List of Publications

Achi Brandt

  1. Brandt, A., A generalization of a combinatorial theorem of Sparre Andersen about sums of random variables, Math. Scand. 9 (1961) 325–358.
  2. Brandt A. and Gillis, J., Magnetohydrodynamic flow in the inlet region of a straight channel, Phys. of Fluids 9 (1966) 690–699.
  3. Brandt, A., Estimates for difference quotients of solutions of Poisson type difference equations, Math. Comp. 20 (1966) 473–499.
  4. Brandt, A., Interior estimates for second order elliptic differential (or finite-difference) equations via the maximum principle, Israel J. Math. 7 (1969) 95–121.
  5. Brandt, A. and Kelson, I., Single particle theory of fission, Phys. Ref. 183 (1969) 1025–1054.
  6. Brandt, A. and Gillis, J., Asymptotic approach to Hartmann Poiseuille flows, J. Comp. Phys. 3 (1969) 523–538.
  7. Brandt, A., Interior Schauder estimates for parabolic differential equations via the maximum principle, Israel J. Math. 7 (1969) 254–262.
  8. Abarbanel, S., Bennett, S., Brandt, A. and Gillis, J., Velocity profiles of flow at low Reynolds numbers, J. Appl. Mech. 37 (1970) 2–4.
  9. Brandt, A. and Intrator, Y., The assignment problem with three job categories, Cas. Pest. Mat. 96 (1971) 8–11.
  10. Brandt, A., Bresler, E., Dinar, N. and Ben-Asher, I., Infiltration from a trickle source; I. Mathematical models, Soil Sci. Soc. Am. Proc. 35 (1971) 675–682.
  11. Bressler, E., Heller, J., Dinar, N., Ben-Asher, I., Brandt, B. and Goldberg, D., Infiltration from a trickle source; II. Experimental data and theoretical predictions, Soil Sci. Soc. Am. Proc. 35 (1971) 683–689.
  12. Brandt, A., Multi-level adaptive technique (MLAT) for fast numerical solutions to boundary value problems, in Proc. 3rd Int. Conf. on Numerical Methods in Fluid Mechanics (Cabannes, H. and Temam, R., eds.), Lecture Notes in Physics 18, Springer-Verlag, 1973,pp. 82–89.
  13. Brandt, A., Generalized local maximum principles for elliptic andparabolic difference equations, Math. Comp. 27 (1973)685–718.
  14. Brandt, A., Multi-level adaptive technique (MLAT); I. The multi-grid method, IBM Research Report RC-6026, IBM T.J. Watson Research Center, Yorktown Heights, New York, 1976.
  15. South, J.C. and Brandt, A., Application of a multi-level grid method to transonic flow calculations, in Transonic Flow Problems in Turbo Machinery (Adam, T.C. and Platzer, M.F., eds.), Hemisphere, Washington, 1977, pp. 180–207.
  16. Brandt, A., Multi-level adaptive solutions to boundary value problems, Math. Comp. 31 (1977) 333–390.
  17. Brandt, A., Multi-level adaptive techniques (MLAT) for partial differential equations: ideas and software, in Mathematical Software, III (Rice, J.R., ed.), Academic Press, New York, 1977, pp. 273–314.
  18. Brandt, A. and Intrator, J., Fast algorithms for long transportation problems, Comp. Ops. Res. 5 (1978) 263–271.
  19. Brandt, A., Multi-level adaptive techniques (MLAT) for singular perturbation problems, in Numerical Analysis of Singular Perturbation Problems (Hemker, P.W. and Miller, J.J.H., eds.), Academic Press, New York, 1979, 53–142.
  20. Brandt, A. and Dinar, N., Multi-grid solutions to elliptic flow problems, in Numerical Methods for Partial Differential Equations (Parter, S., ed.), Academic Press, New York, 1979, pp. 53–147.
  21. Brandt, A., Multi-level adaptive finite elements methods; I. Variational problems, in Special Topics of Applied Mathematics (Frehse, J., Pallaschke, D. and Trottenberg, U., eds.), North Holland,1980, pp. 91–128.
  22. Brandt, A., Dendy, J.E., Jr. and Ruppel H., The multi-grid method for semi-implicit hydrodynamics codes, J. Comp. Phys. 34 (1980) 348–370.
  23. Brandt, A., Multi-level adaptive finite-element computations in fluid dynamics, AIAA J. 18 (1980) 1165–1172.
  24. Brandt, A., Numerical stability and fast solutions to boundary value problems, in Boundary and Interior Layers — Computational and Asymptotic Methods (Miller, J.J.H., ed.), Boole Press, Dublin, 1980, pp. 29–49.
