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A projection-based immersed boundary method is dominated by sparse linear algebra routines. Using the open-source Cusp library, we observe a speedup (with respect to a single CPU core) which reflects the constraints of a bandwidth-dominated…
Programming high-performance sparse GPU kernels is notoriously difficult, requiring both substantial effort and deep expertise. Sparse compilers aim to simplify this process, but existing systems fall short in two key ways. First, they are…
The simulation of the two-dimensional Ising model is used as a benchmark to show the computational capabilities of Graphic Processing Units (GPUs). The rich programming environment now available on GPUs and flexible hardware capabilities…
Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
The Primal-Dual Hybrid Gradient (PDHG) algorithm is a first-order method that can exploit GPUs to solve large-scale linear programming problems. The approach can often be faster than the alternatives, simplex and interior-point methods,…
First order methods, which solely rely on gradient information, are commonly used in diverse machine learning (ML) and data analysis (DA) applications. This is attributed to the simplicity of their implementations, as well as low…
In this paper, we provide an affirmative answer to the long-standing question: Are GPUs useful in solving linear programming? We present cuPDLP.jl, a GPU implementation of restarted primal-dual hybrid gradient (PDHG) for solving linear…
Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…
We present a GPU implementation of vertex-patch smoothers for higher order finite element methods in two and three dimensions. Analysis shows that they are not memory bound with respect to GPU DRAM, but with respect to on-chip scratchpad…
We propose a GPU accelerated proximal message passing algorithm for solving contingency-constrained DC optimal power flow problems (OPF). We consider a highly general formulation of OPF that uses a sparse device-node model and supports a…
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…
The number of cores on graphical computing units (GPUs) is reaching thousands nowadays, whereas the clock speed of processors stagnates. Unfortunately, constraint programming solvers do not take advantage yet of GPU parallelism. One reason…
We present a GPU-accelerated backend for QOCO, a C-based solver for quadratic objective second-order cone programs (SOCPs) based on a primal-dual interior point method. Our backend uses NVIDIA's cuDSS library to perform a direct sparse LDL…
GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…
In this paper, we address a long-standing challenge: how to achieve both efficiency and scalability in solving semidefinite programming problems. We propose breakthrough acceleration techniques for a wide range of low-rank…
We present a matrix-free multigrid method for high-order discontinuous Galerkin (DG) finite element methods with GPU acceleration. A performance analysis is conducted, comparing various data and compute layouts. Smoother implementations are…
This report presents a comprehensive analysis of the performance of GPU accelerated meshfree CFD solvers for two-dimensional compressible flows in Fortran, C++, Python, and Julia. The programming model CUDA is used to develop the GPU codes.…
This paper presents a GPU-accelerated framework for solving block tridiagonal linear systems that arise naturally in numerous real-time applications across engineering and scientific computing. Through a multi-stage permutation strategy…