-
1
-
-
0031234255
-
A posteriori error estimation for finite element solutions of Helmholtz equation. I. The quality of local indicators and estimators
-
I. BABUSKA, F. IBLENBURG, T. STROUBOULIS, AND S. GANGARAJ, A posteriori error estimation for finite element solutions of Helmholtz equation. I. The quality of local indicators and estimators, Internat. J. Numer. Methods Engrg., 40 (1997), pp. 3443-3462.
-
(1997)
Internat. J. Numer. Methods Engrg.
, vol.40
, pp. 3443-3462
-
-
Babuska, I.1
Iblenburg, F.2
Strouboulis, T.3
Gangaraj, S.4
-
2
-
-
0031270949
-
A posteriori error estimation for finite element solutions of Helmholtz equation. II. Estimation of the pollution error
-
I. BABUSKA, F. IHLENBURG, T. STROUBOULIS, AND S. GANGARAJ, A posteriori error estimation for finite element solutions of Helmholtz equation. II. Estimation of the pollution error, Internat. J. Numer. Methods Engrg., 40 (1997), pp. 3883-3900.
-
(1997)
Internat. J. Numer. Methods Engrg.
, vol.40
, pp. 3883-3900
-
-
Babuska, I.1
Ihlenburg, F.2
Strouboulis, T.3
Gangaraj, S.4
-
3
-
-
0001350531
-
An iterative method for the Helmholtz equation
-
A. BAYLISS, C. GOLDSTEIN, AND E. TURKEL, An iterative method for the Helmholtz equation, J. Comput. Phys., 49 (1983), pp. 443-457.
-
(1983)
J. Comput. Phys.
, vol.49
, pp. 443-457
-
-
Bayliss, A.1
Goldstein, C.2
Turkel, E.3
-
4
-
-
0000350889
-
On accuracy conditions for the numerical computation of waves
-
A. BAYLISS, C. GOLDSTEIN, AND E. TURKEL, On accuracy conditions for the numerical computation of waves, J. Comput. Phys., 59 (1985), pp. 396-404.
-
(1985)
J. Comput. Phys.
, vol.59
, pp. 396-404
-
-
Bayliss, A.1
Goldstein, C.2
Turkel, E.3
-
5
-
-
48749141209
-
Adaptive mesh refinement for hyperbolic partial differential equations
-
M. J. BERGER AND J. OLIGER, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53 (1984), pp. 484-512.
-
(1984)
J. Comput. Phys.
, vol.53
, pp. 484-512
-
-
Berger, M.J.1
Oliger, J.2
-
6
-
-
0003459540
-
-
Institut francais du petrole publications, Gulf Publishing Company, Houston, London, Paris, Tokyo
-
T. BOURBIE, O. COUSSY, AND B. ZINSZNER, Acoustics of Porous Media, Institut francais du petrole publications, Gulf Publishing Company, Houston, London, Paris, Tokyo, 1987.
-
(1987)
Acoustics of Porous Media
-
-
Bourbie, T.1
Coussy, O.2
Zinszner, B.3
-
7
-
-
0004219794
-
Multigrid methods
-
Longman Scientific and Technical, Harlow, UK
-
J. BRAMBLE, Multigrid Methods, Pitman Research Notes in Mathematics, Longman Scientific and Technical, Harlow, UK, 1993.
-
(1993)
Pitman Research Notes in Mathematics
-
-
Bramble, J.1
-
8
-
-
0023984323
-
A preconditioning technique for the efficient solution of problems with local grid refinement
-
J. H. BRAMBLE, R. E. EWING, J. E. PASCIAK, AND A. H. SCHATZ, A preconditioning technique for the efficient solution of problems with local grid refinement, Comput. Methods Appl. Mech. Engrg., 67 (1988), pp. 149-159.
-
(1988)
Comput. Methods Appl. Mech. Engrg.
, vol.67
, pp. 149-159
-
-
Bramble, J.H.1
Ewing, R.E.2
Pasciak, J.E.3
Schatz, A.H.4
-
9
-
-
0028751575
-
Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems
-
J. H. BRAMBLE, D. Y. KWAK, AND J. E. PASCIAK, Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems, SIAM J. Numer. Anal., 31 (1994), pp. 1746-1763.
-
(1994)
SIAM J. Numer. Anal.
