Related papers: PittPack: An Open-Source Poisson's Equation Solver…

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

Large deep learning models have demonstrated strong ability to solve many tasks across a wide range of applications. Those large models typically require training and inference to be distributed. Tensor parallelism is a common technique…

We review the derivation of the Kac master equation model for random collisions of particles, its relationship to the Poisson process, and existing algorithms for simulating values from the marginal distribution of velocity for a single…

We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable…

We present a direct Poisson solver for massively parallel simulations on three-dimensional Cartesian grids with non-uniform spacing. The method uses a tensor-based formulation in which the operator is diagonalized numerically along two…

This paper considers the problem of distributed source coding for a large network. A major obstacle that poses an existential threat to practical deployment of conventional approaches to distributed coding is the exponential growth of the…

The Jaccard similarity index is an important measure of the overlap of two sets, widely used in machine learning, computational genomics, information retrieval, and many other areas. We design and implement SimilarityAtScale, the first…

The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the…

The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…

We introduce novel communication strategies in synchronous distributed Deep Learning consisting of decentralized gradient reduction orchestration and computational graph-aware grouping of gradient tensors. These new techniques produce an…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

Connected Components (CC) is a core graph problem with numerous applications. This paper investigates accelerating distributed CC by optimizing memory and network bandwidth utilization. We present two novel distributed CC algorithms,…

Partitioning large machine learning models across distributed accelerator systems is a complex process, requiring a series of interdependent decisions that are further complicated by internal sharding ambiguities. Consequently, existing…

We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order…

It is demonstrated how the non-proprietary OpenACC standard of compiler directives may be used to compactly and efficiently accelerate the rate-determining steps of two of the most routinely applied many-body methods of electronic structure…

The Poisson equation has applications across many areas of physics and engineering, such as the dynamic process simulation of ocean current. Here we present a quantum Fast Poisson Solver, including the algorithm and the complete and modular…

We present a massively parallel solver that accelerates DC loadflow computations for power grid topology optimization tasks. Our approach leverages low-rank updates of the Power Transfer Distribution Factors (PTDFs) to represent substation…

This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic…

This paper presents an optimized and scalable semi-Lagrangian solver for the Vlasov-Poisson system in six-dimensional phase space. Grid-based solvers of the Vlasov equation are known to give accurate results. At the same time, these solvers…

The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…