core CPU baseline. Distributed advection benchmarks show near-ideal weak scaling up to 896 CPU cores across seven compute nodes. These results demonstrate that Pyroclast achieves high performance while remaining accessible through a high-level Python interface. The framework also provides a blueprint for modernizing legacy geodynamics codes. Its modular architecture and Python-native implementation lower the barrier to entry while enabling interoperability with modern machine learning libraries, enabling hybrid physics-based and data-driven workflows.

cs.MS↗

arXiv2025

3D Blocking for Matrix-free Smoothers in 2D Variable-Viscosity Stokes Equations with Applications to Geodynamics

We present the design, implementation, and evaluation of optimized matrix-free stencil kernels for multigrid smoothing in the incompressible Stokes equations with variable viscosity, motivated by geophysical flow problems. We investigate five smoother variants derived from different optimisation strategies: Red-Black Gauss-Seidel, Jacobi, fused Jacobi, blocked fused Jacobi, and a novel Jacobi smoother with RAS-type temporal blocking, a strategy that applies local iterations on overlapping tiles to improve cache reuse. To ensure correctness, we introduce an energy-based residual norm that balances velocity and pressure contributions, and validate all implementations using a high-contrast sinker benchmark representative of realistic geodynamic numerical models. Our performance study on NVIDIA GH200 Grace Hopper nodes of the ALPS supercomputer demonstrates that all smoothers scale well within a single NUMA domain, but the RAS-Jacobi smoother consistently achieves the best performance at higher core counts. It sustains over 90% weak-scaling efficiency up to 64 cores and delivers up to a threefold speedup compared to the C++ Jacobi baseline, owing to improved cache reuse and reduced memory traffic. These results show that temporal blocking, already employed in distributed-memory solvers to reduce communication, can also provide substantial benefits at the socket and NUMA level. This work highlights the importance of cache-aware stencil design for harnessing modern heterogeneous architectures and lays the groundwork for extending RAS-type temporal blocking strategies to three-dimensional problems and GPU accelerators.

physics.comp-ph↗

arXiv2024

A Comparison of Sparse Solvers for Severely Ill-Conditioned Linear Systems in Geophysical Marker-In-Cell Simulations

Solving sparse linear systems is a critical challenge in many scientific and engineering fields, particularly when these systems are severely ill-conditioned. This work aims to provide a comprehensive comparison of various solvers designed for such problems, offering valuable insights and guidance for domain scientists and researchers. We develop the tools required to accurately evaluate the performance and correctness of 16 solvers from 11 state-of-the-art numerical libraries, focusing on their effectiveness in handling ill-conditioned matrices. The solvers were tested on linear systems arising from a coupled hydro-mechanical marker-in-cell geophysical simulation. To address the challenge of computing accurate error bounds on the solution, we introduce the Projected Adam method, a novel algorithm to efficiently compute the condition number of a matrix without relying on eigenvalues or singular values. Our benchmark results demonstrate that Intel oneAPI MKL PARDISO, UMFPACK, and MUMPS are the most reliable solvers for the tested scenarios. This work serves as a resource for selecting appropriate solvers, understanding the impact of condition numbers, and improving the robustness of numerical solutions in practical applications.

math.NA↗

arXiv2023

A High-Performance Design, Implementation, Deployment, and Evaluation of The Slim Fly Network

Novel low-diameter network topologies such as Slim Fly (SF) offer significant cost and power advantages over the established Fat Tree, Clos, or Dragonfly. To spearhead the adoption of low-diameter networks, we design, implement, deploy, and evaluate the first real-world SF installation. We focus on deployment, management, and operational aspects of our test cluster with 200 servers and carefully analyze performance. We demonstrate techniques for simple cabling and cabling validation as well as a novel high-performance routing architecture for InfiniBand-based low-diameter topologies. Our real-world benchmarks show SF's strong performance for many modern workloads such as deep neural network training, graph analytics, or linear algebra kernels. SF outperforms non-blocking Fat Trees in scalability while offering comparable or better performance and lower cost for large network sizes. Our work can facilitate deploying SF while the associated (open-source) routing architecture is fully portable and applicable to accelerate any low-diameter interconnect.

cs.NI↗