Explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems
A new class of inner-outer iterative procedures in conjunction with Picard-Newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented. Explicit preconditioned iterative schemes, based on the explicit computation of a class of domain decomposition ge...
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| Published in: | Computers & mathematics with applications (1987) Vol. 45; no. 1; pp. 263 - 272 |
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| Format: | Journal Article |
| Language: | English |
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2003
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| ISSN: | 0898-1221, 1873-7668 |
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| Abstract | A new class of inner-outer iterative procedures in conjunction with Picard-Newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented. Explicit preconditioned iterative schemes, based on the explicit computation of a class of domain decomposition generalized approximate inverse matrix techniques are presented for the efficient solution of nonlinear boundary value problems on multiprocessor systems. Applications of the new composite scheme on characteristic nonlinear boundary value problems are discussed and numerical results are given. |
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| AbstractList | A new class of inner-outer iterative procedures in conjunction with Picard-Newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented. Explicit preconditioned iterative schemes, based on the explicit computation of a class of domain decomposition generalized approximate inverse matrix techniques are presented for the efficient solution of nonlinear boundary value problems on multiprocessor systems. Applications of the new composite scheme on characteristic nonlinear boundary value problems are discussed and numerical results are given. |
| Author | Gravvanis, G.A. |
| Author_xml | – sequence: 1 givenname: G.A. surname: Gravvanis fullname: Gravvanis, G.A. email: gag@aegean.gr organization: Department of Informatics Athens University of Economics and Business GR 104 34 Athens, Greece |
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| Keywords | Arrow-type matrix Parallel iterative methods Domain decomposition Preconditioning Approximate factorization procedures Approximate inverse matrix techniques |
| Language | English |
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| References | Grote, Huckle (BIB3) 1997; 18 Dongarra, Duff, Sorensen, van der Vorst (BIB5) 1991 Gravvanis (BIB27) 1996; 60 Saad (BIB4) 1996 Bramble, Pasciak, Schatz (BIB21) 1986; 47 Gravvanis, Lipitakis (BIB14) 1996; 32 Lipitakis, Gravvanis (BIB26) 1995; 54 Lipitakis, Gravvanis (BIB15) 1992; 44 Duff, Erisman, Reid (BIB16) 1986 Dryja (BIB25) 1982; 39 Gravvanis (BIB11) 1998; 70 Dongarra, Messina, Sorensen, Voight (BIB6) 1989 Bjorstad, Widlund (BIB20) 1984 Owen (BIB32) 1998 D'Jakanov (BIB34) 1961; 138 Axelsson (BIB1) 1994 van der Vorst, Vuik (BIB30) 1994; 1 Gravvanis (BIB35) 1998 Bramble, Pasciak, Schatz (BIB22) 1986; 46 Chan (BIB23) 1987; 24 Ortega, Rheinboldt (BIB28) 1970 Evans, Sutti (BIB7) 1988 Vuik, van der Vorst (BIB31) 1992; 160 Golub, van Loan (BIB2) 1989 Gravvanis (BIB12) 1997; Volume X Ortega (BIB9) 1988 van der Vorst (BIB29) 1992; 13 Schwarz (BIB19) 1989 Gravvanis (BIB10) 1999; 16 Buleev (BIB33) 1960; 51 O'Leary, Stewart (BIB18) 1990; 90 Gravvanis (BIB8) 1988; Volume 1 Gravvanis (BIB13) 1995; 56 Evans (BIB17) 1985 Dryja (BIB24) 1984; 44 Dryja (10.1016/S0898-1221(03)80018-4_BIB24) 1984; 44 Evans (10.1016/S0898-1221(03)80018-4_BIB17) 1985 Chan (10.1016/S0898-1221(03)80018-4_BIB23) 1987; 24 Gravvanis (10.1016/S0898-1221(03)80018-4_BIB12) 1997; Volume X van der Vorst (10.1016/S0898-1221(03)80018-4_BIB29) 1992; 13 Gravvanis (10.1016/S0898-1221(03)80018-4_BIB8) 1988; Volume 1 Gravvanis (10.1016/S0898-1221(03)80018-4_BIB13) 1995; 56 Ortega (10.1016/S0898-1221(03)80018-4_BIB28) 1970 Gravvanis (10.1016/S0898-1221(03)80018-4_BIB11) 1998; 70 D'Jakanov (10.1016/S0898-1221(03)80018-4_BIB34) 1961; 138 Schwarz (10.1016/S0898-1221(03)80018-4_BIB19) 1989 Gravvanis (10.1016/S0898-1221(03)80018-4_BIB35) 1998 Bramble (10.1016/S0898-1221(03)80018-4_BIB22) 1986; 46 Evans (10.1016/S0898-1221(03)80018-4_BIB7) 1988 Duff (10.1016/S0898-1221(03)80018-4_BIB16) 1986 Gravvanis (10.1016/S0898-1221(03)80018-4_BIB10) 1999; 16 Gravvanis (10.1016/S0898-1221(03)80018-4_BIB27) 1996; 60 O'Leary (10.1016/S0898-1221(03)80018-4_BIB18) 1990; 90 Saad (10.1016/S0898-1221(03)80018-4_BIB4) 1996 Lipitakis (10.1016/S0898-1221(03)80018-4_BIB15) 1992; 44 Owen (10.1016/S0898-1221(03)80018-4_BIB32) 1998 Dryja (10.1016/S0898-1221(03)80018-4_BIB25) 1982; 39 Lipitakis (10.1016/S0898-1221(03)80018-4_BIB26) 1995; 54 van der Vorst (10.1016/S0898-1221(03)80018-4_BIB30) 1994; 1 Golub (10.1016/S0898-1221(03)80018-4_BIB2) 1989 Bjorstad (10.1016/S0898-1221(03)80018-4_BIB20) 1984 Ortega (10.1016/S0898-1221(03)80018-4_BIB9) 1988 Buleev (10.1016/S0898-1221(03)80018-4_BIB33) 1960; 51 Grote (10.1016/S0898-1221(03)80018-4_BIB3) 1997; 18 Axelsson (10.1016/S0898-1221(03)80018-4_BIB1) 1994 Dongarra (10.1016/S0898-1221(03)80018-4_BIB5) 1991 Dongarra (10.1016/S0898-1221(03)80018-4_BIB6) 1989 Bramble (10.1016/S0898-1221(03)80018-4_BIB21) 1986; 47 Vuik (10.1016/S0898-1221(03)80018-4_BIB31) 1992; 160 Gravvanis (10.1016/S0898-1221(03)80018-4_BIB14) 1996; 32 |
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| SubjectTerms | Approximate factorization procedures Approximate inverse matrix techniques Arrow-type matrix Domain decomposition Parallel iterative methods Preconditioning |
| Title | Explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems |
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