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• W1528566150 abstract "This dissertation deals mainly with the design, implementation, and analysis of efficient iterative solution methods for large sparse linear systems on distributed and heterogeneous computing systems as found in Grid computing. First, a case study is performed on iteratively solving large symmetric linear systems on both a multi–cluster and a local heterogeneous cluster using standard block Jacobi precondi- tioning within the software constraints of standard Grid middleware and within the algorith- mic constraints of preconditioned Conjugate Gradient–type methods. This shows that global synchronisation is a key bottleneck operation and in order to alleviate this bottleneck, three main strategies are proposed: exploiting the hierarchical structure of multi–clusters, using asyn- chronous iterative methods as preconditioners, and minimising the number of inner products in Krylov subspace methods. Asynchronous iterative methods have never really been successfully applied to the solution of extremely large sparse linear systems. The main reason is that the slow convergence rates limit the applicability of these methods. Nevertheless, the lack of global synchronisation points in these methods is a highly favourable property in heterogeneous computing systems. Krylov subspace methods offer significantly improved convergence rates, but the global synchronisation points induced by the inner product operations in each iteration step limits the applicability. By using an asynchronous iterative method as a preconditioner in a flexible Krylov subspace method, the best of both worlds is combined. It is shown that this hybrid combination of a slow but asynchronous inner iteration and a fast but synchronous outer iteration results in high convergence rates on heterogeneous networks of computers. Since the preconditionering iteration is performed on heterogeneous computing hardware, it varies in each iteration step. Therefore, a flexible iterative method which can handle a varying preconditioner has to be employed. This partially asynchronous algorithm is implemented on two different types of Grid hardware applied to two different applications using two different types of Grid middleware. The IDR(s) method and its variants are new and powerful algorithms for iteratively solving large nonsymmetric linear systems. Four techniques are used to construct an efficient IDR(s) variant for parallel computing and in particular for Grid computing. Firstly, an efficient and robust IDR(s) variant is presented that has a single global synchronisation point per matrix– vector multiplication step. Secondly, the so–called IDR test matrix in IDR(s) can be chosen freely and this matrix is constructed such that the work, communication, and storage involving this matrix are minimised in the context of multi–clusters. Thirdly, a methodology is presented for a priori estimation of the optimal value of s in IDR(s). Finally, the proposed IDR(s) variant is combined with an asynchronous preconditioning iteration. By using an asynchronous preconditioner in IDR(s), the IDR(s) method is treated as a flexible method, where the preconditioner changes in each iteration step. In order to begin analysing mathematically the effect of a varying preconditioning operator on the convergence properties of IDR(s), the IDR(s) method is interpreted as a special type of deflation method. This leads to a better understanding of the core structure of IDR(s) methods. In particular, it provides an intuitive explanation for the excellent convergence properties of IDR(s). Two applications from computational fluid dynamics are considered: large bubbly flow prob- lems and large (more general) convection–diffussion problems, both in 2D and 3D. However, the techniques presented can be applied to a wide range of scientific applications. Large numerical experiments are performed on two heterogeneous computing platforms: (i) local networks of non–dedicated computers and (ii) a dedicated cluster of clusters linked by a high–speed network. The numerical experiments not only demonstrate the effectiveness of the techniques, but they also illustrate the theoretical results." @default.
• W1528566150 created "2016-06-24" @default.
• W1528566150 creator A5061581710 @default.
• W1528566150 date "2011-04-01" @default.
• W1528566150 modified "2023-09-28" @default.
• W1528566150 title "Efficient Iterative Solution of Large Linear Systems on Heterogeneous Computing Systems" @default.
• W1528566150 cites W1487892164 @default.
• W1528566150 cites W1506342804 @default.
• W1528566150 cites W1509345944 @default.
• W1528566150 cites W1510543252 @default.
• W1528566150 cites W1522545678 @default.
• W1528566150 cites W1530514001 @default.
• W1528566150 cites W1542243431 @default.
• W1528566150 cites W1546004968 @default.
• W1528566150 cites W1546334208 @default.
