A Coarse Grid Correction to Domain Decomposition Based Preconditioners for Meso-Scale Simulation of Concrete

Meso-scale simulation is one of the important ways to study dynamic behaviors of concrete materials, while most of the simulation time is used to solve the sparse linear systems. Because the discrete grid is three dimensional and is of large scale, iterations are the best solutions. But the convergence depends on the distribution of the eigenvalues of the coefficient matrix, to make the eigenvalues distributed more closely each other, it is required to adopt preconditioning techniques. In this paper, with the characteristics of the sparse linear systems considered, there provides a coarse grid correction algorithm, which is based on domain decomposition preconditioners and aggregation of sub-domains, with each aggregated into a single super-node. A linear system with small scale size is formed, which contains the global information and the solution is used to correct the solution components of the original auxiliary linear system. For incomplete factorization preconditioner parallelized with block Jacobi, classic additive Schwarz, and factors combination techniques, the experiments show that the presented algorithm can improve the convergence rate and the efficiency.

Download Full-text

A parallel algorithm for direct solution of large sparse linear systems, well suitable to domain decomposition methods

European Journal of Computational Mechanics ◽

10.13052/ejcm.18.589-605 ◽

2009 ◽

pp. 589-605

Author(s):

Ibrahima Gueye ◽

Xavier Juvigny ◽

Frédéric Feyel ◽

François-Xavier Roux ◽

Georges Cailletaud

Keyword(s):

Domain Decomposition ◽

Parallel Algorithm ◽

Linear Systems ◽

Decomposition Methods ◽

Computational Effort ◽

Direct Solution ◽

Sparse Linear Systems ◽

Domain Decomposition Methods ◽

Direct Solver ◽

Upper Level

The goal of this paper is to develop a parallel algorithm for the direct solution of large sparse linear systems and integrate it into domain decomposition methods. The computational effort for these linear systems, often encountered in numerical simulation of structural mechanics problems by finite element codes, is very significant in terms of run-time and memory requirements.In this paper, a two-level parallelism is exploited. The exploitation of the lower level of parallelism is based on the development of a parallel direct solver with a nested dissection algorithm and to introduce it into the FETI methods. This direct solver has the advantage of handling zero-energy modes in floating structures automatically and properly. The upper level of parallelism is a coarse-grain parallelism between substructures of FETI. Some numerical tests are carried out to evaluate the performance of the direct solver.

Download Full-text

Accelerating advanced preconditioning methods on hybrid architectures

CLEI electronic journal ◽

10.19153/cleiej.24.1.6 ◽

2021 ◽

Vol 24 (1) ◽

Author(s):

Ernesto Dufrechou

Keyword(s):

Linear Systems ◽

Large Scale ◽

Krylov Subspace ◽

Linear Equations ◽

Memory Systems ◽

Sparse Linear Systems ◽

Data Parallel ◽

Systems Of Linear Equations ◽

Sparse Systems ◽

Computational Bottleneck

Many problems, in diverse areas of science and engineering, involve the solution of largescale sparse systems of linear equations. In most of these scenarios, they are also a computational bottleneck, and therefore their efficient solution on parallel architectureshas motivated a tremendous volume of research.This dissertation targets the use of GPUs to enhance the performance of the solution of sparse linear systems using iterative methods complemented with state-of-the-art preconditioned techniques. In particular, we study ILUPACK, a package for the solution of sparse linear systems via Krylov subspace methods that relies on a modern inverse-based multilevel ILU (incomplete LU) preconditioning technique.We present new data-parallel versions of the preconditioner and the most important solvers contained in the package that significantly improve its performance without affecting its accuracy. Additionally we enhance existing task-parallel versions of ILUPACK for shared- and distributed-memory systems with the inclusion of GPU acceleration. The results obtained show a sensible reduction in the runtime of the methods, as well as the possibility of addressing large-scale problems efficiently.

Download Full-text

Toward improved parameterization of a macro-scale hydrologic model in a discontinuous permafrost boreal forest ecosystem

10.5194/hess-2017-25 ◽

2017 ◽

Author(s):

Abraham Endalamaw ◽

W. Robert Bolton ◽

Jessica M. Young-Robertson ◽

Don Morton ◽

Laryy Hinzman ◽

...

