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The problem is solved by the preconditioned conjugate gradient method with preconditioners that can be inverted easily by using separation of variables. ... We recall the link with the second-order Richardson method and compare it with the conjugate gradient method. ...
Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three dimensional models gain importance. ... This paper presents a short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers. ...  and Adams and Ong  in the context of preconditioned conjugate gradient methods. ...doi:10.1137/0910073 fatcat:owvjyuc5rrbzrjifjlaptljqku
Preconditioned Conjugate Gradient Solution The preconditioned conjugate gradient procedure is an ‘‘ac- celerated’’ variant of the classical conjugate gradient proce- dure. ... The method should be readily implementable on parallel processors since a vast literature exists on the amenability of the preconditioned conjugate gradient solution procedure to both concurrent and vector ...doi:10.2514/3.21090 fatcat:xbfqm7k4efdpboo4fmbutqdkta
Several other writers have studied the parallelization of the preconditioned conjugate gradient method in the context of the finite element method. ... Jordan and Hughes (1992) present algorithms for the implemen- tation of the finite element method for computational mechanics on Connection Machine systems. ...
In this paper, the graph cut problem is reformulated as an unconstrained ' 1 norm minimization that can be solved effectively using interior point methods. ... This reformulation exposes connections between graph cuts and other related continuous optimization problems. ...  also describe how the preconditioned conjugate gradients method can be used to solve ' 1 regularized logistic regression problems. ...doi:10.1109/tpami.2008.82 pmid:18703837 fatcat:wkngxrhvxnb3piylyvdxl76eze
We show that using the multisplitting algorithm as a preconditioner for conjugate gradient inversion of the domain wall fermion Dirac operator could effectively reduce the inter-node communication cost ... This method could be useful for supercomputers with far more on-node flops than inter-node communication bandwidth. ... We use the name MSPCG, as it is through the process of applying the multisplitting algorithm to the DWF Dirac equation that we realize the necessity of including the snake terms in the local matrix. ...arXiv:1811.08488v1 fatcat:r5b62fvi65fyvdhjbwtymxcolq
Parallel normalized explicit preconditioned conjugate gradient -type methods for distributed memory systems based on the block -row distribution (for the vectors and the explicit approximate inverse), ... A new class of parallel normalized preconditioned conjugate gradient type methods in conjunction with normalized approximate inverses algorithms, based on normalized approximate factorization procedures ... John Morrison of the Department of Computer Science, University College of Cork for proposing and allowing us to perform the test runs on the Departments' cluster. ...doi:10.1109/ipdps.2006.1639612 dblp:conf/ipps/GravvanisG06 fatcat:xgpjihtncrex7amdfbrjx2x2ay
The assembled system of equations were solved in parallel using a conjugate gradient algorithm for unsymmetric, nonpositive definite systems. Numer- ical studies were done on connection machine 2. ... Carter et al. (1989) have proposed a parallel finite element program strategy using a parallel preconditioned-conjugate-gradient (PCG) solution procedure for substructuring analysis on MIMD multiprocessing ...
CONJUGATE GRADIENT AND LANCZOS HISTORY 51 exploited; indeed, the method will converge in k or fewer iterations if the operator has k distinct eigenvalues. ... This paper gives some of the history of the conjugate gradient and Lanczos algorithms and an annotated bibliography for the period 1948-1976. ... "The Reproducing Kernel Method II," J. Math. Phys. Derives a connection between the conjugate gradient algorithm and the reproducing kernel method. 196. /CN/ Dixon, L. ...doi:10.1137/1031003 fatcat:3xaapzhscfe3navaz2arpm76te
Recent Advances in Numerical Methods and Applications II
In this paper, the Schur complement method with parallel preconditioned conjugate gradient (PCG) solver is introduced in two-dimensional parallel time-stepping finite element formulation to analyse rotating ... machine considering the electromagnetic field, external circuit and rotor movement. ... The used DDM is the Schur complement method with a parallel Krylov method, the parallel preconditioned conjugate gradient method  , which is currently one of the most popular methods for systems with ...doi:10.1142/9789814291071_0081 fatcat:wuzfvhvwsnhrhpryrqpgmjyo44
The algorithms considered consist of the classical conjugate gradient method, preconditioning techniques that are well suited for parallel computers such as polynomial preconditioners and several versions ... s, the analysis shows that conjugate gradient methods do not perform as well as algorithms for dense matrix computations on the considered architecture due to lack of data locality. ... Introduction Several studies [1, 3] have shown that, on sequential machines, the conjugate gradient method with preconditioning is one of the best methods for solving sparse symmetric positive definite ...doi:10.1016/0377-0427(88)90341-x fatcat:h2sutev7yrezhnx5c6p2olptki
Lecture Notes in Computer Science
In this paper we present an analysis of parallelization properties and implementation details of the new Algebraic multigrid solvers. ... This work was supported by the Russian Foundation for Basic Research (project RFBR-15-01-06363) and by the Institute of mathematics (IMATH) of the University of Toulon. ... Computations have been performed at the BULL's Computing Center, IMATH and Mésocentre of the University of Aix-Marseille, France. ...doi:10.1007/978-3-319-21909-7_2 fatcat:sfknigej5rgddnr7zmkn54lfrm
. / Domain decomposition methods niveau continu, la matrice complement de Schur au niveau discret) est ensuite inverse par un algorithme de gradient conjugue preconditionne. ... Sur cet exemple significatif, la methode proposee est competitive a la fois au niveau du temps calcul et de la place memoire. ... Conjugate gradient algorithm The solution of the interface problem (4) by a standard preconditioned conjugate gradient method, with preconditioner M, now leads to the following algorithm: Conjugate gradient ...doi:10.1016/0377-0427(91)90150-i fatcat:eqrtxq2osbhsvjujyz3j7c7tz4
‘“‘Comparison of preconditioned conjugate gradient method and LDL factorization for structural analysis.’’ Proc., /st Int. Conf. on Comp. and Information Technol. for Arch., Engrg., and Constr., H. ... *‘A data parallel finite element method for computational fluid dynam- ics on the connection machine system.’’ Comp. Methods in Appl. Mech. and Engrg., 99, 113-134. Johan, Z., Mathur, K. ...
We describe a new high-performance conjugate-gradient (HPCG) benchmark. HPCG is composed of computations and data-access patterns commonly found in scientific applications. ... HPCG strives for a better correlation to existing codes from the computational science domain and to be representative of their performance. ... Acknowledgements The authors thank the Department of Energy National Nuclear Security Agency for the funding provided for this work. ...doi:10.1177/1094342015593158 fatcat:dy7dmuxbwzdhrackranpeonjoq
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