Related papers: Domain Decomposition method on GPU cluster
We extend the tensor-product direct solver from the Laplacian to the Schr\"odinger operator $-\Delta + V$. When the potential $V_1$ is separable, the operator $-\Delta + V_1$ is inverted or exponentiated at cost $O(N^{1+1/d})$ in $d$…
The observed and expected continued growth in the number of nodes in large-scale parallel computers gives rise to two major challenges: global communication operations are becoming major bottlenecks due to their limited scalability, and the…
We present an overview of our project of simulation of unquenched lattice QCD with optimal domain-wall quarks, using a GPU cluster currently constituting of 16 units of Nvidia Tesla S1070 plus 64 graphic cards with Nvidia GTX285 (total 128…
Linear solvers are key components in any software platform for scientific and engineering computing. The solution of large and sparse linear systems lies at the core of physics-driven numerical simulations relying on partial differential…
Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of…
Graphical Processing Units (GPUs) are more and more frequently used for lattice QCD calculations. Lattice studies often require computing the quark propagators for several masses. These systems can be solved using multi-shift inverters but…
This paper explores a family of generalized sweeping preconditionners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission…
A combination of block-Jacobi and deflation preconditioning is used to solve a high-order discontinuous collocation-based discretization of the Schur complement of the Poisson-Neumann system as arises in the operator splitting of the…
Neural Architecture Search (NAS) methods have shown to output networks that largely outperform human-designed networks. However, conventional NAS methods have mostly tackled the single dataset scenario, incuring in a large computational…
We outline the essential features of a Linux PC cluster which is now being developed at National Taiwan University, and discuss how to optimize its hardware and software for lattice QCD with overlap Dirac quarks. At present, the cluster…
Data centers handle vast volumes of data that require efficient lossless compression, yet emerging probabilistic models based methods are often computationally slow. To address this, we introduce RAS, the Range Asymmetric Numeral System…
This paper proposes a novel two-stage hybrid domain decomposition algorithm to speed up the dynamic simulations and the analysis of power systems that can be computationally demanding due to the high penetration of renewables. On the first…
The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…
Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given…
Two-level domain decomposition preconditioners lead to fast convergence and scalability of iterative solvers. However, for highly heterogeneous problems, where the coefficient function is varying rapidly on several possibly non-separated…
This paper investigates the multi-GPU performance of a 3D buoyancy driven cavity solver using MPI and OpenACC directives on different platforms. The paper shows that decomposing the total problem in different dimensions affects the strong…
We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…
In this paper, we propose an innovative isogeometric low-rank solver for the linear elasticity model problem, specifically designed to allow multipatch domains. Our approach splits the domain into subdomains, each formed by the union of…
We demonstrate algorithm-based fault tolerance for silent, transient data corruption in "black-box" preconditioners. We consider both additive Schwarz domain decomposition with an ILU(k) subdomain solver, and algebraic multigrid, both…
We propose a novel GPU-cluster scheduler for distributed DL (DDL) workloads that enables proximity based consolidation of GPU resources based on the DDL jobs' sensitivities to the anticipated communication-network delays. Our scheduler…