, vol.31
, pp. 1746-1763
-
-
Bramble, J.H.1
Kwak, D.Y.2
Pasciak, J.E.3
-
10
-
-
84968476488
-
The analysis of smoothers for multigrid algorithms
-
J. H. BRAMBLE AND J. E. PASCIAK, The analysis of smoothers for multigrid algorithms, Math. Comp., 58 (1992), pp. 467-488.
-
(1992)
Math. Comp.
, vol.58
, pp. 467-488
-
-
Bramble, J.H.1
Pasciak, J.E.2
-
11
-
-
84968468806
-
New estimates for multilevel algorithms including the v-cycle
-
J. H. BRAMBLE AND J. E. PASCIAK, New estimates for multilevel algorithms including the v-cycle, Math. Comp., 60 (1993), pp. 447-471.
-
(1993)
Math. Comp.
, vol.60
, pp. 447-471
-
-
Bramble, J.H.1
Pasciak, J.E.2
-
12
-
-
0000681145
-
Overlapping Schwarz algorithms for solving Helmholtz's equation
-
Domain Decomposition Methods 10, J. Mandel, C. Farhat, and X.-C. Cai, eds., AMS, Providence, RI
-
X.-C. CAI, M. CASARIN, F. ELLIOTT, JR., AND O. WIDLUND, Overlapping Schwarz algorithms for solving Helmholtz's equation, in Domain Decomposition Methods 10, J. Mandel, C. Farhat, and X.-C. Cai, eds., Contemp. Math. 218, AMS, Providence, RI, 1998, pp. 391-399.
-
(1998)
Contemp. Math.
, vol.218
, pp. 391-399
-
-
Cai, X.-C.1
Casarin, M.2
Elliott F., Jr.3
Widlund, O.4
-
13
-
-
0001836507
-
Domain decomposition method and the Helmholtz problem
-
G. Cohen, L. Halpern, and P. Joly, eds., SIAM, Philadelphia
-
B. DESPRÉS, Domain decomposition method and the Helmholtz problem, in Mathematical and Numerical Aspects of Wave Propagation Phenomena, G. Cohen, L. Halpern, and P. Joly, eds., SIAM, Philadelphia, 1991, pp. 44-52.
-
(1991)
Mathematical and Numerical Aspects of Wave Propagation Phenomena
, pp. 44-52
-
-
Després, B.1
-
14
-
-
0012818396
-
An alternating-direction iteration method for Helmholtz problems
-
J. DOUGLAS, JR., J. L. HENSLEY, AND J. E. ROBERTS, An alternating-direction iteration method for Helmholtz problems, Appl. Math., 38 (1993), pp. 289-300.
-
(1993)
Appl. Math.
, vol.38
, pp. 289-300
-
-
Douglas J., Jr.1
Hensley, J.L.2
Roberts, J.E.3
-
15
-
-
0012775712
-
Some recent results on Schwarz type domain decomposition algorithms
-
Domain Decomposition Methods in Science and Engineering, A. Quarteroni, J. Periaux, Y. Kuznetsov, and O. Widlund, eds., SIAM, Philadelphia
-
M. DRYJA AND O. WIDLUND, Some recent results on Schwarz type domain decomposition algorithms, in Domain Decomposition Methods in Science and Engineering, A. Quarteroni, J. Periaux, Y. Kuznetsov, and O. Widlund, eds., Contemp. Math. 157, SIAM, Philadelphia, 1994, pp. 53-61.
-
(1994)
Contemp. Math.
, vol.157
, pp. 53-61
-
-
Dryja, M.1
Widlund, O.2
-
16
-
-
0000011239
-
Variational iterative methods for nonsymmetric systems of linear equations
-
S. C. EISENSTAT, H. C. ELMAN, AND M. H. SCHULTZ, Variational iterative methods for nonsymmetric systems of linear equations, SIAM J. Numer. Anal., 20 (1983), pp. 345-357.
-
(1983)
SIAM J. Numer. Anal.
, vol.20
, pp. 345-357
-
-
Eisenstat, S.C.1
Elman, H.C.2
Schultz, M.H.3
-
17
-
-
0036344991
-
A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations
-
H. C. ELMAN, O. G. ERNST, AND D. P. O'LEARY, A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations, SIAM J. Sci. Comput., 23 (2002), pp. 1291-1315.
