Related papers: Multigrid Solvers in Reconfigurable Hardware
This paper presents a novel method designed to generate multigrid solvers optimized for octree-based software frameworks. Our approach focuses on accurately capturing local features within a domain while leveraging the efficiency inherent…
Adaptive multi-grid methods have proven very successful in dealing with critical slow down for the Wilson-Dirac solver in lattice gauge theory. Multi-grid algorithms developed for Staggered fermions using the K\"ahler-Dirac…
We present a convergent and scalable multigrid solver for high-frequency Helmholtz equations. Standard multigrid methods do not converge for high-frequency Helmholtz problems, and a common cure is adding a complex shift and using the…
In this chapter, we study the feasibility of implementing SOR in reconfigurable hardware. We use Handel-C, a higher level design tool, to code our design, which is analyzed, synthesized, and placed and routed using the FPGAs proprietary…
Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators. We are motivated by the problem of developing high-order accurate numerical…
In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
Sparse linear system solvers ($Ax=b$) are critical computational kernels in Electronic Design Automation (EDA), underpinning vital simulations for modern IC and system design. Applications like power integrity verification and…
Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as…
We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence…
Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…
Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and…
In this paper, several two-grid finite element algorithms for solving parabolic integro-differential equations (PIDEs) with nonlinear memory are presented. Analysis of these algorithms is given assuming a fully implicit time discretization.…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
This work presents a GPU-accelerated solver for the unit commitment (UC) problem in large-scale power grids. The solver uses the Primal-Dual Hybrid Gradient (PDHG) algorithm to efficiently solve the relaxed linear subproblem, achieving…
Multigrid is a powerful solver for large-scale linear systems arising from discretized partial differential equations. The convergence theory of multigrid methods for symmetric positive definite problems has been well developed over the…
This paper introduces a geometric multigrid preconditioner for the Shifted Boundary Method (SBM) designed to solve PDEs on complex geometries. While SBM simplifies mesh generation by using a non-conforming background grid, it often results…