Related papers: A GPU-based Multi-level Algorithm for Boundary Val…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An…
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…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…
In this thesis we develop techniques to efficiently solve numerical Partial Differential Equations (PDEs) using Graphical Processing Units (GPUs). Focus is put on both performance and re--usability of the methods developed, to this end a…
A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018),…
Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value…
We study exact sparse linear regression with an $\ell_0-\ell_2$ penalty and develop a branch-and-bound (BnB) algorithm explicitly designed for GPU execution. Starting from a perspective reformulation, we derive an interval relaxation that…
This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been…
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…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
Hypergraph partitioning is a pervasive NP-hard problem, and accelerating its computation on GPU can both slice time-to-solution and raise quality of results. In this work, we implement a multi-level hypergraph partitioning algorithm on GPU…
DC Optimal Power Flow (DCOPF) is a key operational tool for power system operators, and it is embedded as a subproblem in many challenging optimization problems (e.g., line switching). However, traditional CPU-based solve routines (e.g.,…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
Dynamic programming (DP) is a cornerstone of combinatorial optimization, yet its inherently sequential structure has long limited its scalability in scenario-based stochastic programming (SP). This paper introduces a GPU-accelerated…
We propose a GPU-based distributed optimization algorithm, aimed at controlling optimal power flow in multi-phase and unbalanced distribution systems. Typically, conventional distributed optimization algorithms employed in such scenarios…
We present an efficient implementation for running three-dimensional numerical simulations of fluid-structure interaction problems on single GPUs, based on Nvidia CUDA through Numba and Python. The incompressible flow around moving bodies…