8 papers
This paper introduces two new families of multirate time step adaptivity controllers and a set of fifth-order embedded MERK methods, demonstrating their superior performance and flexibility in efficiently solving problems with multiple time scales through adaptive simulations.
This paper presents the first direct programming of FP64 tensor cores on NVIDIA GPUs to accelerate high-order finite element simulations within the MFEM library, achieving up to 2× performance and 83% energy efficiency gains while demonstrating near-perfect weak scaling across nearly 10,000 GPUs on the Alps exascale system.
This paper introduces \texttt{EinSum}, a tensor-relational extension of Einstein Summation Notation that automatically rewrites computations to leverage efficient numerical kernels for dense operations while utilizing relational systems to manage large-scale sparsity.
This paper presents a fully device-resident, multi-GPU architecture that achieves near-zero host-device communication and 99.7% parallel efficiency through lock-free work-stealing and optimized shared-memory tiling, enabling the verification of Goldbach's conjecture up to $10^{13}$ in just 133.5 seconds on a four-GPU system with a 45.6× speedup over previous methods.
This technical note presents a JAX-compatible implementation of the Self-Scaled Broyden family of quasi-Newton methods, including BFGS, DFP, and Broyden variants with Zoom line search, built upon the Optimistix library to facilitate their adoption within the JAX community.
Threadle is a high-performance, memory-efficient C# engine designed to store and query massive, multilayer, mixed-mode networks by utilizing a pseudo-projection approach that avoids the prohibitive memory costs of materializing two-mode data projections.
This paper presents an efficient algorithm that utilizes partial Gröbner basis computation and sparse interpolation to find simple generating sets for subfields of rational function fields, demonstrating improved performance and practical utility in applications like structural parameter identifiability.
This paper presents numerically stable, closed-form algorithms for computing the eigenvalues of real, diagonalizable $3 \times 3$ matrices using four specific invariants, demonstrating that these methods are both more accurate for repeated eigenvalues and approximately ten times faster than the LAPACK library while maintaining comparable precision.