Daniel Bielich | Searcharxiv

arXiv2026

Report of the 2026 Workshop on Next-Generation Ecosystems for Scientific Computing: Harnessing Community, Software, and AI for Cross-Disciplinary Team Science

Scientific computing is undergoing rapid transformation as advances in artificial intelligence, heterogeneous computing, automation, and data-intensive research reshape not only computational tools but also the institutions, workforce models, and collaborative practices that support scientific discovery. This report synthesizes insights from the 2026 Workshop on Next-Generation Ecosystems for Scientific Computing, the second in a three-year series focused on strengthening scientific computing ecosystems through socio-technical co-design. Workshop discussions identified four interdependent strategic themes: software ecosystems for AI-enabled scientific discovery; trust, validation, and traceability; human-AI teaming and paradigm shifts; and workforce, pedagogy, and governance. The report translates these themes into eight priorities for community action spanning shared research infrastructure, trust and traceability, user experience, human-AI teaming, workforce development, cross-sector coordination, stewardship and sustainability, and evaluation of scientific value. Together, these priorities outline directions for building scientific computing ecosystems that remain trustworthy, sustainable, innovative, and resilient as AI assumes a growing role in scientific work.

cs.CE↗

arXiv2021

Low-Synch Gram-Schmidt with Delayed Reorthogonalization for Krylov Solvers

The parallel strong-scaling of Krylov iterative methods is largely determined by the number of global reductions required at each iteration. The GMRES and Krylov-Schur algorithms employ the Arnoldi algorithm for nonsymmetric matrices. The underlying orthogonalization scheme is left-looking and processes one column at a time. Thus, at least one global reduction is required per iteration. The traditional algorithm for generating the orthogonal Krylov basis vectors for the Krylov-Schur algorithm is classical Gram Schmidt applied twice with reorthogonalization (CGS2), requiring three global reductions per step. A new variant of CGS2 that requires only one reduction per iteration is applied to the Arnoldi-QR iteration. Strong-scaling results are presented for finding eigenvalue-pairs of nonsymmetric matrices. A preliminary attempt to derive a similar algorithm (one reduction per Arnoldi iteration with a robust orthogonalization scheme) was presented by Hernandez et al.(2007). Unlike our approach, their method is not forward stable for eigenvalues.

math.NA↗