{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

A13 x1 b1 ax 4 0 a22 a23 5 4 x2 5 4 b2 5 5 at at a33

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: into LDLT 3 2 3 2 D1 I L=4 I 5 D = 4 D2 5 D3 !T !T I 23 13 6 Domain Decomposition Factorization procedure function L D] = dd(A) % dd: block factorization of a matrix A into LDLT for k = 1:2 Dk = Akk Solve Dk !k3 = Ak3 for !k3 end D3 = A33 ; !T D1!13 ; !T D2!23 13 23 Note: i. D1 and D2 can be factored without knowledge of each other or D3, ! 13, and ! 23 ii. The factorizations of D1 and D2 can be done in parallel iii. Design modi cations only change those matrices a ected iv. The procedure can be done recursively v. D3 is called the Schur complement of A { For N N grid problems, George (1973) 1 shows that factorization takes O(N 3) FLOPs { Banded and pro le techniques require O(N 4) FLOPs { Nested dissection has the optimal order of operations J.A. George (1973), Nested dissection of a regular nite element mesh, SIAM J. Numer. Anal., 10, 345-363 1 7 Nested Dissection Two-dimensional nested dissection { Bisect the domain { Number unknowns on the ne level rst { Number unknowns on the interface between two regions next { Number unknowns at the juncture of four regions last Nested ordering of a 4 4 mesh 12 1 3 8 4 X X 2 9 7 5 6 X 8 9 8 X XX 7 8 9 X X 4 2 67 X X 5 1 5 XX 3 6 34 XX X X X X X X X XX X X X XX XXXXX...
View Full Document

  • Fall '98
  • JosephE.Flaherty
  • Trigraph, G protein coupled receptors, London, Brighton and South Coast Railway locomotives, Block Tridiagonal Systems

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern