Related papers: Nonsymmetric Algebraic Multigrid Based on Local Ap…
We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…
In this paper we present a Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem. The space-time discretization is based on arbitrarily high order discontinuous Galerkin spectral element methods in time and a…
We present a unified treatment of the Fourier spectra of spherically symmetric nonlocal diffusion operators. We develop numerical and analytical results for the class of kernels with weak algebraic singularity as the distance between source…
Current Adaptive Mesh Refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient…
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…
We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast direct solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions.…
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…
Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual…
The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis. While algebraic multigrid (AMG) offers optimal linear scaling, its performance is severely constrained by the trade-off between…
Algebraic multigrid (AMG) is conventionally applied in a black-box fashion, agnostic to the underlying geometry. In this work, we propose that using geometric information -- when available -- to assist with setting up the AMG hierarchy is…
We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of…
The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…
Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…
We present a generic algorithm for learning and approximate inference with an intuitive epistemic interpretation: iteratively focus on a subset of the model and resolve inconsistencies using the parameters under control. This framework,…
Multigrid algorithms are among the fastest iterative methods known today for solving large linear and some non-linear systems of equations. Greatly optimized for serial operation, they still have a great potential for parallelism not fully…
We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an…
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…
Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational…
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…
Method for a mosaic image representation (MIR) is proposed for a selective treatment of image fragments of different transition frequency. MIR method is based on piecewise-constant image approximation on a non-uniform orthogonal grid…