-
(2002)
SIAM J. Sci. Comput.
, vol.23
, pp. 1291-1315
-
-
Elman, H.C.1
Ernst, O.G.2
O'Leary, D.P.3
-
18
-
-
0021416130
-
Necessary and sufficient conditions for the existence of a conjugate gradient method
-
V. FABER AND T. MANTEUFFEL, Necessary and sufficient conditions for the existence of a conjugate gradient method, SIAM J. Numer. Anal., 21 (1984), pp. 352-362.
-
(1984)
SIAM J. Numer. Anal.
, vol.21
, pp. 352-362
-
-
Faber, V.1
Manteuffel, T.2
-
19
-
-
0001027363
-
Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices
-
R. W. FREUND, Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Comput., 13 (1992), pp. 425-448.
-
(1992)
SIAM J. Sci. Comput.
, vol.13
, pp. 425-448
-
-
Freund, R.W.1
-
21
-
-
0000257076
-
Numerical modeling for electromagnetic methods of geophysics
-
M. Nabighian, ed., Society of Exploration Geophysicists, Tulsa, OK
-
G. HOHMANN, Numerical modeling for electromagnetic methods of geophysics, in Electromagnetic Methods in Applied Geophysics I: Theory, M. Nabighian, ed., Society of Exploration Geophysicists, Tulsa, OK, 1988, pp. 312-363.
-
(1988)
Electromagnetic Methods in Applied Geophysics I: Theory
, pp. 312-363
-
-
Hohmann, G.1
-
22
-
-
38249035216
-
Necessary and sufficient conditions for the simplification of the generalized conjugate-gradient algorithms
-
W. JOUBERT AND D. YOUNG, Necessary and sufficient conditions for the simplification of the generalized conjugate-gradient algorithms, Linear Algebra Appl., 88/89 (1987), pp. 449-485.
-
(1987)
Linear Algebra Appl.
, vol.88-89
, pp. 449-485
-
-
Joubert, W.1
Young, D.2
-
23
-
-
0012768502
-
Parallel multidomain iterative algorithms for the Helmholtz wave equation
-
S. KIM, Parallel multidomain iterative algorithms for the Helmholtz wave equation, Appl. Numer. Math., 17 (1995), pp. 411-429.
-
(1995)
Appl. Numer. Math.
, vol.17
, pp. 411-429
-
-
Kim, S.1
-
24
-
-
0039243579
-
Domain decomposition iterative procedures for solving scalar waves in the frequency domain
-
S. KIM, Domain decomposition iterative procedures for solving scalar waves in the frequency domain, Numer. Math., 79 (1998), pp. 231-259.
-
(1998)
Numer. Math.
, vol.79
, pp. 231-259
-
-
Kim, S.1
-
25
-
-
0032378531
-
On the use of rational iterations and domain decomposition methods for solving the Helmholtz problem
-
S. KIM, On the use of rational iterations and domain decomposition methods for solving the Helmholtz problem, Numer. Math., 79 (1998), pp. 529-552.
-
(1998)
Numer. Math.
, vol.79
, pp. 529-552
-
-
Kim, S.1
-
27
-
-
0030129492
-
Artificial damping techniques for scalar waves in the frequency domain
-
S. KIM AND M. LEE, Artificial damping techniques for scalar waves in the frequency domain, Comput. Math. Appl., 31 (1996), pp. 1-12.
-
(1996)
Comput. Math. Appl.
, vol.31
, pp. 1-12
-
-
Kim, S.1
Lee, M.2
-
28
-
-
0018655886
-
Constant Q-wave propagation and attenuation
-
E. KJARTANSSON, Constant Q-wave propagation and attenuation, J. Geophys. Res., 84 (1979), pp. 4737-4748.
-
(1979)
J. Geophys. Res.
, vol.84
, pp. 4737-4748
-
-
Kjartansson, E.1
-
29
-
-
0028369940
-
Domain decomposition methods in computational mechanics
-
P. LE TALLEC, Domain decomposition methods in computational mechanics, Comput. Mech. Adv., 1 (1994), pp. 121-220.
-
(1994)
Comput. Mech. Adv.
