Related papers: A Tuned and Scalable Fast Multipole Method as a Pr…
Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct…
This article introduces a highly parallel algorithm for molecular dynamics simulations with short-range forces on single node multi- and many-core systems. The algorithm is designed to achieve high parallel speedups for strongly…
We present an algorithm to parallelize the inverse fast multipole method (IFMM), which is an approximate direct solver for dense linear systems. The parallel scheme is based on a greedy coloring algorithm, where two nodes in the hierarchy…
The Fast Multipole Method (FMM) reduces the computation of pairwise two-body interactions among $N$-particles to order $N$, whose computation cost should be of order $N^2$ by brute force. However, its implementation is somewhat complicated…
Kernel matrix-vector multiplication (KMVM) is a foundational operation in machine learning and scientific computing. However, as KMVM tends to scale quadratically in both memory and time, applications are often limited by these…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for the on-going and the future high precious sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity,…
Current integration, architectural design and manufacturing technologies are not suited for the computing density and power efficiency requested by Exascale computing. New approaches in hardware architecture are thus needed to overcome the…
This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method…
Fast algorithms for the computation of $N$-body problems can be broadly classified into mesh-based interpolation methods, and hierarchical or multiresolution methods. To this last class belongs the well-known fast multipole method (FMM),…
Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle…
Large language models (LLMs) have demonstrated remarkable success as foundational models, benefiting various downstream applications through fine-tuning. Recent studies on loss scaling have demonstrated the superior performance of larger…
In the era of big data, it is desired to develop efficient machine learning algorithms to tackle massive data challenges such as storage bottleneck, algorithmic scalability, and interpretability. In this paper, we develop a novel efficient…
Evaluation of pair potentials is critical in a number of areas of physics. The classicalN-body problem has its root in evaluating the Laplace potential, and has spawned tree-algorithms, the fast multipole method (FMM), as well as kernel…
Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…
Large Language Models (LLMs) continue to demonstrate superior performance with increasing scale, yet training models with billions to trillions of parameters requires staggering computational resources, e.g. a one-trillion-parameter…
Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through…
In the recent years, multi-core processor designs have found their way into many computing devices. To exploit the capabilities of such devices in the best possible way, signal processing algorithms have to be adapted to an operation in…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the…