Keyword(s):

Spatial Heterogeneity ◽

Vegetation Cover ◽

Large Scale ◽

Small Scale ◽

Hydrological Models ◽

Landscape Model ◽

Coarse Resolution ◽

Fine Resolution ◽

Resolution Dataset ◽

Meso Scale

Abstract. Modeling hydrological processes in the Alaskan sub-arctic is challenging because of the extreme spatial heterogeneity in soil properties and vegetation communities. However, modeling and predicting hydrological processes is critical in this region due to its vulnerability to the effects of climate change. Coarse spatial resolution datasets used in land surface modeling poised a new challenge in simulating the spatially distributed and basin integrated processes since these datasets do not adequately represent the small-scale hydrologic, thermal and ecological heterogeneity. The goal of this study is to improve the prediction capacity of meso-scale to large-scale hydrological models by introducing a small-scale parameterization scheme, which better represents the spatial heterogeneity of soil properties and vegetation cover in the Alaskan sub-arctic. The small-scale parameterization schemes are derived from observations and fine resolution landscape modeling in the two contrasting sub-basins of the Caribou Poker Creek Research Watershed (CPCRW) in Interior Alaska: one nearly permafrost-free (LowP) and one that is permafrost-dominated (HighP). The fine resolution landscape model used in the small-scale parameterization scheme is derived from the watershed topography. We found that observed soil thermal and hydraulic properties – including the distribution of permafrost and vegetation cover heterogeneity – are better represented in the fine resolution landscape model than the coarse resolution datasets. Parameters derived from coarse resolution dataset and from the fine resolution landscape model are implemented into the Variable Infiltration Capacity (VIC) meso-scale hydrological model to simulate runoff, evapotranspiration (ET) and soil moisture in the two sub-basins of the CPCRW. Simulated hydrographs based on the small-scale parameterization capture most of the peak and low flows with similar accuracy in both sub-basins compared to the parameterization based on coarse resolution dataset. On average, small-scale parameterization improves the total runoff simulation approximately by up to 50 % in the LowP sub-basin and 10 % in the HighP sub-basin from the large-scale parameterization. This study shows that the proposed small-scale landscape model can be used to improve the performance of meso-scale hydrological models in the Alaskan sub-arctic watersheds.

Download Full-text

Solution of Sparse Linear Systems with the Software Package LIS for Meso-scale Finite Element Simulation of Concrete Fractures

Materials Science and Engineering ◽

10.1142/9789813226517_0118 ◽

2017 ◽

Author(s):

Jian-Ping Wu

Keyword(s):

Finite Element ◽

Finite Element Simulation ◽

Linear Systems ◽

Software Package ◽

Sparse Linear Systems ◽

Element Simulation ◽

Concrete Fractures ◽

Meso Scale

Download Full-text

A GaBP-GPU Algorithm of Solving Large-Scale Sparse Linear Systems

Journal of Information and Computational Science ◽

10.12733/jics20102886 ◽

2014 ◽

Vol 11 (3) ◽

pp. 911-921

Author(s):

Hanyuan Zheng

Keyword(s):

Linear Systems ◽

Large Scale ◽

Sparse Linear Systems

Download Full-text

On the Convergence of System-AMG in Reservoir Simulation

SPE Journal ◽

10.2118/182630-pa ◽

2018 ◽

Vol 23 (02) ◽

pp. 589-597 ◽

Cited By ~ 3

Author(s):

Sebastian Gries

Keyword(s):

Linear Systems ◽

Reservoir Simulation ◽

Extreme Case ◽

Coarse Grid ◽

Algebraic Multigrid ◽

Volume Balance ◽

Coarse Grid Correction ◽

Speed Up ◽

Level Problem ◽

Flexible Framework

Summary System-algebraic multigrid (AMG) provides a flexible framework for linear systems in simulation applications that involve various types of physical unknowns. Reservoir-simulation applications, with their driving elliptic pressure unknown, are principally well-suited to exploit System-AMG as a robust and efficient solver method. However, the coarse grid correction must be physically meaningful to speed up the overall convergence. It has been common practice in constrained-pressure-residual (CPR) -type applications to use an approximate pressure/saturation decoupling to fulfill this requirement. Unfortunately, this can have significant effects on the AMG applicability and, thus, is not performed by the dynamic row-sum (DRS) method. This work shows that the pressure/saturation decoupling is not necessary for ensuring an efficient interplay between the coarse grid correction process and the fine-level problem, demonstrating that a comparable influence of the pressure on the different involved partial-differential equations (PDEs) is much more crucial. As an extreme case with respect to the outlined requirement, linear systems from compositional simulations under the volume-balance formulation will be discussed. In these systems, the pressure typically is associated with a volume balance rather than a diffusion process. It will be shown how System-AMG can still be used in such cases.

Download Full-text