A Bibliography of Publications of Achi Brandt

Achi Brandt

Dept. of Applied Mathematics and Computer Science

The Weizmann Institute of Science Rehovot Israel

Tel: ?n/a? FAX: ?n/a?

E-mail: mabrandt@weizmann.weizmann.ac.il (Internet)

19 September 2023 Version 1.44

Abstract

This bibliography records publications of Achi Brandt.

Title word cross-reference

2 [SRB06b]. L_{2} [Bra94]. N [BB91, LB02a, LB02b]. O(N) [LB02b]. O(N log N) [LB02a].

-body [BB91]. -Norm [Bra94]. -sum [SRB06b].

1977 [Ric77].

205 [BB83].

3-state [KDB89].

Accelerated [BY93]. Acceleration [BR01]. Accuracy [LB06]. Accurate [BMBG99, BMBG00, Bra00]. achieving [TDBS02]. activities [Bra92b]. Adaptive [Bra77b, Bra73a, Bra76, Bra77a, Bra79, Bra80b, Bra80a, BV98a]. advection [BLB^{+}95, YVB98]. Algebraic [BBB^{+}11, BMR82, BMR84, Bra86a, BBKL15b, LB12, Bra00, BBKL15a]. Algorithm [RSB10, BZ97, LB06, SRB06b]. Algorithms [BG97, BI78, BC83, BGR94, BM95, BG96, SRB08]. AMG [BMR82, BMR84, BBKL11]. Analysis [Bra94, Bra89, BG03, LB04]. Andersen [Bra61]. anisotropic [BBKL15b]. antiferromagnet [ABJS95a, ABJS95b]. Application [SB77, BMR82, HLBA^{+}91]. Applications [Bra84c, SB96, BL11]. applied [RBMM91a]. approach [BG69, BIW09, RB88]. approaches [BRA86b, Bra87]. April [MC92]. arising [BC83]. arrangement [SRB06a]. assignment [BI71]. assimilation [BZ97, BG03]. Asymptotic [BG69]. asymptotically [BV98b]. atmospheric [BZ97, BG03]. August [Gle87]. automatic [BMR82].

Band [YYD^{+}12]. Based [RSB11, BLB^{+}95, RLM^{+}00]. Berkeley [Gle87]. body [BB91]. Bootstrap [BBB^{+}11, BBKL11, BBKL15a]. Boundary [Bra77b, BIYS00, Bra73a, Bra80c, BC83, BMxx, MB91]. Boundary-Value [Bra77b, BIYS00].

calculating [BGR94, BIW09]. calculation [BD99a]. calculations [LB02a, SB77]. Carlo [BR01]. case [Bra86a]. categories [BI71]. CDC [BB83]. Center [Ric77, Bra97]. Chains [BBB^{+}11]. channel [BG66]. characteristics [YVB98]. closed [YVB98]. Coarse [BR01, BY91a]. coarse-grid [BY91a]. Coarse-to-Fine [BR01]. Coarsening [RSB11, Bra00]. codes [BDR80]. Coefficients [Bra94, ABDP81]. Colorado [MC92]. combinatorial [Bra61]. complementarity [BC83]. composite [LB04]. compressible [Bra82b]. Computation [Bra90b, Bra97, Bra02]. computational [Bra92b, Bra05]. computations [Bra80a, BMR82, Bra88, Bra90a, Bra91, Bra92a]. computers [Bra81b]. conditions [BMxx, MB91]. conducted [Ric77]. Conference [MMD^{+}89, MC92]. Conferences [SB96]. Congress [Gle87]. Conservation [SB93]. Constant [Bra94]. Constraints [BIYS00, RSB10]. contractions [SRB06a]. convergence [BY93]. Copper [MMD^{+}89, MC92]. correction [BY91a]. corresponding [BIW09]. Coupling [BG97]. critical [KDR^{+}88, KDB89]. Cyber [BB83]. Cycle [Bra94].

data [BZ97, BG03, BHD^{+}71]. decomposed [BD92, BD94]. decomposition [BIW09]. Density [RSB10]. developments [Bra88]. Difference [Bra66, Bra69a, Bra73b, BY90, BY91b]. Differential [BMR83, Bra69a, Bra69b, Bra77a]. diffusion [ABDP81, BBKL15b]. Dimensional [SB93, TDBS02]. discontinuous [ABDP81]. discrete [BRA86b]. discrete-state [BRA86b]. distance [BBKL15b]. domain [BIW09]. domains [BD92, BD94, RB88]. down [KDR^{+}88, KDB89]. Dynamics [Bra84c, Bra80a, BL11, SB96].

