8. Bibliography

8.1. Books/articles/proceedings/theses…

[BFG] A.Bouras, V.Fraysse & L.Giraud. A relaxation strategy for inner-outer linear solvers in DD methods. Report CERFACS TR/PA/00/17 (2000).

[BGLS] J.F.Bonnans, J.C.Gilbert, C.Lemarechal & C.Sagastizabal. Numerical optimization: theoretical and practical aspects. Ed. Springer mathematics & applications collection, 27 (1997).

[Ci00] B.A. Cipra. The best of the 20th century: editors name top10 algorithms. SIAM News, 33-4 (2000).

[Che05] K.Chen. Matrix preconditioning techniques and applications. Ed. Cambridge University Press (2005).

[CM01] F.Chaitin-Chatelin & T.Meskausas. Inner-outer iterations for mode solvers in structural mechanics: application to Code_Aster. Report CERFACS (2001).

[Cu94] J.C. Culioli. Introduction to optimization. Ed. Ellipse (1994).

[Dav06] T.A. Davis. Direct methods for sparse linear systems. Ed. SIAM (2006).

[Duf06] I.S.Duff et al.*Direct methods for sparse matrices*. Ed. Clarendon Press (2006).

[Go89] G.H.Golub & D.P.O’Learly. Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. SIAM review, 31-1 (1989), pp50-102.

[Gol96] G.Golub & C.Van Loan. Matrix computations. Ed. Johns Hopkins University Press (1996).

[GV97] G.H.Golub & H.A.Van der Vorst. Closer to the solution: Iterative linear solvers. The state of the art in numerical analysis. Ed. Clarendon press (1997), pp93-92.

[GY97] G.H.Golub & Q.Ye. Inexact preconditioned conjugate gradient method with inner-outer iteration. Stanford University Report, SCCM -97-04 (1997).

[Jo84] P.Joly. Conjugate gradient methods. Report no. 84016 of the numerical analysis lab of PARIS VI (1984).

[LT98] P.Lascaux & R.Théodor. Numerical matrix analysis applied to the art of the engineer. Ed. Masson (1998).

[Liu89] J.W.H.Liu. Computer solution of large sparse positive definite systems. Prentice Hall (1981).

[Mer15] Sylvain Mercier Fast nonlinear solvers in solid mechanics, thesis from the University of Toulouse

[Meu99] G.Meurant. Computer solution of large linear systems. Ed. Elsevier (1999).

[Min08] Mr. Minoux. Mathematical programming, theory and algorithms. Ed. Lavoisier (2008).

[Saa03] Y.Saad. Iterative methods for sparse matrices. Ed. PWS (2003).

[Sh94] J.R. Shewchuk. An introduction to the conjugate gradient method without the agonizing pain. Carnegie Mellon University Internal Report (1994).

[SV00] Y.Saad & H.A.Van Der Vorst. Iterative solution of linear system in the 20th century. J.Comp. Call. Math., 123 (2000), pp35-65.

[Van01] H.Van Der Vorst. Iterative Krylov methods for large linear systems. Ed. Cambridge University Press (2001).

8.2. Reports/reports EDF

[Anf03] N.Anfaoui. A study of the performance of Code_Aster: optimization proposal. PARIS VI DESS applied mathematics internship (2003).

[BH89] T. Buffard & J.M. Herard. A polynomial preconditioning method for SPD systems. Note EDF R&D HE-41/89.16 (1989).

[Boi01] O.Boiteau. Solution algorithm for the generalized problem. Code_Aster R5.01.01 (2001) Reference Documentation.

[Boi03] O.Boiteau. Analysis of the implementation of the conjugate gradient in the Code_Aster and tests of other variants via the CXML library. Report EDF R&D CR-I23/03/014 (2003).

[Boi08] O.Boiteau. Domain decomposition and parallelism. Code_Aster Reference Documentation. R6.01.03 (2008).

[Boi08b] O.Boiteau. Improvement of the robustness of code TELEMAC in parallel mode. Report EDF R&D I23/08/008 (2008).

[Boi09] O.Boiteau. Overview of direct linear solvers and use of product MUMPS. Code_Aster Reference Documentation. R6.02.03 (2009).

[Des07] T.Desoza. Evaluation and development of parallelism in Code_Aster. Master internship ENPC (2007) and grade EDF R&D HT-62/08/01464 (2008).

[Greg] J.P. Gregoire. Algorithm of GCPC for the resolution of a symmetric linear system: general presentation and instructions for use. Note EDF R&D HI/4333-07 (1982)

Effective vectorization of the GC in the case of sparse symmetric matries. Note EDF R&D HI-72/6710 (1990).

GC parallelization for sparse matrices on CRAY C98. Note EDF R&D HI‑76/95/019 (1996)

Acceleration of the convergence of the preconditioned conjugate gradient using incomplete factorization by level. Note EDF R&D HI-76/00/005 (2000).

Distributed memory parallelization of GC and user code. Note EDF R&D HI‑76/01/007 (2001).

GCPC and quick calculation of eigenvalues. Note EDF R&D HI-76/01/001 (2001).

[Ni92] B.Nitrosso. Direct methods for sparse matrices SPD. Basic techniques at the state of the art. Note EDF R&D HE-41/92/27 (1992)

[Pel01] J.Pellet. Dualization of limit conditions. Code_Aster R3.03.01 (2001) Reference Documentation.

[Tar04] N.Tardieu. Parallelization of MEF ++, principles and performances. R&D Report EDF (2004).

[Tar09] N.Tardieu. Multigrid solver for structural mechanics. Note EDF R&D HT-62/08/01615 (2009)

8.3. Internet resources

[MUR] Official product website MURGE: http://murge.gforge.inria.fr/.

[PET] Official bookstore website PETSc: http://www.mcs.anl.gov/petsc/petsc-as/.

[PLM] G.Poole, Y.C.Liu & J.Mandel: Advancing analysis capabilities in ANSYS though solver technology. (2001) available on site ANSYS.

[WG] William Gropp’s professional website: < http://www.cs.uiuc.edu/homes/wgropp>` http://www.cs.uiuc.edu/homes/wgropp`_ < http://www.cs.uiuc.edu/homes/wgropp>``_.