, vol.1
, pp. 121-220
-
-
Le Tallec, P.1
-
30
-
-
0033693515
-
First-order system least-squares for the Helmholtz equation
-
B. LEE, T. A. MANTEUFFEL, S. F. McCORMICK, AND J. RUGE, First-order system least-squares for the Helmholtz equation, SIAM J. Sci. Comput., 21 (2000), pp. 1927-1949.
-
(2000)
SIAM J. Sci. Comput.
, vol.21
, pp. 1927-1949
-
-
Lee, B.1
Manteuffel, T.A.2
McCormick, S.F.3
Ruge, J.4
-
31
-
-
0030235899
-
Multifrequency viscoacoustic modeling and inversion
-
Q. LIAO AND G. McMECHAN, Multifrequency viscoacoustic modeling and inversion, Geophys., 61 (1996), pp. 1371-1378.
-
(1996)
Geophys.
, vol.61
, pp. 1371-1378
-
-
Liao, Q.1
McMechan, G.2
-
33
-
-
84966244637
-
The fast adaptive composite grid (FAC) method for elliptic equations
-
S. McCORMICK AND J. THOMAS, The fast adaptive composite grid (FAC) method for elliptic equations, Math. Comp., 45 (1986), pp. 439-456.
-
(1986)
Math. Comp.
, vol.45
, pp. 439-456
-
-
McCormick, S.1
Thomas, J.2
-
34
-
-
0012879227
-
Additive Schwarz methods with nonreflecting boundary conditions for the parallel computation of Helmholtz problems
-
Domain Decomposition Methods 10, J. Mandel, C. Farhat, and X.-C. Cai, eds., 218, AMS, Providence, RI
-
L. McINNES, R. SUSAN-RESIGA, D. KEYES, AND H. ATASSI, Additive Schwarz methods with nonreflecting boundary conditions for the parallel computation of Helmholtz problems, in Domain Decomposition Methods 10, J. Mandel, C. Farhat, and X.-C. Cai, eds., Contemp. Math. 218, AMS, Providence, RI, 1998, pp. 325-333.
-
(1998)
Contemp. Math.
, pp. 325-333
-
-
McInnes, L.1
Susan-Resiga, R.2
Keyes, D.3
Atassi, H.4
-
35
-
-
0000048673
-
GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
-
Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Comput., 7 (1986), pp. 856-869.
-
(1986)
SIAM J. Sci. Comput.
, vol.7
, pp. 856-869
-
-
Saad, Y.1
Schultz, M.H.2
-
36
-
-
0012821396
-
Some numerical methods of solving Helmholtz wave equation
-
G. Cohen, L. Halpern, and P. Joly, eds., SIAM, Philadelphia
-
V. SHAIDUROV AND E. OGORODNIKOV, Some numerical methods of solving Helmholtz wave equation, in Mathematical and Numerical Aspects of Wave Propagation Phenomena, G. Cohen, L. Halpern, and P. Joly, eds., SIAM, Philadelphia, 1991, pp. 73-79.
-
(1991)
Mathematical and Numerical Aspects of Wave Propagation Phenomena
, pp. 73-79
-
-
Shaidurov, V.1
Ogorodnikov, E.2
-
37
-
-
0012826532
-
Analysis of the implicit Euler local uniform grid refinement method
-
R. A. TROMPERT AND J. G. VERWER, Analysis of the implicit Euler local uniform grid refinement method, SIAM J. Sci. Comput., 14 (1993), pp. 259-278.
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 259-278
-
-
Trompert, R.A.1
Verwer, J.G.2
-
38
-
-
0027543612
-
Convergence analysis of multigrid algorithms for nonselfadjoint and indefinite elliptic problems
-
J. WANG, Convergence analysis of multigrid algorithms for nonselfadjoint and indefinite elliptic problems, SIAM J. Numer. Anal., 30 (1993), pp. 275-285.
-
(1993)
SIAM J. Numer. Anal.
, vol.30
, pp. 275-285
-
-
Wang, J.1
-
39
-
-
0000570696
-
Iterative methods by space decomposition and subapace correction
-
J. Xu, Iterative methods by space decomposition and subapace correction, SIAM Rev., 34 (1992), pp. 581-613.
-
(1992)
SIAM Rev.
, vol.34
, pp. 581-613
-
-
Xu, J.1
|