  25. Alcouffe, R.E., Brandt, A., Dendy, J.E., Jr. and Painter, J.W., The multi-grid methods for the diffusion equation with strongly discontinuous coefficients, SIAM J. Sci. Stat. Comp. 2 (1981) 430–454.
  26. Brandt, A., Stages in developing multigrid solutions, in Proc. 2nd Int. Congr. on Numerical Methods for Engineering (Absi, E., Glowinski, R., Lascaux, P. and Veysseyre, H., eds.), Dunod,Paris, 1980, pp. 23–43.
  27. Brandt, A., Multi-grid solvers on parallel computers, in Elliptic Problem Solvers (Schultz, M., ed.), Academic Press, New York,1981, pp. 39–84.
  28. Brandt, A., Multi-grid solvers for non-elliptic and singular-perturbation steady-state problems, Weizmann Institute of Science, Rehovot, December 1981.
  29. Brandt, A., Multi-grid solutions to steady-state compressible Navier-Stokes equations, I, in Computing Methods in Applied Sciences and Engineering, V (Glowinski, R. and Lions, J.L., eds.), North Holland, 1982, pp. 407–422.
  30. Brandt, A., Guide to multigrid development, in Multigrid Methods (Hackbusch, W. and Trottenberg, U., eds.), Springer-Verlag,1982, pp. 220–312.
  31. Brandt, A., Introductory remarks on multigrid methods, in Numerical Methods for Fluid Dynamics (Morton, K.W. and Baines,M.J., eds.), Academic Press, New York, 1982, pp. 127–134.
  32. Brandt, A., McCormick, S. and Ruge, J., Algebraic multigrid (AMG) for automatic multigrid solution with application to geodetic computations, Institute for Computational Studies, POB 1852, Fort Collins, Colorado, 1982.
  33. Brandt, A., McCormick, S. and Ruge, J., Multi-grid methods for differential eigenproblems, SIAM J. Sci. Stat. Comp. 4 (1983) 244–260.
  34. Brandt, A. and Cryer, C.W., Multi-grid algorithms for the solution of linear complementarity problems arising from free boundary problems, SIAM J. Sci. Stat. Comp. 4 (1983) 655–684.
  35. Barkai, D. and Brandt, A., Vectorized multigrid Poisson solver,Appl. Math. Comp. 13 (1983) 215–227.
  36. Brandt, A. and Ophir, D., GRIDPACK: Toward unification of general grid programming, in PDE Software: Modules Interfaces and Systems (Engquist, B. and Smedsaas, T., eds.), North Holland, 1984,pp. 269–288.
  37. Brandt, A., McCormick, S. and Ruge, J., Algebraic multigrid (AMG) for sparse matrix equations, in Sparsity and its Applications (Evans, D.J., ed.), Cambridge University Press, Cambridge, 1984, pp. 257–284.
  38. Brandt, A., Multigrid Techniques: 1984 Guide, with Applications to Fluid Dynamics, 1984, 191 pages, ISBN-3-88457-081-1;GMD-Studien Nr. 85; Available from GMD-AIW, Postfach 1316, D-53731,St. Augustin 1, Germany, 1984.
  39. Brandt, A., Local and multi-level parallel processing mill, inRechnerarchiteckturen für die Numerische Simulation auf der Basis Superschneller Lösungsverfahren, I (Trottenberg, U. and Wypior, P.,eds.), GMD-Studien Nr. 88, 1984, pp. 31–40.
  40. Brandt, A., Fulton, S.R. and Taylor, G.D., Improved spectralmultigrid methods for periodic elliptic problems, J. Comp. Phys.58 (1985) 96–112.
  41. Brandt, A., Introduction –- levels and scales, in Multigrid Methods for Integral and Differential Problems (Paddon, D. and Holstein, H., eds.), Clarendon Press, Oxford, 1985, pp. 1–10.
  42. Brandt, A. and Ta'asan, S., Multigrid solutions to quasi-ellipticschemes, in Progress and Supercomputing in Computational Fluid Dynamics (Murman, E.M. and Abarbanel, S.S., eds.), Birkhäuser, Boston, 1985, pp. 235–255.
  43. Brandt, A., Algebraic multigrid theory: The symmetric case, in Preliminary Proc. Int. Multigrid Conf., Copper Mountain, Colorado, April 6–8, 1983; Appl. Math. Comp. 19 (1986) 23–56.
