Related papers: Subdomain Deflation Combined with Local AMG: a Cas…
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…
Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with…
We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear…
Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…
Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of…
This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner…
This documentation is designed for beginners in Graphics Processing Unit (GPU)-programming and who want to get familiar with OpenACC and OpenMP offloading models. Here we present an overview of these two programming models as well as of the…
This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood ($\pmb{\mathbb{P}}_2/\mathbb{P}_1$) and Scott-Vogelius ($\pmb{\mathbb{P}}_2/\mathbb{P}_1^{disc}$) discretizations of the Stokes equations. The…
This paper presents our work on designing scalable linear solvers for large-scale reservoir simulations. The main objective is to support implementation of parallel reservoir simulators on distributed-memory parallel systems, where MPI…
We develop a new approach to tackle communication constraints in a distributed learning problem with a central server. We propose and analyze a new algorithm that performs bidirectional compression and achieves the same convergence rate as…
The numerical simulation of cardiac electrophysiology is a highly challenging problem in scientific computing. The Bidomain system is the most complete mathematical model of cardiac bioelectrical activity. It consists of an elliptic and a…
We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the…
Extreme and isolated eigenvalues are known to be harmful to the convergence of an iterative solver. These eigenvalues can be produced by strong heterogeneity in the underlying physics. We can improve the quality of the spectrum by…
This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition…
This paper introduces the Bi-linear consensus Alternating Direction Method of Multipliers (Bi-cADMM), aimed at solving large-scale regularized Sparse Machine Learning (SML) problems defined over a network of computational nodes.…
This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which aim to take advantage of separable structures of the original problem by solving a sequence of lower-dimensional MILPs. The…
Topology optimization problems generally support multiple local minima, and real-world applications are typically three-dimensional. In previous work [I. P. A. Papadopoulos, P. E. Farrell, and T. M. Surowiec, Computing multiple solutions of…
Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…