edge [SRB06a]. efficiency [ASB10, TDBS02, TDB03]. efficient [ZSTB10]. eigenbasis [LB02a]. eigenfunctions [LB02a]. Eigenproblems [BMR83]. elastic [ZSTB10]. elasticity [RB88]. element [Bra80a]. elements [Bra80b]. Elliptic [BIYS00, Bra69a, BD79, Bra81a, BFT85, BT85]. Energy [RSB10]. entering [BY92, Bra92c]. equation [ABDP81, LB02b]. Equations [Bra66, Bra69a, Bra69b, Bra77a, Bra82b, BMR84, BL90a, BL90b, BL97, LB06]. Estimates [Bra66, Bra69a, Bra69b]. Euler [TDBS02]. evaluation [BV98b, BV98a]. example [TDBS02]. Experimental [BHD^{+}71].

Fast [BI78, BMBG99, BD99a, LB12, RSB10, YVB98, BB91, Bra73a, Bra80c, BL90a, BL90b, BMBG00]. Fermion [BABH^{+}91]. fermionic [BABS90]. fibrous [BIW09]. field [Bra92a]. Fifth [MC92]. Fine [BR01]. finite [Bra69a, Bra73b, Bra80b, Bra80a]. finite-difference [Bra69a, Bra73b]. finite-element [Bra80a]. first [BY90, BY91b]. first-order [BY90, BY91b]. fission [BK69]. Flow [BR01, ABBG70, BG66, BD79, RBMM91a, RBMM91b, SB77]. flows [BG69, BY90, BY91a, BY91b, BY92, Bra92c, BY93, BD99b]. Fluid [Bra84c, Bra80a, BL11, TDB03]. Fourth [MMD^{+}89]. framework [TDBS02]. free [BC83, MB91]. fully [ASB10]. Functions [YYD^{+}12].

Gauss [Bra97]. Gaussian [BG96, BG97]. General [Bra00, TDBS02, BO84, BL88]. generalization [Bra61]. Generalized [Bra73b]. geodetic [BMR82]. geometry [BIW09]. global [BLB^{+}95]. Graph [LB12, RSB11, SRB06a, BIW09]. grid [ABDP81, Bra76, BD79, Bra81b, Bra81a, Bra82b, BO84, BY91a, SB77]. GRIDPACK [BO84]. grids [BV98a]. Group [BR01]. Guide [Bra84c, BL11].

Hartmann [BG69]. Helmholtz [LB06]. high [BY91a, BY92, Bra92c, BY93, ZSTB10]. high-resolution [ZSTB10]. high-Reynolds [BY91a, BY92, Bra92c, BY93]. highly [BMxx, Bra00]. hybrid [BB91]. hydrodynamics [BDR80].

ideas [Bra77a]. II [BHD^{+}71]. III [Ric77]. implicit [ASB10, BDR80]. Improved [BFT85, BY91a]. Inadequacy [BY90, BY91b]. incompressible [BY92, Bra92c]. indefinite [BT86]. Infiltration [BBDBA71, BHD^{+}71]. inlet [BG66]. instantons [BABS90]. Institute [Bra90b]. Integral [BIYS00, BL90a, BL90b, Bra91, BV98b, BV98a]. integrals [BG96, BD99a]. interactions [Bra91]. Interior [Bra69a, Bra69b]. International [Gle87]. Introduction [Bra85]. Introductory [Bra82a]. Inversion [BMBG99, BMBG00]. Ising [KDB89]. islands [BM95]. Isotropic [BG97]. issue [MC92]. iterants [BM95]. iterative [Bra90a].

job [BI71].

kernels [Bra91, BV98b].