  44. Brandt, A. and Ta'asan, S., Multigrid method for nearly singular and slightly indefinite problems, in Multigrid Methods, II (Hackbusch, W. and Trottenberg, U., eds.), Springer-Verlag, 1986, pp. 100–122.
  45. Brandt, A., Ron, D. and Amit, D.J., Multi-level approaches to discrete-state and stochastic problems, in Multigrid Methods, II (Hackbusch, W. and Trottenberg, U., eds.), Springer-Verlag, 1986, pp. 66–99.
  46. Bai, D. and Brandt, A., Local mesh refinement multilevel techniques, SIAM J. Sci. Stat. Comp. 8 (1987) 109–134.
  47. Proc. ICM-86 (Int. Congr. of Mathematicians, Berkeley, CA,August 1986), 1987, pp. 1319–1334.
  48. Brandt, A. and Lanza, A., Multigrid in general relativity:I. Schwarzschild spacetime, Class. Quantum Grav. 5 (1988)713–732.
  49. Brandt, A., Multilevel computations: Review and recent developments, in Multigrid Methods: Theory, Applications and Supercomputing (McCormick, S.F., ed.), Marcel-Dekker, 1988, pp. 35–62.
  50. Ruge, J. and Brandt, A., A multigrid approach for elasticity problems on “thin” domains, in Multigrid Methods: Theory, Applications and Supercomputing (McCormick, S.F., ed.), Marcel-Dekker,1988, pp. 541–555.
  51. Kandel, D., Domany, E., Ron, D., Brandt A. and Loh, E., Jr., Simulations without critical slowing down, Phys. Rev. Lett. 60 (1988) 1591–1594.
  52. Brandt, A., Rigorous local mode analysis of multigrid, in Preliminary Proc. 4th Copper Mountain Conf. on Multigrid Methods, Copper Mountain, Colorado, April 1989.
  53. Kandel, D., Domany, E. and Brandt, A., Simulations without critical slowing down — Ising and 3-state Potts models, Phys. Rev. B 40 (1989) 330–344.
  54. Brandt, A., The Weizmann Institute Research in Multilevel Computation: 1988 Report, in Proc. 4th Copper Mountain Conf. on Multigrid Methods (Mandel, J. et al, eds.), SIAM, 1989,pp. 13–53.
  55. Brandt, A. and Lubrecht, A.A., Multilevel matrix multiplication and fast solution of integral equations, J. Comp. Phys. 90 (1990) 348–370.
  56. Ben-Av, R., Brandt, A. and Solomon, S., The fermiomic matrix, instantons, zero modes and multigrid, Nucl. Phys. B 329 (1990) 193.
  57. Brandt, A., The scope of multiresolution iterative computations,SIAM News 23 (1990) 8–9.
  58. Brandt, A. and Yavneh, I., Inadequacy of first-order upwind difference scheme for some recirculating flows, J. Comp. Phys.93 (1991) 128–143.
  59. Brandt, A., Multilevel computations of integral transforms and particle interactions with oscillatory kernels, Comp. Phys. Comm.65 (1991) 24–38.
  60. Ben-Av, R., Brandt, A., Harmatz, M., Katznelson, E., Lauwers, P.G., Solomon, S. and Wolowesky, K., Fermion simulation using parallel transported multigrid, Phys. Lett. B 253 (1991) 185.
  61. Balsara, D.S., and Brandt, A., Multilevel methods for fast solution of N-body and hybrid systems, in Multigrid Methods, III (Hackbusch, W. and Trottenberg, U., eds.), Birkhäuser Verlag, Basel,1991, pp. 131–142.
  62. Mikulinsky, V. and Brandt, A., Multigrid treatment of free boundary conditions, in Multigrid Methods: Special Topics and Applications, II (Hackbusch, W. and Trottenberg, U., eds.), GMD-Studien Nr. 189, 1991, pp. 940–949.
  63. Brandt, A. and Greenwald, J., Parabolic multigrid revisited, in Multigrid Methods, III (Hackbusch, W. and Trottenberg, U., eds.), Birkhäuser Verlag, Basel, 1991, pp. 143–154.
  64. Ruge, J., Brandt, A., McWilliams, J. and Milliff, R., Multigrid methods applied to turbulent flow problems, in Multigrid Methods,III (Hackbusch, W. and Trottenberg, U., eds.), Birkhäuser Verlag, Basel, 1991, pp. 91–103.
  65. Harmatz, M. and Lauwers, P.G. with Ben-Av, R., Brandt, A., Katznelson, E., Solomon, S. and Wolowesky, K., Parallel-transported multigrid and its application to the Schwinger model, Nucl. Phys. B (Proc. Suppl.) 20 (1991).
  66. Brandt, A. and Yavneh, I., Improved coarse-grid correction for high-Reynolds flows, in Proc. 5th Copper Mountain Conf. on Multigrid Methods, Copper Mountain, Colorado, April, 1991.
  67. Brandt, A. and Yavneh, I., On multigrid solution of high-Reynolds incompressible entering flows, J. Comp. Phys. 101 (1992)151–164.
  68. Brandt, A., Multiscale computational methods: research activities,in Proc. 1991 Hang Zhou International Conf. on Scientific Computation (Chan, T. and Shi, Z.-C., eds.), World Scientific Publishing Co., Singapore, 1992, pp. 1–7.
  69. Brandt, A., Multigrid methods in lattice field computations, Nucl. Phys. B (Proc. Suppl.) 26 (1992) 137–180.
  70. Brandt, A. and Yavneh, I., Accelerated multigrid convergence and high-Reynolds recirculating flows, SIAM J. Sci. Comp. 14 (1993) 607–626.
  71. Sidilkover, D. and Brandt, A., Multigrid solution to steady-state two-dimensional conservation laws, SIAM J. Num. Anal. 30 (1993), 249.
  72. Brandt, A., Rigorous quantitative analysis of multigrid: I. Constant coefficients two level cycle with L2 norm, SIAM J. Num. Anal. 31 (1994) 1695–1730.
  73. Brandt, A., Galun, M., and Ron, D., Optimal multigrid algorithms for calculating thermodynamic limits, J. Stat. Phys. 74 (1994) 313–348.
  74. Brandt, A. and Diskin, B., Multigrid solvers on decomposed domains, in Domain Decomposition Methods in Science and Engineering (A. Quarteroni, J. Periaux, Yu. A. Kuznetsov and O. Widlund, eds.)Contemp. Math., V. 157, American Mathematical Society,1994, pp. 135–155.
  75. Brandt, A. and Mikulinsky, V., Recombining iterants in multigrid algorithms and problems with small islands, SIAM J. Sci. Comp.16 (1995) 20–28.
  76. Bates, J.R., Li, Y., Brandt, A., McCormick, S.F. and Ruge, J.,A global shallow water numerical model based on the semi-Lagrangian advection of potential vorticity, Quart. J. Roy. Met. Soc.121 (1995) 1981–2005.
  77. Adler, J., Brandt, A., Janke, W. and Shmulyian, S., Three state potts antiferromagnet on the triangular lattice, J. Phys. A:Math. Gen. 28 (1995) 5117–5129.
  78. Brandt, A. and Venner, C.H., Multilevel evaluation of integral transforms on adaptive grids. Multigrid Methods V, Lecture Notesin Computational Science and Engineering 3 (W. Hackbusch and G. Wittum, eds.), Springer Verlag, Berlin, (1999) pp. 20–44.
  79. Brandt, A. and Dym, J., Fast robust discontinuity detection using multiple scales.
  80. Brandt, A. and Zaslavsky, L.Y., Multiscale algorithm for atmospheric data assimilation, SIAM J. Sci. Comp., Vol. 18 (1997), No. 3.
  81. Brandt, A. and Dym, J., Effective boundary treatment for the biharmonic Dirichlet problem, in Proc. Seventh Copper Mountain Conference on Multigrid Methods (N.D. Melson et al, eds.) NASA Conference Publication 3339 (1996) 97–108.
  82. Ruge, J.W., Li, Y., McCormick, S., Brandt, A. and Bates, J.R., A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based shallow-water model on the sphere, SIAM J. Sci. Comp.,21 (2000) 2381–2399.
  83. Schlick, T. and Brandt, A., A multigrid tutorial with application to molecular dynamics (a report on a workshop), IEEE Computational Science and Engineering, 3 (1996) 78–83.
  84. Brandt, A. and Diskin, B., Multigrid solvers for non-aligned sonic flows: the constant coefficient case, Computer & Fluids 28 (1999) 511–549.
  85. Brandt, A. and Galun, M., Optimal multigrid algorithm for the massive Gaussian model and path integrals, J. Stat. Phys.,82 (1996) 1503–1518.
  86. Yavneh, I., Venner, C.H. and Brandt, A., Fast multigrid solution of the advection problem with closed characteristics, SIAM J. Sci. Comp. 19 (1998) 111–125.
  87. Brandt, A. and Galun, M., Optimal multigrid algorithms for variable-coupling isotropic Gaussian models, J. Stat. Phys. 88 (1997) 637–664.
  88. Sharon, E., Brandt, A. and Basri, R., Completion energies and scale. IEEE Conference on Computer Vision and Pattern Recognition (CVPR–97), pp. 884–890, Puerto Rico, 1997. IEEE Trans. on Pattern Analysis and Machine Intelligence 22 (2000) 1117–1131.
  89. Brandt, A., The Gauss Center Research in Scientific Computation, Electronic Trans. Num. An. 6 (1997), 1–34.
  90. Brandt, A. and Livshits, I., Wave-ray multigrid method for standing wave equations, Electronic Trans. Num. An. 6 (1997), 162–181.
  91. Brandt, A. and Venner, C.H., Multilevel evaluation of integral transforms with asymptotically smooth kernels, SIAM J. Sci. Comp. 19 (1998), 468–492.
  92. Brandt, A., Barriers to Achieving Textbook Multigrid Efficiency in CFD, ICASE Interim Report No. 32, NASA/CR-1998-207647. Appears as Appendix C in the textbook Multigrid, by U. Trottenberg, C.W. Oosterleeand A. Schüller, Academic Press, London, 2000.
  93. Brandt, A. and Dym, J., Fast computation of multiple line integrals, SIAM J. Sci. Comp. 20 (1999) 1417–1429.
  94. Brandt, A., Israeli, M., Yavneh, I. and Siegal, A., Multigrid solution of an elliptic boundary-value problem with integral constraints, SIAM J. Sci. Comp. 21 (2000) 1357–1369.
  95. Brandt, A. and Diskin, B., Multigrid solvers for non-aligned sonic flows, SIAM J. Sci. Comp. 21 (1999) 473–501.
  96. Brandt, A., Mann, J., Brodski, M. and Galun, M., A fast and accurate multilevel inversion of the Radon transform, SIAM J. Appl. Math.60 (1999) 437–462.
  97. Bai, D. and Brandt, A., Multiscale computation of molecular systems, in Proc. AFOSR Grantees and Contractors Meeting in Computational and Physical Mathematics, Wright-Patterson AFB, Ohio, July 20–22, 1998.
  98. Li, Y., Ruge, J., Bates, J.R. and Brandt, A., A proposed adiabatic formulation of three-dimensional global atmospheric models based on potential vorticity. Tellus 52A (2000) 129–139.
  99. Sharon, E., Brandt, A. and Basri, R., Fast multiscale image segmentation. Proc. IEEE Conf. on Computer Vision and Pattern Recognition, South Carolina, 2000, pp. 70-77.
  100. Brandt, A. and Ron, D., Renormalization multigrid (RMG): Statistically optimal renormalization group flow and coarse-to-fine Monte Carlo acceleration, J. Stat. Phys. 102 (2001) 231–257.
  101. Brandt, A., General highly accurate algebraic coarsening schemes. Electronic Trans. Num. Anal. 10 (2000) 1–20.
  102. Thomas, J.L., Diskin, B. and Brandt, A., Distributed relaxation multigrid and defect correction applied to the compressible Navier Stokes equations, AIAA paper 99–3334, Proc. 14th AIAA CFDConference, Norfolk, VA, July, 1999.
  103. Thomas, J.L., Diskin, B. and Brandt, A., Textbook multigridefficiency for the incompressible Navier-Stokes equations: High Reynolds number wakes and boundary layers. ICASE Report No. 99–51(1999). Computers and Fluids, 30 (7–8), (2001) 853–874.
  104. Brandt, A., Bernholc, J. and Binder, K. (Eds.), Multiscale Computational Methods in Chemistry and Physics. NATO Science Series: Computer and System Sciences, Vol. 177, IOS Press, Amsterdam (2001).
  105. Bai, D. and Brandt, A., Multiscale computation of polymer models. In [108],pp. 250–266.
  106. Sandak, B. and Brandt, A., Multiscale fast summation of long rangecharge and dipolar interactions. In [108], pp. 6–31. Also: J. Comp. Chem., 22 (2001), 717–731.
