Related papers: Hierarchical Jacobi Iteration for Structured Matri…
The ability to timely process significant amounts of continuously updated spatial data is mandatory for an increasing number of applications. Parallelism enables such applications to face this data-intensive challenge and allows the devised…
We present a new algorithm to quickly generate high-performance GPU implementations of complex imaging and vision pipelines, directly from high-level Halide algorithm code. It is fully automatic, requiring no schedule templates or…
In this paper, we introduce innovative approaches for accelerating the Jacobi method for matrix diagonalization, specifically through the formulation of large matrix diagonalization as a Semi-Markov Decision Process and small matrix…
Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…
Solving partial differential equations with deep learning makes it possible to reduce simulation times by multiple orders of magnitude and unlock scientific methods that typically rely on large numbers of sequential simulations, such as…
Sparse linear systems are typically solved using preconditioned iterative methods, but applying preconditioners via sparse triangular solves introduces bottlenecks due to irregular memory accesses and data dependencies. This work leverages…
Hardware heterogeneity is here to stay for high-performance computing. Large-scale systems are currently equipped with multiple GPU accelerators per compute node and are expected to incorporate more specialized hardware in the future. This…
The kernel-free boundary integral (KFBI) method has successfully solved partial differential equations (PDEs) on irregular domains. Diverging from traditional boundary integral methods, the computation of boundary integrals in KFBI is…
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
This manuscript presents GPU optimizations for the 2D Hierarchical Poincar\'e-Steklov (HPS) discretization scheme. HPS is a multi-domain spectral collocation method that combines high-order discretizations with direct solvers to accurately…
GPU-based heterogeneous architectures are now commonly used in HPC clusters. Due to their architectural simplicity specialized for data-level parallelism, GPUs can offer much higher computational throughput and memory bandwidth than CPUs in…
Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…
We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…
For the purposes of electric circuit simulation, we consider an iterative simulation model based on solving systems of linear equations by Gauss-Jordan elimination (GJE) for individual moments in time. To accelerate the simulation, we…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our…
The parallel simulation of Spiking Neural P systems is mainly based on a matrix representation, where the graph inherent to the neural model is encoded in an adjacency matrix. The simulation algorithm is based on a matrix-vector…
Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces…