Related papers: Numerical Study of Geometric Multigrid Methods on …
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
Real-time remote sensing applications like search and rescue missions, military target detection, environmental monitoring, hazard prevention and other time-critical applications require onboard real time processing capabilities or…
Eulerian nonlinear uncertainty propagation methods often suffer from finite domain limitations and computational inefficiencies. A recent approach to this class of algorithm, Grid-based Bayesian Estimation Exploiting Sparsity, addresses the…
Exascale computing delivers the raw power to simulate ever larger and more chemically realistic systems, but realizing this potential requires codes that can efficiently use thousands of processors. Our real-space multigrid (RMG) density…
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 introduce a homogeneous multigrid method in the sense that it uses the same embedded discontinuous Galerkin (EDG) discretization scheme for Poisson's equation on all levels. In particular, we use the injection operator developed in…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…
The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners,…
Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient algorithms suitable for…
Graph partitioning, a well studied problem of parallel computing has many applications in diversified fields such as distributed computing, social network analysis, data mining and many other domains. In this paper, we introduce FGPGA, an…
Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…
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 a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the iterative solution of the linear systems of equations…
We present the deep neural network multigrid solver (DNN-MG) that we develop for the instationary Navier-Stokes equations. DNN-MG improves computational efficiency using a judicious combination of a geometric multigrid solver and a…
The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of…
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…
Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/polyhedral (henceforth, collectively termed as \emph{polytopic}) elements have received considerable attention in recent years. Due to the physical frame basis functions…
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…
The conductor-like polarization model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in chemical simulations. However, its application in quantum mechanical calculations of large-scale…