  107. Livne, O. and Brandt, A., O(N log N) multilevel calculation of N eigenfunctions. In [108], pp. 112–136.
  108. Brandt, A. and Iliyn, V., Multilevel approach in statistical physics of liquids. In [108], pp. 187–197.
  109. Brandt, A. and Galun, M., Fast and accurate multiscale methods for image reconstruction. In [108], pp. 360–362.
  110. Brandt, A. and Ron, D., Renormalization multigrid (RMG): coarse-to-fine Monte Carlo acceleration and optimal derivation of macroscopic descriptions. In [108], pp. 163–186.
  111. Thomas, J.L., Diskin, B., Brandt, A. and South, J.C. Jr., Generalframework for achieving textbook multigrid efficiency: quasi-1-DEuler example. In: Frontiers of Computational Fluid Dynamics –- 2002(D.A. Caughey and M.M. Hafez, eds.), World Scientific Publishing Company, Singapore, pp. 61–80.
  112. Brandt, A. and Livshits, I., Accuracy properties of the multigrid algorithm for Helmholz equations. SIAM J. Sci. Computing, 28 (4), (2006) 1228–1251.
  113. Livne, O. and Brandt, A., N roots of secular equation in O(N) operations, submitted to SIAM J. Matrix Anal. Appl., 24 (2002) 439–453.
  114. Brandt, A., Multiscale scientific computation: review 2001. In Barth, T.J., Chan, T.F. and Haimes, R. (eds.): Multiscale and Multiresolution Methods: Theory and Applications, Springer Verlag, Heidelberg, 2001, pp. 1–96. Available in www.wisdom.weizmann.ac.il/~achi/review00.ps
  115. Brandt, A., Diskin, B. and Thomas, J.L., Textbook multigrid efficiency for computational fluid dynamics simulations, AIAA paper 2001–2570,15th AIAA Computational Fluid Dynamics Conference, Anaheim, CA,June 11–14, 2001.
  116. Sharon, E., Brandt, A. and Basri, R., Segmentation and boundary detection using multiscale intensity measurements, Proc. IEEEConf. on Computer Vision and Pattern Recognition, Hawaii, 2001.
  117. Livne, O.E., Brandt, A. and Boag, A., Multigrid Analysis of Scattering by Large Planar Structures. Micro. Opt. Tech. Let. 32 (2002) 454–458.
  118. Brandt, A. and Ilyin, V., Multilevel Monte Carlo methods for studyinglarge-scale phenomena in fluids. In Proc. Conf. Physics of LiquidMatter: Modern Problems (Kiev, Ukraine, Sept. 14–19, 2001); J. ofMolecular Liquids, 105 (2003) 253–256.
  119. Livne, O.E. and Brandt, A., Multiscale Eigenbasis Calculations: NEigenfunctions in O(N log N). In Barth, T.J., Chan, T.F. and Haimes, R. (eds.): Multiscale and Multiresolution Methods: Theory and Applications, Lecture Notes in Computational Science and Engineering, Springer-Verlag, Heidelberg, 20 (2001) 347–358.
  120. Livne, O.E. and Brandt, A. Local Mode Analysis of Multicolor and Composite Relaxation Schemes, Computers and Math. withApplications, 47 (2004) 301–317.
  121. Thomas, J.L., Diskin, B. and Brandt, A., Textbook multigrid for fluid simulations, Annual Reviews in Fluid Mehanics 35 (2003) 317–340.
  122. Ron, D., Swendsen, R.H. and Brandt, A., Computer simulations at thefixed point using an inverse renormalization group transformation,Physica A 346 (2005) 387–399.
  123. Livne, O.E., Brandt, A. and Boag, A., Multigrid analysis by largequasi-planar structures, Project 2721 – Final Report, Defense Directorate for Research and Development, March 2002.
  124. Ron, D., Swendsen, R.H. and Brandt, A., Inverse Monte Carlo renormalization group transformations for critical phenomena, Phys. Rev. Lett.,89 (2002), #27.
  125. Brandt, A. and Ron, D., Multigrid solvers and Multilevel Optimization Strategies. In: Multilevel Optimization and VLSICAD, (J. Cong andJ.R. Shinnerl, eds.), Kluwer Academic Publishers, Boston, 2003, pp. 1–69.
  126. Boag, A., Michielssen, E. and Brandt, A., Non uniform polar gridalgorithm for fast field evaluation, IEEE Antennas and Wireless Propagation Lett. 1 (2002) 142–145.
  127. Brandt, A., Multiscale computation: from fast solvers to systematic upscaling. In: Computational Fluid and Solid Mechanics (K.J. Bathe,ed.), Elsevier (2003) 1871–1873.
