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Saul Abarbanel; half a century of scientific work. (English) Zbl 1434.01039


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01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Abarbanel, Saul
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[1] Abarbanel, S., Time dependent temperature distribution in radiating solids, J. Math. Phys., 29, 246-257 (1960) · Zbl 0101.31103 · doi:10.1002/sapm1960391246
[2] Abarbanel, S., Radiative heat transfer in free-molecule flow, J. Aerosp. Sci., 28, 299-307 (1961) · Zbl 0098.17203 · doi:10.2514/8.8964
[3] Abarbanel, S., The distribution of flow properties behind a spherical detonation wave, Isr. J. Technol., 4, 82-86 (1966)
[4] Abarbanel, S.; Chertock, A., Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for hyperbolic PDEs, I, J. Comput. Phys., 160, 42-66 (2000) · Zbl 0987.65087 · doi:10.1006/jcph.2000.6420
[5] Abarbanel, S.; Chertock, A.; Yefet, A., Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for hyperbolic PDEs, II, J. Comput. Phys., 160, 67-87 (2000) · Zbl 0987.65088 · doi:10.1006/jcph.2000.6421
[6] Abarbanel, S.; Ditkowski, A., Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes, J. Comput. Phys., 133, 279-288 (1997) · Zbl 0891.65099 · doi:10.1006/jcph.1997.5653
[7] Abarbanel, S.; Ditkowski, A., Wave propagation in advected acoustics within a non-uniform medium under the effect of gravity, Appl. Numer. Math., 93, 61-68 (2015) · Zbl 1326.76089 · doi:10.1016/j.apnum.2014.04.003
[8] Abarbanel, S.; Duth, P.; Gottlieb, D., Splitting methods for low Mach number Euler and Navier-Stokes equations, Comput. Fluids, 17, 1-12 (1989) · Zbl 0664.76088 · doi:10.1016/0045-7930(89)90003-0
[9] Abarbanel, S.; Dwoyer, D.; Gottlieb, D., Improving the convergence rate to steady state of parabolic ADI methods, J. Comput. Phys., 67, 1-18 (1986) · Zbl 0608.65055 · doi:10.1016/0021-9991(86)90111-7
[10] Abarbanel, S.; Goldberg, M., Numerical solution of quasi-conservative hyperbolic systems—the cylindrical shock problem, J. Comput. Phys., 10, 1-21 (1972) · Zbl 0243.65071 · doi:10.1016/0021-9991(72)90087-3
[11] Abarbanel, S.; Gottlieb, D., Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives, J. Comput. Phys., 41, 1-33 (1981) · Zbl 0467.76062 · doi:10.1016/0021-9991(81)90077-2
[12] Abarbanel, S.; Gottlieb, D., A mathematical analysis of the PML method, J. Comput. Phys., 134, 357-363 (1997) · Zbl 0887.65122 · doi:10.1006/jcph.1997.5717
[13] Abarbanel, S.; Gottlieb, D., On the construction and analysis of absorbing layers in CEM, Appl. Numer. Math., 27, 331-340 (1998) · Zbl 0924.35160 · doi:10.1016/S0168-9274(98)00018-X
[14] Abarbanel, S.; Gottlieb, D.; Carpenter, M., On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations, SIAM J. Sci. Comput., 17, 777-782 (1996) · Zbl 0858.65096 · doi:10.1137/S1064827595282520
[15] Abarbanel, S.; Gottlieb, D.; Hesthaven, J., Well-posed perfectly matched layers for advective acoustics, J. Comput. Phys., 154, 266-283 (1999) · Zbl 0947.76076 · doi:10.1006/jcph.1999.6313
[16] Abarbanel, S.; Gottlieb, D.; Hesthaven, J., Long time behavior of the perfectly matched layer equations in computational electromagnetics, J. Sci. Comput., 17, 405-422 (2002) · Zbl 1005.78014 · doi:10.1023/A:1015141823608
[17] Abarbanel, S.; Gottlieb, D.; Hesthaven, J., Non-linear PML equations for time dependent electromagnetics in three dimensions, J. Sci. Comput., 28, 125-137 (2006) · Zbl 1176.78035 · doi:10.1007/s10915-006-9072-1
[18] Abarbanel, S.; Zwas, G., An iterative finite-difference method for hyperbolic systems, Math. Comput., 23, 549-565 (1969) · Zbl 0184.52301 · doi:10.1090/S0025-5718-1969-0247783-2
