Related papers: StructMG: A Fast and Scalable Structured Algebraic…
Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…
With the growing complexity and capability of contemporary robotic systems, the necessity of sophisticated computing solutions to efficiently handle tasks such as real-time processing, sensor integration, decision-making, and control…
Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
In this work, we make two improvements on the staggered grid hydrodynamics (SGH) Lagrangian scheme for modeling 2-dimensional compressible multi-material flows on triangular mesh. The first improvement is the construction of a dynamic local…
We propose and investigate new robust preconditioners for space-time Isogeometric Analysis of parabolic evolution problems. These preconditioners are based on a time parallel multigrid method. We consider a decomposition of the space-time…
This study introduces a hybrid machine learning-based scale-bridging framework for predicting the permeability of fibrous textile structures. By addressing the computational challenges inherent to multiscale modeling, the proposed approach…
Bundle adjustment is an important global optimization step in many structure from motion pipelines. Performance is dependent on the speed of the linear solver used to compute steps towards the optimum. For large problems, the current state…
Boundary value problems based on the convection-diffusion equation arise naturally in models of fluid flow across a variety of engineering applications and design feasibility studies. Naturally, their efficient numerical solution has…
An idealized multigrid algorithm for the computation of propagators of staggered fermions is investigated. Exemplified in four-dimensional $SU(2)$ gauge fields, it is shown that the idealized algorithm preserves criticality under…
We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling…
We investigate the problem of minimizing the expectation of smooth nonconvex functions in a distributed setting with multiple parallel workers that are able to compute stochastic gradients. A significant challenge in this context is the…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
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…
Preconditioned Krylov subspace (KSP) methods are widely used for solving large-scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs). These linear systems are often nonsymmetric due to the…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Reduction multigrids have recently shown good performance in hyperbolic problems without the need for Gauss-Seidel smoothers. When applied to the hyperbolic limit of the Boltzmann Transport Equation (BTE), these methods result in very close…
Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…