  128. Brandt, A. and Livshits, I., Remarks on the wave-ray multigrid solvers for Helmholtz equations. In: Computational Fluid and Solid Mechanics (K.J. Bathe, ed.), Elsevier (2003) 1874.
  129. Safro, I., Ron, D. and Brandt, A., Graph minimum linear arrangement by multilevel weighted edge contractions. J. of Algorithms,60 (2006) 24–41.
  130. Galun, M., Sharon, E., Basri, R., and Brandt, A., Texture segmentation by multiscale aggregation of filter responses and shape elements,IEEE Int. Conf. on Computer Vision, Nice, ICCV–03 Proceedings(2003) 716–723.
  131. Gorelick, L., Galun, M., Sharon, E., Basri, R. and Brandt, A., “Shape Representation and Classification Using the Poisson Equation.” CVPR–04Proceedings 61–67, 2004. IEEE Trans. Pattern Anal. Machine Intelligence 28 (12), Dec. (2006).
  132. Garb, Kh., Brandt, A. and Boag, A., Directional aggregation approach for fast field evaluation, AP-S/USRI 2004 paper #1484, 2004 IEEE AP-S International Symposium on Antennas and Propagation, Monterey, California,June 20–26.
  133. Brandt, A. and Gandlin, R., Multigrid for Atmospheric Data Assimilation Analysis. In: Hyperbolic Problems: Theory, Numerics, Applications (T.Y. Hou and E. Tadmor, eds.), Springer 2003, pp. 369–376.
  134. Brandt, A. and Ilyin, V., Multilevel Monte Carlo method for simulations of fluids, condmat/0304686, 30 Apr. 2003, 12pp.
  135. Gandlin, R. and Brandt, A., Two multigrid algorithms for an inverse problem in electrical impedance tomography, Proc. 2003 Copper MountainConf. Multigrid Methods.
  136. Brandt, A., Systematic multiscaling in materials science computations, Proc. 2nd Int. Conf. on Multiscale Materials Modeling, Oct. 2004.
  137. Safro, I., Ron, D. and Brandt, A., Multilevel algorithm for the minimum 2-sum problem. J. Graph Algorithms and Applications, Vol. 10, no. 2 (2006) 237–258.
  138. Kushnir, D., Galun, M. and Brandt, A., Fast multiscale clustering and manifold identification, J. Pattern Recognition, 39 (2006) 1876–1891.
  139. Sharon, E., Galun, M., Sharon, D., Basri, R. and Brandt, A., Hierarchy and adaptivity in segmenting visual scenes, Nature, 442 (2006) 810–813.
  140. Brandt, A., Multiscale solvers and systematic upscaling in computational physics, Computer Physics Communication, 169 (2005) 438–441.
  141. Axelrod-Ballin, A., Eyal, E., Galun, M., Furman-Haran, E., Gomori, M.J., Basri, R., Degani, H. and Brandt, A., 3D automatic segmentation of the rat uterus in MRI, The International Society for Optical Engineering Conf. on Medical Imaging, San Diego, SPIE-06 (2006).
  142. Brandt, A., Ilyin, V., Makedonska, N. and Suwan, I. Multilevel summation and Monte Carlo simulations, J. Molecular Liquids127 (2006) 37–39.
  143. Schumacher, J. Kushnir, D., Brandt, A., Sreenivasan, K.R. and Zilken, H. Statistics and geometry in high-Schmidt number scalarmixing, iTi Turbulence Conference Proc., 2005.
  144. Kushnir, D., Schumacher, J. and Brandt, A., Geometry of intensive scalar mixing events in turbulence, Phys. Rev. Lett., 97 (2006), letter 124502.
  145. Axelrod-Ballin, A., Galun, M., Gomori, M.J., Filippi, M., Valsasina, P., Basri, R. and Brandt, A., Integrated segmentation and classification approach applied to multiple sclerosis analysis, IEEE Conf. on Computer Vision and Pattern Recognition, New York, CVPR–06, I:1122-1129, 2006.
  146. Eyal, E., Akselrod-Ballin, A., Galun, M., Furman-Haran, E., Basri, R., Brandt, A. and Degani, H., Dynamic monitoring of the rat uterus using 3D automatic segmentation, Conf. of the International Society forMagnetic Resonance in Medicine, Seattle, IMSRM–06 (2006).
  147. Akselrod-Ballin, A., Galun, M., Gomori, M.J., Basri, R., Brandt, A., Atlas guided identification of brain structures by combining 3D segmentation and SVM classification, Medical Image Computing and Computer-Assisted Intervention, Copenhagen, MICCAI–06, 2006.
  148. Brandt, A., Iliev, O. and Willems, J., A domain decomposition approach for calculating the graph corresponding to a fibrous geometry,2008. Proc. Domain Decomposition, 18 (2008).
  149. Alpert, S., Galun, M., Basri, R. and Brandt, A., Image segmentation by probabilistic bottom-up aggregation and cue integration, PAMI (IEEE J. on Pattern Anal. & Machine Intelligence) 34 (2012) 315–327.
  150. Akselrod-Ballin, A., Galun, M, Gomory, M.J., Basri, R. and Brandt, A., Prior knowledge driven multiscale segmentation of brain MRI, Medical Image Computing and Computer-Assisted Intervention, Brisbane, Australia,MICCAI-007 (2007).
  151. Galun, M., Basri, R. and Brandt, A., Multiscale edge detection and fiber enhancement using differences of oriented means, IEEE International Conf. on Computer Vision, Rio De Janeiro, ICCV–07(2007).
  152. Brandt, A., Principles of systematic upscaling, in Bridging the Scales in Science and Engineering, J. Fish (Ed.), Oxford University Press, 2010, pp. 193–215.
  153. Kushnir, D., Galun, M. and Brandt, A., Efficient multilevel eigensolvers with applications to data analysis tasks, IEEE Trans. Pattern Anal. and Machine Intelligence 32(8):(1377-1391) (2010).
  154. Safro, I., Ron, D. and Brandt, A., Multilevel algorithms for linear ordering problems, Journal of Experimental Algorithmics 13:1.4–1.20, 2008.
  155. Safro, I., Ron, D. and Brandt, A., Fast multilevel algorithms for linear ordering problems. In: Computational Optimization:New Research Developments, Nova Scotia Publishers, pp. 313-324, (2010).
  156. Akselrod-Ballin, A., Galun, M., Gomori, J.M., Filippi, M., Valsasina, P., Basri, R. and Brandt, A., Integrated segmentation and classification approach applied to multiple sclerosis analysis, IEEE Transactions on Biomedical Imaging 56 (10), 2461–2469,2009.
  157. Goldschmidt, Y., Galun, M., Sharon, E., Basri, R. and Brandt, A., Fast multiscale clustering by integrating collective features,submitted to Neural Information Processing Systems Conference,NIPS–07.
  158. Zhu, Y., Sifakis, E., Teran, J. and Brandt, A., An efficient parallelizable multigrid framework for the simulation of elastic solids. ACM Transactions on Graphics (accepted), 2010.
  159. Ron, D., Safro, I. and Brandt, A., A fast multigrid algorithm for energy minimization under planar density constraints. Multiscale Modeling and Simulation (SIAM) 8(5): 1599-1620, 2010.
  160. Adams, M.F., Samtaney, R. and Brandt, A., Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics. J. Comp. Phys. Vol. 229, No. 18, 6208-6219, (2010).
  161. Ron, D., Safro, R. and Brandt, A., Relaxation based coarsening and multiscale graph organization. Multiscale Modeling & Simulation 9 (2011) 407–423.
  162. Brandt, A., Brannick, J., Kahl, K. and Livshits, I., Bootstrap AMG, SIAM J. Sci. Comput. 33 (2011) 612–632.
  163. Livne, O.E. and Brandt, A.E., MuST: The Multilevel Sinc Transform.
  164. Alpert, S., Galun, M., Brandt, A. and Basri, R., Image segmentation by probabilistic bottom-up aggregation and cue integration. IEEE Trans. Pattern Anal. and Machine Intelligence, (2010).
  165. Brandt, A. and Livne, O., Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Revised Edition. Society for Industrial and Applied Mathematics: Philadelphia, 2011.
  166. Bolten, M., Brandt, A., Brannick, J., Frommer, A., Kahl, K. and Livshits, I. A bootstrap algebraic multilevel method for Markov chains. To appear in SIAM J. Sci. Comput. (2011).
  167. Livne, O. and Brandt, A. Lean Algebraic Multigrid (LAMG): FastGraph Laplacian Solver. SIAM J. Sci. Comp. 34 (4), B499-B522(2012).
  168. Ron, D., Brandt, A. and Swendsen, R.H. Surprising convergence of the Monte Carlo renormalization group for the three-dimensional Ising model. Submitted toPhys. Rev. E95, 053305, May 2017.

Patents