Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials

Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with curre...

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Vydáno v:Computational mechanics Ročník 50; číslo 3; s. 321 - 333
Hlavní autoři: Jönsthövel, T. B., van Gijzen, M. B., MacLachlan, S., Vuik, C., Scarpas, A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.09.2012
Springer
Springer Nature B.V
Témata:
Algebra
Algorithms
Asphalt
Classical and Continuum Physics
Comparative analysis
Composite materials
Composite materials industry
Computational Science and Engineering
Computed tomography
Computer simulation
Conjugate gradient method
Conjugates
Eigenvalues
Engineering
Finite element method
Iterative methods
Iterative solution
Linear systems
Material properties
Methods
Original Paper
Parallel computers
Rigid structures
Stiffness
Theoretical and Applied Mechanics
Vectors (mathematics)
65Z05
Structural mechanics
65F10
Deflation
Conjugate gradients
Preconditioners
Rigid body modes
CT scan
65F08
Algebraic multigrid
ISSN:0178-7675, 1432-0924
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Shrnutí:Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms. In this paper, we consider the simulation of asphalt concrete, which is a mixture of components with large differences in material stiffness. The discontinuities in material stiffness give rise to many small eigenvalues that negatively affect the convergence of iterative solution algorithms such as the preconditioned conjugate gradient (PCG) method. This paper considers the deflated preconditioned conjugate gradient (DPCG) method in which the rigid body modes of sets of elements with homogeneous material properties are used as deflation vectors. As preconditioner we consider several variants of the algebraic multigrid smoothed aggregation method. We evaluate the performance of the DPCG method on a parallel computer using up to 64 processors. Our test problems are derived from real asphalt core samples, obtained using CT scans. We show that the DPCG method is an efficient and robust technique for solving these challenging linear systems.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-011-0661-y