• W1528566150 cites W1549518189 @default.
• W1528566150 cites W1549992525 @default.
• W1528566150 cites W1552224009 @default.
• W1528566150 cites W1555993967 @default.
• W1528566150 cites W1568776721 @default.
• W1528566150 cites W1569198079 @default.
• W1528566150 cites W1572639095 @default.
• W1528566150 cites W1573548168 @default.
• W1528566150 cites W1595596071 @default.
• W1528566150 cites W1603765807 @default.
• W1528566150 cites W1608601220 @default.
• W1528566150 cites W1620307392 @default.
• W1528566150 cites W1634025860 @default.
• W1528566150 cites W164384110 @default.
• W1528566150 cites W1776802267 @default.
• W1528566150 cites W181135967 @default.
• W1528566150 cites W1825216778 @default.
• W1528566150 cites W1867116712 @default.
• W1528566150 cites W1879847300 @default.
• W1528566150 cites W1965537434 @default.
• W1528566150 cites W1967649477 @default.
• W1528566150 cites W1971662204 @default.
• W1528566150 cites W1973166496 @default.
• W1528566150 cites W1978002393 @default.
• W1528566150 cites W1981220107 @default.
• W1528566150 cites W1987493287 @default.
• W1528566150 cites W1995078768 @default.
• W1528566150 cites W1999697508 @default.
• W1528566150 cites W2008656134 @default.
• W1528566150 cites W2011740685 @default.
• W1528566150 cites W2019434176 @default.
• W1528566150 cites W2019697755 @default.
• W1528566150 cites W2021327387 @default.
• W1528566150 cites W2024363833 @default.
• W1528566150 cites W2041876368 @default.
• W1528566150 cites W2046160677 @default.
• W1528566150 cites W2047714674 @default.
• W1528566150 cites W2048909289 @default.
• W1528566150 cites W2049617798 @default.
• W1528566150 cites W2049707517 @default.
• W1528566150 cites W2050455866 @default.
• W1528566150 cites W2051133095 @default.
• W1528566150 cites W2051260978 @default.
• W1528566150 cites W2052487661 @default.
• W1528566150 cites W2059715946 @default.
• W1528566150 cites W2059807497 @default.
• W1528566150 cites W2062817961 @default.
• W1528566150 cites W2063573213 @default.
• W1528566150 cites W2066692739 @default.
• W1528566150 cites W2068395392 @default.
• W1528566150 cites W2068757253 @default.
• W1528566150 cites W2069304294 @default.
• W1528566150 cites W2073751862 @default.
• W1528566150 cites W2074780612 @default.
• W1528566150 cites W2077783617 @default.
• W1528566150 cites W2079308547 @default.
• W1528566150 cites W2083715026 @default.
• W1528566150 cites W2084049033 @default.
• W1528566150 cites W2091257550 @default.
• W1528566150 cites W2095222360 @default.
• W1528566150 cites W2099297649 @default.
• W1528566150 cites W2100680297 @default.
• W1528566150 cites W2101315150 @default.
• W1528566150 cites W2102596415 @default.
• W1528566150 cites W2102891817 @default.
• W1528566150 cites W2103290518 @default.
• W1528566150 cites W2103363198 @default.
• W1528566150 cites W2103817093 @default.
• W1528566150 cites W2107832679 @default.
• W1528566150 cites W2108026329 @default.
• W1528566150 cites W2109482637 @default.
• W1528566150 cites W2109728563 @default.
• W1528566150 cites W2110622223 @default.
• W1528566150 cites W2111982028 @default.
• W1528566150 cites W2111987198 @default.
• W1528566150 cites W2113830538 @default.
• W1528566150 cites W2114482929 @default.
• W1528566150 cites W2114535880 @default.
• W1528566150 cites W2115097789 @default.
• W1528566150 cites W2119395117 @default.
• W1528566150 cites W2125482922 @default.
• W1528566150 cites W2127116424 @default.
• W1528566150 cites W2127179283 @default.
• W1528566150 cites W2127190985 @default.
• W1528566150 cites W2127927798 @default.

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