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Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…

Designing efficient and scalable sparse linear algebra kernels on modern multi-GPU based HPC systems is a daunting task due to significant irregular memory references and workload imbalance across the GPUs. This is particularly the case for…

The material point method (MPM) is a hybrid particle-grid method widely used for simulating large deformation with history-dependent behavior. Standard MPM often relies on a dense background grid, which can be highly inefficient when…

Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…

Sparse matrix multiplication is traditionally performed in memory and scales to large matrices using the distributed memory of multiple nodes. In contrast, we scale sparse matrix multiplication beyond memory capacity by implementing sparse…

In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…

We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise…

Multilinear transformations are key in high-performance computing (HPC) and artificial intelligence (AI) workloads, where data is represented as tensors. However, their high computational and memory demands, which grow with dimensionality,…

Heterogeneous computing is becoming mainstream in all scopes. This new era in computer architecture brings a new paradigm called Accelerator Level Parallelism (ALP). In ALP, accelerators are used concurrently to provide unprecedented levels…

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

Sparse data structures are commonly used in neural networks to reduce the memory footprint. These data structures are compact but cause irregularities such as random memory accesses, which prevent efficient use of the memory hierarchy. GPUs…

This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often understood as the acronym of "Algebraic Multi-Grid", but it…

Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi-) Monte Carlo method are closely related to the sparse tensor product approximation between the spatial variable and the parameter. In this…

As users and developers, we are witnessing the opening of a new computing scenario: the introduction of hybrid processors into a single die, such as an accelerated processing unit (APU) processor, and the plug-and-play of additional…

A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…

We address the communication overhead of distributed sparse matrix-(multiple)-vector multiplication in the context of large-scale eigensolvers, using filter diagonalization as an example. The basis of our study is a performance model which…

Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…

As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…

Several manufacturers have already started to commercialize near-bank Processing-In-Memory (PIM) architectures. Near-bank PIM architectures place simple cores close to DRAM banks and can yield significant performance and energy improvements…

We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model (coarsened with respect to variables) and a coarse…