Lagrangian [BLB^{+}95, RLM^{+}00]. LAMG [LB12]. Laplacian [LB12]. large [Bra87]. lattice [ABJS95a, ABJS95b, Bra92a]. Laws [SB93]. Lean [LB12]. Level [Bra77b, Bra84a, Bra94, YYD^{+}12, Bra73a, Bra76, Bra77a, Bra79, Bra80b, Bra80a, Bra84b, BRA86b, Bra87, SB77]. Levels [Bra85]. limits [BGR94]. line [BD99a]. Linear [LB12, BC83, SRB06a, SRB08]. Local [BB87, Bra84a, Bra84b, LB04, Bra73b, Bra89]. long [BI78]. low [ABBG70].

Madison [Ric77]. Magnetohydrodynamic [BG66]. magnetohydrodynamics [ASB10]. March [Ric77]. Markov [BBB^{+}11]. massive [BG96]. Mathematical [BBDBA71, Ric77]. Mathematicians [Gle87]. Mathematics [Ric77]. matrix [BABS90, BMR84, BL90a, BL90b]. maximum [Bra69a, Bra69b, Bra73b]. mesh [BB87]. Method [BBB^{+}11, Bra76, BDR80, BT86, BL97, SB77, ZSTB10]. Methods [BMR83, MMD^{+}89, ABDP81, BB91, Bra80b, Bra82a, BFT85, Bra92b, Bra92a, MC92, RBMM91a, RBMM91b]. Mill [Bra84a, Bra84b]. Minimization [RSB10]. minimum [SRB06a, SRB06b]. MLAT [Bra73a, Bra76, Bra77a, Bra79]. mode [Bra89, LB04]. model [BLB^{+}95, BG96, HLBA^{+}91, RLM^{+}00]. Models [BG97, BBDBA71, KDB89]. modes [BABS90]. Molecular [SB96]. Monte [BR01]. Mountain [MMD^{+}89, MC92]. Multi [Bra73a, Bra76, Bra77b, Bra77a, BD79, Bra79, Bra80b, Bra80a, Bra81b, Bra81a, Bra82b, Bra84a, BRA86b, Bra87, ABDP81, Bra84b, SB77]. Multi-grid [BD79, Bra81b, Bra81a, Bra82b, ABDP81, Bra76]. Multi-Level [Bra77b, Bra84a, Bra73a, Bra76, Bra77a, Bra79, Bra80b, Bra80a, BRA86b, Bra87, Bra84b, SB77]. multicolor [LB04]. Multigrid [BC83, BMR83, Bra84c, BT85, BT86, BL88, Bra92a, BD92, BD94, Bra94, BG97, BD99b, BMxx, BIYS00, BR01, BG03, BR03, BL11, LB12, MMD^{+}89, MB91, RSB10, RBMM91a, RBMM91b, SB96, SB93, TOS01, YYD^{+}12, ASB10, BB83, BABS90, BABH^{+}91, BDR80, BMR82, Bra82a, BMR84, BFT85, Bra86a, Bra89, BG91, BY92, Bra92c, BY93, BGR94, BM95, BG96, BL97, BBKL15a, HLBA^{+}91, LB06, MC92, RB88, RLM^{+}00, TDBS02, TDB03, YVB98, ZSTB10]. Multilevel [BB91, BBB^{+}11, Bra88, BL90a, BL90b, Bra90b, Bra91, BV98b, BV98a, BMBG99, SRB08, BB87, BMBG00, BR03, BBKL15b, SRB06a, SRB06b, LB11]. multiple [BD99a]. multiplication [BL90a, BL90b]. multiresolution [Bra90a]. Multiscale [Bra92b, BZ97, Bra02, Bra05, LB02a, RSB11, Bra97]. MuT [LB11].

Narrow [YYD^{+}12]. Navier [Bra82b]. nearly [BT86]. non [Bra81a]. non-elliptic [Bra81a]. nonaligned [BD99b]. nonlinear [RLM^{+}00]. Norm [Bra94]. numbers [ABBG70]. Numerical [Bra80c, BLB^{+}95, Bra73a].

one [TDBS02]. one-dimensional [TDBS02]. open [BBKL15a]. operations [LB02b]. operators [Bra73b]. Optimal [BGR94, BG96, BG97, BR01]. optimization [BR03]. order [Bra69a, BY90, BY91b]. ordering [SRB08]. Organization [RSB11]. oscillating [BMxx]. oscillatory [Bra91]. outlook [BBKL15a].

Parabolic [BG91, Bra69b]. Parallel [Bra84a, HLBA^{+}91, BABH^{+}91, Bra81b, