Coarse grid acceleration of a parallel block preconditioner

Vuik, C.; Frank, Jason

doi:10.1016/s0167-739x(01)00035-8

Cited by 2 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is especially the case for solving elliptic equations. In [11], a reason for this problem is given which relates the loss of convergence to the presence of small eigenvalues arising from the domain decomposition. These eigenvalues can be 'eliminated' by applying a deflation operator using constant vectors for approximating the corresponding eigenvectors.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Deflation Accelerated Schwarz Method for CFD

Verkaik

Vuik

Paarhuis

et al. 2005

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Accurate simulation of glass melting furnaces requires the solution of very large linear algebraic systems of equations. To solve these equations efficiently a Schwarz domain decomposition (multi-block) method can be used. However, it can be observed that the convergence of the Schwarz method deteriorates when a large number of subdomains is used. This is due to small eigenvalues arising from the domain decomposition which slow down the convergence. Recently, a deflation approach was proposed to solve this problem using constant approximate eigenvectors. This paper generalizes this view to piecewise linear vectors and results for two CFD problems are presented. It can be observed that the number of iterations and wall clock time decrease considerably. The reason for this is that the norm of the initial residual is much smaller and the rate of convergence is higher.

show abstract

Section: Introductionmentioning

confidence: 99%

“…These eigenvalues can be 'eliminated' by applying a deflation operator using constant vectors for approximating the corresponding eigenvectors. The authors of [11] present convergence rates for solving Poisson's equation which are independent on the number of blocks.…”

Section: Introductionmentioning

confidence: 99%

The Deflation Accelerated Schwarz Method for CFD

Verkaik

Vuik

Paarhuis

et al. 2005

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Among these alternatives we find the two-level preconditioners. There are many variations within this family of preconditioners, but basically we can discern at least two subfamilies: algebraic [1,4,12,14,18,20,23,28,32] and operator dependent [15,16,17]. Within the operator dependent preconditioners we should highlight the spectral methods [21,25].Notice that {Γ J } 1≤J≤P form a disjoint partition of Γ.…”

mentioning

confidence: 99%

Parallel Implementation of a Two-level Algebraic ILU(k)-based Domain Decomposition Preconditioner

Nievinski

Souza

Goldfeld³

et al. 2018

Tend. Mat. Apl. Comput.

View full text Add to dashboard Cite

We discuss the parallel implementation of a two-level algebraic ILU(k)-based domain decomposition preconditioner using the PETSc library. We present strategies to improve performance and minimize communication among processes during setup and application phases. We compare our implementation with an off-the-shelf preconditioner in PETSc for solving linear systems arising in reservoir simulation problems, and show that for some cases our implementation performs better.The multilevel preconditioner has been an active research area for the last 30 years. One of the main representatives of this class is the algebraic multigrid (AMG) method [19,22,30,31], when used as a preconditioner rather than as a solver. It is widely used in oil reservoir simulation as part of the CPR (constrained pressure residual) preconditioner [6,33]. Despite its general acceptance there is room for new alternatives, as there are problems where AMG can perform poorly, see, for instance [13]. Among these alternatives we find the two-level preconditioners. There are many variations within this family of preconditioners, but basically we can discern at least two subfamilies: algebraic [1,4,12,14,18,20,23,28,32] and operator dependent [15,16,17]. Within the operator dependent preconditioners we should highlight the spectral methods [21,25].Notice that {Γ J } 1≤J≤P form a disjoint partition of Γ. See Figure 2.Finally, we define extended subdomains Ω J and extended local interfaces Γ J , which incorporate the portions of the interface connected to the subdomain interior Ω Int J . We define Ω J as(a jk = 0 or a k j = 0) .(2.6)

show abstract

Coarse grid acceleration of a parallel block preconditioner

Cited by 2 publications

References 27 publications

The Deflation Accelerated Schwarz Method for CFD

The Deflation Accelerated Schwarz Method for CFD

Parallel Implementation of a Two-level Algebraic ILU(k)-based Domain Decomposition Preconditioner

Contact Info

Product

Resources

About