Related papers: Vertex-based auxiliary space multigrid method and …
This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for…
Algebraic multigrid is an iterative method that is often optimal for solving the matrix equations that arise in a wide variety of applications, including discretized partial differential equations. It automatically constructs a sequence of…
In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver…
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…
One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum…
We propose a robust, adaptive coarse-grid correction scheme for matrix-free geometric multigrid targeting PDEs with strongly varying coefficients. The method combines uniform geometric coarsening of the underlying grid with heterogeneous…
In this study, we present an $hp$-multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier-Stokes equations using an augmented Lagrangian formulation. Our method relies on conforming…
Reconstruction of evolutionary relationships between species is an important topic in the field of computational biology. Pairwise compatibility graphs (PCGs) are used to model such relationships. A graph is a PCG if its edges can be…
This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-DG) method for computing high dimensional partial differential equations (PDEs) and its software implementation. The C\texttt{++} software package called AdaM-DG,…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…
Methods for solving hyperbolic systems typically depend on unknown ordering (e.g., Gauss-Seidel, or sweep/wavefront/marching methods) to achieve good convergence. For many discretisations, mesh types or decompositions these methods do not…
We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial differential equations (PDEs) with large near-kernels, such as…
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…
Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…
The paper proposes a novel adaptive search space decomposition method and a novel gradient-free optimization-based formulation for the pre- and post-buckling analyses of space truss structures. Space trusses are often employed in structural…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
This paper presents a multigrid algorithm for the computation of the rank-R canonical decomposition of a tensor for low rank R. Standard alternating least squares (ALS) is used as the relaxation method. Transfer operators and coarse-level…
In this paper, we present very first results for the adaptive solution on a grid of the phase space of the Vlasov equation arising in particles accelarator and plasma physics. The numerical algorithm is based on a semi-Lagrangian method…
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…