Related papers: A New Semi-Structured Algebraic Multigrid Method
In this work, we introduce a Self-Aware Polymorphic Architecture (SAPA) design approach to support emerging context-aware applications and mitigate the programming challenges caused by the ever-increasing complexity and heterogeneity of…
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on…
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…
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…
A merger of two optimization frameworks is introduced: SEquential Subspace OPtimization (SESOP) with MultiGrid (MG) optimization. At each iteration of the algorithm, the search direction implied by the coarse-grid correction process of MG…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
The ability to perform mathematical computations using metastructures is an emergent paradigm that carries the potential of wave-based analog computing to the realm of near-speed-of-light, low-loss, compact devices. We theoretically…
We describe ASAGA, an asynchronous parallel version of the incremental gradient algorithm SAGA that enjoys fast linear convergence rates. Through a novel perspective, we revisit and clarify a subtle but important technical issue present in…
Inspired by the developments in quantum computing, building domain-specific classical hardware to solve computationally hard problems has received increasing attention. Here, by introducing systematic sparsification techniques, we…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…
For several decades, the CPU has been the standard model to use in the majority of computing. While the CPU does excel in some areas, heterogeneous computing, such as reconfigurable hardware, is showing increasing potential in areas like…
Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models…
A novel language system has given rise to promising alternatives to standard formal and processor network models of computation. An interstring linked with a abstract machine environment, shares sub-expressions, transfers data, and…
We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a "neural computations" point of view into large scale…
To improve the computational efficiency of heat transfer topology optimization, a Multigrid Assisted Reanalysis (MGAR) method is proposed in this study. The MGAR not only significantly improves the computational efficiency, but also…
The Shifted Boundary Method (SBM) trades some part of the burden of body-fitted meshing for increased algebraic complexity. While the resulting linear systems retain the standard $\mathcal{O}(h^{-2})$ conditioning of second-order operators,…
Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are…
Heterogeneous many-cores are now an integral part of modern computing systems ranging from embedding systems to supercomputers. While heterogeneous many-core design offers the potential for energy-efficient high-performance, such potential…
This paper presents our work on designing a parallel platform for large-scale reservoir simulations. Detailed components, such as grid and linear solver, and data structures are introduced, which can serve as a guide to parallel reservoir…
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…