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Positive linear programs (LPs) model many graph and operations research problems. One can solve for a $(1+\epsilon)$-approximation for positive LPs, for any selected $\epsilon$, in polylogarithmic depth and near-linear work via variations…
The TREE method has been widely used for long-range interaction {\it N}-body problems. We have developed a parallel TREE code for two-component classical plasmas with open boundary conditions and highly non-uniform charge distributions. The…
An implementation of adaptive mesh refinement algorithms is presented for use with multilayer shallow water equations. Currently, adaptive mesh refinement is implemented with a single layer shallow water model in the GeoClaw framework. This…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…
Algorithms for finding minimum or bounded vertex covers in graphs use a branch-and-reduce strategy, which involves exploring a highly imbalanced search tree. Prior GPU solutions assign different thread blocks to different sub-trees, while…
Building concurrent spatial trees is more complicated than binary search trees since a space hierarchy should be preserved during modifications. We present a non-blocking quadtree-quadboost-that supports concurrent insert, remove, move, and…
We present an efficient algorithm for simultaneously training sparse generalized linear models across many related problems, which may arise from bootstrapping, cross-validation and nonparametric permutation testing. Our approach leverages…
Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…
Skin modeling is an ongoing research area that highly benefits from modern parallel algorithms. This article aims at applying shape optimization to compute cell size and arrangement for elastic energy minimization of a cellular composite…
We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning.…
The lattice Boltzmann method exhibits excellent scalability on current supercomputing systems and has thus increasingly become an alternative method for large-scale non-stationary flow simulations, reaching up to a trillion grid nodes.…
As the data size in Machine Learning fields grows exponentially, it is inevitable to accelerate the computation by utilizing the ever-growing large number of available cores provided by high-performance computing hardware. However, existing…
Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…
Identifying clusters of similar elements in a set is a common task in data analysis. With the immense growth of data and physical limitations on single processor speed, it is necessary to find efficient parallel algorithms for clustering…
Current Adaptive Mesh Refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient…