-
1
-
-
17044389388
-
Numerical solution of the Dirac equation by a mapped Fourier grid method
-
E. Ackad and M. Horbatsch, Numerical solution of the Dirac equation by a mapped Fourier grid method. J. Phys. A: Math. General 38 (2005) 3157-3171.
-
(2005)
J. Phys. A: Math. General
, vol.38
, pp. 3157-3171
-
-
Ackad, E.1
Horbatsch, M.2
-
2
-
-
0003796630
-
-
Academic Press, New York
-
R.A. Adams, Sobolev spaces. Academic Press, New York (1975).
-
(1975)
Sobolev spaces
-
-
Adams, R.A.1
-
3
-
-
0035594730
-
Mathematical concepts of open quantum boundary conditions
-
A. Arnold, Mathematical concepts of open quantum boundary conditions. Transport Theory Statist. Phys. 30 (2001) 561-584.
-
(2001)
Transport Theory Statist. Phys
, vol.30
, pp. 561-584
-
-
Arnold, A.1
-
5
-
-
0040214718
-
Approximation by trigonometric polynomials in a certain class of periodic functions of several variables
-
K.I. Babenko, Approximation by trigonometric polynomials in a certain class of periodic functions of several variables. Dokl. Akad. Nauk SSSR 132 (1960) 672-675.
-
(1960)
Dokl. Akad. Nauk SSSR
, vol.132
, pp. 672-675
-
-
Babenko, K.I.1
-
6
-
-
0003660984
-
PETSc users manual
-
Tech. Report ANL-95/11, Revision 2.1.5, Argonne National Laboratory
-
S. Balay, K. Buschelman, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith and H. Zhang, PETSc users manual. Tech. Report ANL-95/11 - Revision 2.1.5, Argonne National Laboratory (2004).
-
(2004)
-
-
Balay, S.1
Buschelman, K.2
Eijkhout, V.3
Gropp, W.D.4
Kaushik, D.5
Knepley, M.G.6
McInnes, L.C.7
Smith, B.F.8
Zhang, H.9
-
10
-
-
0004258344
-
-
Habilitationsschrift, Institut für Informatik, TU München and Shaker Verlag, Aachen
-
H. Bungartz, Finite elements of higher order on sparse grids. Habilitationsschrift, Institut für Informatik, TU München and Shaker Verlag, Aachen (1998).
-
(1998)
Finite elements of higher order on sparse grids
-
-
Bungartz, H.1
-
11
-
-
0001335132
-
A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives
-
H. Bungartz and M. Griebel, A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives. J. Complexity 15 (1999) 167-199.
-
(1999)
J. Complexity
, vol.15
, pp. 167-199
-
-
Bungartz, H.1
Griebel, M.2
-
13
-
-
0000323375
-
Multigrid methods for nearly singular linear equations and eigenvalue problems
-
Z. Cai, J. Mandel and S. McCormick, Multigrid methods for nearly singular linear equations and eigenvalue problems. SIAM J. Numer. Anal. 34 (1997) 178-200.
-
(1997)
SIAM J. Numer. Anal
, vol.34
, pp. 178-200
-
-
Cai, Z.1
Mandel, J.2
McCormick, S.3
-
14
-
-
0036103889
-
Subspace correction multi-level methods for elliptic eigenvalue problems
-
T. Chan and I. Sharapov, Subspace correction multi-level methods for elliptic eigenvalue problems. Numer. Linear Algebra Appl. 9 (2002) 1-20.
-
(2002)
Numer. Linear Algebra Appl
, vol.9
, pp. 1-20
-
-
Chan, T.1
Sharapov, I.2
-
15
-
-
36148972266
-
A general framework for compactly supported splines and wavelets
-
C. Chui and Y. Wang, A general framework for compactly supported splines and wavelets. J. Approx. Theory 71 (1992) 263-304.
-
(1992)
J. Approx. Theory
, vol.71
, pp. 263-304
-
-
Chui, C.1
Wang, Y.2
-
17
-
-
0001695987
-
The theory of complex spectra
-
E. Condon, The theory of complex spectra. Phys. Rev. 36 (1930) 1121-1133.
-
(1930)
Phys. Rev
, vol.36
, pp. 1121-1133
-
-
Condon, E.1
-
19
-
-
34249975165
-
Symmetric iterative interpolation processes
-
G. Deslauriers and S. Dubuc, Symmetric iterative interpolation processes. Constr. Approx. 5 (1989) 49-68.
-
(1989)
Constr. Approx
, vol.5
, pp. 49-68
-
-
Deslauriers, G.1
Dubuc, S.2
-
21
-
-
29344456764
-
Number of lattice points in the hyperbolic cross
-
N. Dobrovol'skii and A. Roshchenya, Number of lattice points in the hyperbolic cross. Math. Notes 11 (1998) 319-324.
-
(1998)
Math. Notes
, vol.11
, pp. 319-324
-
-
Dobrovol'skii, N.1
Roshchenya, A.2
-
23
-
-
84977266737
-
Die Berechnung optischer und elektrostatischer Gitterpotentiale
-
P. Ewald, Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 64 (1921) 253-287.
-
(1921)
Ann. Phys
, vol.64
, pp. 253-287
-
-
Ewald, P.1
-
24
-
-
0001164755
-
Phase space approach for optimizing grid representations: The mapped Fourier method
-
E. Fattal, R. Baer and R. Kosloff, Phase space approach for optimizing grid representations: the mapped Fourier method. Phys. Rev. E 53 (1996) 1217-1227.
-
(1996)
Phys. Rev. E
, vol.53
, pp. 1217-1227
-
-
Fattal, E.1
Baer, R.2
Kosloff, R.3
-
25
-
-
0033295857
-
Absorbing boundary conditions for the Schrödinger equation
-
T. Fevens and H. Jiang, Absorbing boundary conditions for the Schrödinger equation. SIAM J. Scientific Comput. 21 (1999) 255-282.
-
(1999)
SIAM J. Scientific Comput
, vol.21
, pp. 255-282
-
-
Fevens, T.1
Jiang, H.2
-
26
-
-
34547507756
-
-
R. Feynman, There's plenty of room at the bottom: An invitation to enter a new world of physics. Engineering and Science XXIII, Feb. issue (1960), http://www.zyvex.com/nanotech/feynman.html.
-
R. Feynman, There's plenty of room at the bottom: An invitation to enter a new world of physics. Engineering and Science XXIII, Feb. issue (1960), http://www.zyvex.com/nanotech/feynman.html.
-
-
-
-
27
-
-
0037042658
-
Wavelet approximation of correlated wavefunctions. I. Basics
-
H.-J. Fiad, W. Hackbusch, D. Kolb and R. Schneider, Wavelet approximation of correlated wavefunctions. I. Basics., J. Chem. Phys. 116 (2002) 9641-9857.
-
(2002)
J. Chem. Phys
, vol.116
, pp. 9641-9857
-
-
Fiad, H.-J.1
Hackbusch, W.2
Kolb, D.3
Schneider, R.4
-
28
-
-
34547544100
-
Best N term approximation in electronic structure calculations. I. One electron reduced density matrix
-
Tech. Report 05-9, Berichtsreihe des Mathematischen Seminars der Universität Kiel
-
H.-J. Fiad, W. Hackbusch and R. Schneider, Best N term approximation in electronic structure calculations. I. One electron reduced density matrix. Tech. Report 05-9, Berichtsreihe des Mathematischen Seminars der Universität Kiel (2005).
-
(2005)
-
-
Fiad, H.-J.1
Hackbusch, W.2
Schneider, R.3
-
29
-
-
22944452424
-
Coupled-cluster theory with simplified linear-rl2 corrections: The CCSD(R12) model
-
H. Fliegl, W. Klopper and C. Hättig, Coupled-cluster theory with simplified linear-rl2 corrections: The CCSD(R12) model. J. Chem. Phys. 122 (2005) 084107.
-
(2005)
J. Chem. Phys
, vol.122
, pp. 084107
-
-
Fliegl, H.1
Klopper, W.2
Hättig, C.3
-
32
-
-
0030099613
-
Information complexity of multivariate Fredholm equations in Sobolev classes
-
K. Frank, S. Heinrich and S. Pereverzev, Information complexity of multivariate Fredholm equations in Sobolev classes. J. Complexity 12 (1996) 17-34.
-
(1996)
J. Complexity
, vol.12
, pp. 17-34
-
-
Frank, K.1
Heinrich, S.2
Pereverzev, S.3
-
33
-
-
34547507126
-
-
G. Friesecke, The configuraton-interaction equations for atoms and molecules: Charge quantization and existence of solutions. Preprint, June 28, 1999, Mathematical Insitute, University of Oxford, UK.
-
G. Friesecke, The configuraton-interaction equations for atoms and molecules: Charge quantization and existence of solutions. Preprint, June 28, 1999, Mathematical Insitute, University of Oxford, UK.
-
-
-
-
34
-
-
0001032475
-
On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique
-
J. Garcke and M. Griebel, On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique. J. Comput. Phys. 165 (2000) 694-716.
-
(2000)
J. Comput. Phys
, vol.165
, pp. 694-716
-
-
Garcke, J.1
Griebel, M.2
-
35
-
-
0242440688
-
Numerical integration using sparse grids
-
T. Gerstner and M. Griebel, Numerical integration using sparse grids. Numer. Algorithms 18 (1998) 209-232.
-
(1998)
Numer. Algorithms
, vol.18
, pp. 209-232
-
-
Gerstner, T.1
Griebel, M.2
-
36
-
-
0141991028
-
Dimension-adaptive tensor-product quadrature
-
T. Gerstner and M. Griebel, Dimension-adaptive tensor-product quadrature. Computing 71 (2003) 65-87.
-
(2003)
Computing
, vol.71
, pp. 65-87
-
-
Gerstner, T.1
Griebel, M.2
-
37
-
-
0001610807
-
Multilevel algorithms considered as iterative methods on semidefinite systems
-
M. Griebel, Multilevel algorithms considered as iterative methods on semidefinite systems. SIAM J. Sci. Stat. Comput. 15 (1994) 547-565.
-
(1994)
SIAM J. Sci. Stat. Comput
, vol.15
, pp. 547-565
-
-
Griebel, M.1
-
39
-
-
0034337983
-
Optimized tensor-product approximation spaces
-
M. Griebel and S. Knapek, Optimized tensor-product approximation spaces. Constr. Approx. 16 (2000) 525-540.
-
(2000)
Constr. Approx
, vol.16
, pp. 525-540
-
-
Griebel, M.1
Knapek, S.2
-
40
-
-
0242503926
-
On additive Schwarz preconditioners for sparse grid discretizations
-
M. Griebel and P. Oswald, On additive Schwarz preconditioners for sparse grid discretizations. Numer. Math. 66 (1994) 449-463.
-
(1994)
Numer. Math
, vol.66
, pp. 449-463
-
-
Griebel, M.1
Oswald, P.2
-
41
-
-
21844511143
-
On the abstract theory of additive and multiplicative Schwarz algorithms
-
M. Griebel and P. Oswald, On the abstract theory of additive and multiplicative Schwarz algorithms. Numer. Math. 70 (1995) 161-180.
-
(1995)
Numer. Math
, vol.70
, pp. 161-180
-
-
Griebel, M.1
Oswald, P.2
-
42
-
-
0000277689
-
Tensor product type subspace splitting and multilevel iterative methods for anisotropic problems
-
M. Griebel and P. Oswald, Tensor product type subspace splitting and multilevel iterative methods for anisotropic problems. Adv. Comput. Math. 4 (1995) 171-206.
-
(1995)
Adv. Comput. Math
, vol.4
, pp. 171-206
-
-
Griebel, M.1
Oswald, P.2
-
44
-
-
84956246254
-
Adaptive Riemannian metric for plane-wave electronic-structure calculations
-
F. Gygi, Adaptive Riemannian metric for plane-wave electronic-structure calculations. Europhys. Lett. 19 (1992) 617.
-
(1992)
Europhys. Lett
, vol.19
, pp. 617
-
-
Gygi, F.1
-
45
-
-
4244217973
-
Electronic-structure calculations in adaptive coordinates
-
F. Gygi, Electronic-structure calculations in adaptive coordinates. Phys. Rev. B 48 (1993) 11692.
-
(1993)
Phys. Rev. B
, vol.48
, pp. 11692
-
-
Gygi, F.1
-
46
-
-
0035099429
-
Comparison of global and local adaptive coordinates for density-functional calculations
-
D. Hamann, Comparison of global and local adaptive coordinates for density-functional calculations. Phys. Rev. B 63 (2001) 075107.
-
(2001)
Phys. Rev. B
, vol.63
, pp. 075107
-
-
Hamann, D.1
-
47
-
-
33745196196
-
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
-
V. Hernandez, J. Roman and V. Vidal, SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Software 31 (2005) 351-362.
-
(2005)
ACM Trans. Math. Software
, vol.31
, pp. 351-362
-
-
Hernandez, V.1
Roman, J.2
Vidal, V.3
-
49
-
-
34547517374
-
-
R. Hochmuth, S. Knapek and G. Zumbusch, Tensor products of Sobolev spaces and applications. Tech. Report 685, SFB 256, Univ. Bonn (2000).
-
R. Hochmuth, S. Knapek and G. Zumbusch, Tensor products of Sobolev spaces and applications. Tech. Report 685, SFB 256, Univ. Bonn (2000).
-
-
-
-
52
-
-
84980086883
-
On the eigenfunctions of many-particle systems in quantum mechanics
-
T. Kato, On the eigenfunctions of many-particle systems in quantum mechanics. Commun. Pure Appl. Math. 10 (1957) 151-177.
-
(1957)
Commun. Pure Appl. Math
, vol.10
, pp. 151-177
-
-
Kato, T.1
-
53
-
-
0000271460
-
Exact non-reflecting boundary conditions
-
J. Keller and D. Givoli, Exact non-reflecting boundary conditions. J. Comput. Phys. 82 (1989) 172-192.
-
(1989)
J. Comput. Phys
, vol.82
, pp. 172-192
-
-
Keller, J.1
Givoli, D.2
-
55
-
-
34547511039
-
-
S. Knapek, Hyperbolic cross approximation of integral operators with smooth kernel. Tech. Report 665, SFB 256, Univ. Bonn (2000).
-
S. Knapek, Hyperbolic cross approximation of integral operators with smooth kernel. Tech. Report 665, SFB 256, Univ. Bonn (2000).
-
-
-
-
56
-
-
2942668468
-
Efficient solution of symmetric eigenvalue problem using multigrid preconditioners in the locally optimal block conjugate gradient method
-
A. Knyazev and K. Neymeyr, Efficient solution of symmetric eigenvalue problem using multigrid preconditioners in the locally optimal block conjugate gradient method. Electronic Trans. Numer. Anal. 15 (2003) 38-55.
-
(2003)
Electronic Trans. Numer. Anal
, vol.15
, pp. 38-55
-
-
Knyazev, A.1
Neymeyr, K.2
-
57
-
-
34547528034
-
Convergence of expansions in a Gaussian basis
-
M. Defranceschi and Y. Ellinger Eds, Kluwer, Dordrecht
-
W. Kutzelnigg, Convergence of expansions in a Gaussian basis. Strategies and Applications in Quantum Chemistry, M. Defranceschi and Y. Ellinger Eds., Kluwer, Dordrecht (1996).
-
(1996)
Strategies and Applications in Quantum Chemistry
-
-
Kutzelnigg, W.1
-
58
-
-
33344477526
-
Minimal parametrization of an n-electron state
-
W. Kutzelnigg and D. Mukherjee, Minimal parametrization of an n-electron state. Phys. Rev. A 71 (2005) 022502.
-
(2005)
Phys. Rev. A
, vol.71
, pp. 022502
-
-
Kutzelnigg, W.1
Mukherjee, D.2
-
59
-
-
19844366465
-
Computational chemistry from the perspective of numerical analysis
-
C. Le Bris, Computational chemistry from the perspective of numerical analysis. Acta Numer. 14 (2005) 363-444.
-
(2005)
Acta Numer
, vol.14
, pp. 363-444
-
-
Le Bris, C.1
-
61
-
-
0016940739
-
Comparative analysis of Cuthill-McKee and reverse Cuthill-McKee ordering algorithms for sparse matrices
-
W. Liu and A. Sherman, Comparative analysis of Cuthill-McKee and reverse Cuthill-McKee ordering algorithms for sparse matrices. SIAM J. Numer Anal. 13 (1976) 198-213.
-
(1976)
SIAM J. Numer Anal
, vol.13
, pp. 198-213
-
-
Liu, W.1
Sherman, A.2
-
62
-
-
34547525226
-
-
O. Livne and A. Brandt, O(N log N) multilevel calculation of N eigenfunctions. Multiscale Computational Methods in Chemistry and Physics, A. Brandt, J. Bernholc and K. Binder Eds., NATO Science Series III: Computer and Systems Sciences, IOS Press 177 (2001) 112-136.
-
O. Livne and A. Brandt, O(N log N) multilevel calculation of N eigenfunctions. Multiscale Computational Methods in Chemistry and Physics, A. Brandt, J. Bernholc and K. Binder Eds., NATO Science Series III: Computer and Systems Sciences, IOS Press 177 (2001) 112-136.
-
-
-
-
63
-
-
0039863907
-
On approximate approximations using Gaussian kernels
-
V. Maz'ya and G. Schmidt, On approximate approximations using Gaussian kernels. IMA J. Numer. Anal. 16 (1996) 13-29.
-
(1996)
IMA J. Numer. Anal
, vol.16
, pp. 13-29
-
-
Maz'ya, V.1
Schmidt, G.2
-
64
-
-
28844460348
-
Variational two-electron reduced density matrix theory for many-electron atoms and molecules: Implementation of the spin- and symmetry-adapted T-2 condition through first-order semidefinite programming
-
D. Mazziotti, Variational two-electron reduced density matrix theory for many-electron atoms and molecules: Implementation of the spin- and symmetry-adapted T-2 condition through first-order semidefinite programming. Phys. Rev. A 72 (2005) 032510.
-
(2005)
Phys. Rev. A
, vol.72
, pp. 032510
-
-
Mazziotti, D.1
-
65
-
-
34547545065
-
-
and 2, North-Holland, Amsterdam
-
A. Messiah, Quantum mechanics. Vol. 1 and 2, North-Holland, Amsterdam, 1961/62.
-
(1961)
Quantum mechanics
, vol.1
-
-
Messiah, A.1
-
67
-
-
0004139365
-
Multilevel finite element approximation
-
Teubner, Stuttgart
-
P. Oswald, Multilevel finite element approximation. Teubner Skripten zur Numerik, Teubner, Stuttgart (1994).
-
(1994)
Teubner Skripten zur Numerik
-
-
Oswald, P.1
-
70
-
-
0037147161
-
High-precision Hy-CI variational calculations for the ground state of neutral helium and heliumlike ions
-
J.S. Sims and S.A. Hagstrom, High-precision Hy-CI variational calculations for the ground state of neutral helium and heliumlike ions. Int. J. Quant. Chem. 90 (2002) 1600-1609.
-
(2002)
Int. J. Quant. Chem
, vol.90
, pp. 1600-1609
-
-
Sims, J.S.1
Hagstrom, S.A.2
-
71
-
-
36149026675
-
The theory of complex spectra
-
J. Slater, The theory of complex spectra. Phys. Rev. 34 (1929) 1293-1322.
-
(1929)
Phys. Rev
, vol.34
, pp. 1293-1322
-
-
Slater, J.1
-
72
-
-
0001048297
-
Quadrature and interpolation formulas for tensor products of certain classes of functions
-
S. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions. Soviet Math. Dokl. 4 (1963) 240-243.
-
(1963)
Soviet Math. Dokl
, vol.4
, pp. 240-243
-
-
Smolyak, S.1
-
73
-
-
0001048298
-
Russian original in Dokl
-
Russian original in Dokl. Akad. Nauk SSSR 148 (1963) 1042-1045.
-
(1963)
Akad. Nauk SSSR
, vol.148
, pp. 1042-1045
-
-
-
77
-
-
34547522251
-
-
H. Yserentant, On the electronic Schrödinger equation. Report 191, SFB 382, Univ. Tübingen (2003).
-
H. Yserentant, On the electronic Schrödinger equation. Report 191, SFB 382, Univ. Tübingen (2003).
-
-
-
-
78
-
-
2942635358
-
On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives
-
H. Yserentant, On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives. Numer. Math. 98 (2004) 731-759.
-
(2004)
Numer. Math
, vol.98
, pp. 731-759
-
-
Yserentant, H.1
-
79
-
-
0001918867
-
The approximation of classes of periodic functions of many variables
-
D. Zung, The approximation of classes of periodic functions of many variables. Russian Math. Surveys 38 (1983) 117-118.
-
(1983)
Russian Math. Surveys
, vol.38
, pp. 117-118
-
-
Zung, D.1
-
80
-
-
33751113798
-
Approximation by trigonometric polynomials of functions of several variables on the torus
-
D. Zung, Approximation by trigonometric polynomials of functions of several variables on the torus. Math. USSR Sbornik 59 (1988) 247-267.
-
(1988)
Math. USSR Sbornik
, vol.59
, pp. 247-267
-
-
Zung, D.1
|