[19] Abarbanel, S.; Zwas, G., The motion of shock waves and products of detonation confined between a wall and a rigid piston, J. Math. Anal. Appl., 28, 517-544 (1969) · Zbl 0165.57804 · doi:10.1016/0022-247X(69)90006-7
[20] Berenger, J., A perfectly matched layer for the absorbtion of electromagnetic waves, J. Comput. Phys., 114, 185-200 (1994) · Zbl 0814.65129 · doi:10.1006/jcph.1994.1159
[21] Carpenter, M.; Gottlieb, D.; Abarbanel, S., The stability of numerical boundary treatments for compact high-order finite-difference schemes, J Comput. Phys., 108, 272-295 (1993) · Zbl 0791.76052 · doi:10.1006/jcph.1993.1182
[22] Carpenter, M.; Gottlieb, D.; Abarbanel, S., Stable and accurate boundary treatments for compact, high-order finite-difference schemes, Appl. Numer. Math., 12, 55-87 (1993) · Zbl 0778.65057 · doi:10.1016/0168-9274(93)90112-5
[23] Carpenter, M.; Gottlieb, D.; Abarbanel, S., Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes, J Comput. Phys., 111, 220-236 (1994) · Zbl 0832.65098 · doi:10.1006/jcph.1994.1057
[24] Carpenter, M.; Gottlieb, D.; Abarbanel, S.; Don, W-S, The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: a study of the boundary error, SIAM J. Sci. Comput., 16, 1241-1252 (1995) · Zbl 0839.65098 · doi:10.1137/0916072
[25] Engquist, B.; Majda, A., Absorbing boundary conditions for the numerical simulation of waves, Math. Comput., 31, 629-651 (1977) · Zbl 0367.65051 · doi:10.1090/S0025-5718-1977-0436612-4
[26] Kreiss, H-O; Oliger, J., Comparison of accurate methods for the integration of hyperbolic problems, Tellus, 24, 199-215 (1972) · doi:10.3402/tellusa.v24i3.10634
[27] Kreiss, H.-O., Scherer, G.: Finite Element Andfinite Difference Methods for Hyperbolic Partial Differential Equations, Mathematical Aspects of Finite Element And Finite Difference Methods For Hyperbolic Partial Differential Equations. Academic Press, New York (1974) · Zbl 0355.65085
[28] Lax, P., Weak solutions of nonlinear hyperbolic equations and their numerical computation, Commun. Pure Appl. Math., 7, 159-193 (1954) · Zbl 0055.19404 · doi:10.1002/cpa.3160070112
[29] Lax, P.; Wendroff, B., Systems of conservation laws, Commun. Pure Appl. Math., 13, 217-237 (1960) · Zbl 0152.44802 · doi:10.1002/cpa.3160130205
[30] Lele, S., Compact finite difference schemes with spectral-like resolotion, J. Comput. Phys., 103, 16-42 (1992) · Zbl 0759.65006 · doi:10.1016/0021-9991(92)90324-R
[31] MacCormack, R., Baldwin, B.: A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interaction. AIAA paper 75-1 (1975)
[32] Orszag, S., Numerical simulation of incompressible flows within simple boundaries. I. Galerkin (spectral) representations, Stud. Appl. Math., 50, 293-327 (1971) · Zbl 0237.76012 · doi:10.1002/sapm1971504293
[33] Turkel, E.; Abarbanel, S.; Gottlieb, D., Multidimensional difference schemes with fourth order accuracy, J. Comput. Phys., 21, 85-113 (1976) · Zbl 0328.65045 · doi:10.1016/0021-9991(76)90021-8
[34] Neumann, J.; Richtmyer, R., A method for numerical calculation of hydrodynamic shocks, J. Appl. Phys., 21, 232-237 (1950) · Zbl 0037.12002 · doi:10.1063/1.1699639
[35] Ziolkowski, R., Time-derivative Lorentz-material model-based absorbing boundary condition, IEEE Trans. Antennas Propag., 45, 1530-1535 (1997) · doi:10.1109/8.633862
[36] Zwas, G.; Abarbanel, S., Third and fourth order accurate schemes for hyperbolic equations of conservation law form, Math. Comput., 25, 229-236 (1971) · Zbl 0221.65167 · doi:10.1090/S0025-5718-1971-0303766-4
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