國立虎尾科技大學 |

Efficient Iterative and Multigrid Solvers with Applications.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Efficient Iterative and Multigrid Solvers with Applications./
作者:	Lu, Cao.
面頁冊數:	1 online resource (116 pages)
附註:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
標題:	Applied mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9781369332025

Efficient Iterative and Multigrid Solvers with Applications.
Lu, Cao.

Efficient Iterative and Multigrid Solvers with Applications. - 1 online resource (116 pages)

Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Iterative methods are some of the most important techniques in solving large scale linear systems. Compared to direct methods, iterative solvers have the advantage of lower storage cost and better scalability as the problem size increases. Among the methods, multigrid solvers and multigrid preconditioners are often the optimal choices for solving systems that arise from partial differential equations (PDEs). In this dissertation, we introduce several efficient algorithms for various scientific applications. Our first algorithm is a specialized geometric multigrid solver for ill-conditioned systems from Helmholtz equations. Such equations appear in climate models with pure Neumann boundary condition and small wave numbers. In numerical linear algebra, ill-conditioned and even singular systems are inherently hard to solve. Many standard methods are either slow or non-convergent. We demonstrate that our solver delivers accurate solutions with fast convergence. The second algorithm, HyGA, is a general hybrid geometric+algebraic multigrid framework for elliptic type PDEs. It leverages the rigor, accuracy and efficiency of geometric multigrid (GMG) for hierarchical unstructured meshes, with the flexibility of algebraic multigrid (AMG) at the coarsest level. We conduct numerical experiments using Poisson equations in both 2-D and 3-D, and demonstrate the advantage of HyGA over classical GMG and AMG.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369332025Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Efficient Iterative and Multigrid Solvers with Applications.
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100 1 $a Lu, Cao. $3 1180548
245 1 0 $a Efficient Iterative and Multigrid Solvers with Applications.
264 0 $c 2016
300 $a 1 online resource (116 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Advisers: Xiangmin Jiao; Roman Samulyak.
502 $a Thesis (Ph.D.) $c State University of New York at Stony Brook $d 2016.
504 $a Includes bibliographical references
520 $a Iterative methods are some of the most important techniques in solving large scale linear systems. Compared to direct methods, iterative solvers have the advantage of lower storage cost and better scalability as the problem size increases. Among the methods, multigrid solvers and multigrid preconditioners are often the optimal choices for solving systems that arise from partial differential equations (PDEs). In this dissertation, we introduce several efficient algorithms for various scientific applications. Our first algorithm is a specialized geometric multigrid solver for ill-conditioned systems from Helmholtz equations. Such equations appear in climate models with pure Neumann boundary condition and small wave numbers. In numerical linear algebra, ill-conditioned and even singular systems are inherently hard to solve. Many standard methods are either slow or non-convergent. We demonstrate that our solver delivers accurate solutions with fast convergence. The second algorithm, HyGA, is a general hybrid geometric+algebraic multigrid framework for elliptic type PDEs. It leverages the rigor, accuracy and efficiency of geometric multigrid (GMG) for hierarchical unstructured meshes, with the flexibility of algebraic multigrid (AMG) at the coarsest level. We conduct numerical experiments using Poisson equations in both 2-D and 3-D, and demonstrate the advantage of HyGA over classical GMG and AMG.
520 $a Besides the aforementioned algorithms, we introduce an orthogonally projected implicit null-space method (OPINS) for saddle point systems. The traditional null-space method is inefficient because it is expensive to find the null-space explicitly. Some alternatives, notably constraint-preconditioned or projected Krylov methods, are relatively efficient, but they can suffer from numerical instability. OPINS is equivalent to the null-space method with an orthogonal projector, without forming the orthogonal basis of the null space explicitly. Our results show that it is more stable than projected Krylov methods while achieving similar efficiency.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a State University of New York at Stony Brook. $b Applied Mathematics and Statistics. $3 1179106
773 0 $t Dissertation Abstracts International $g 78-05B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10192360 $z click for full text (PQDT)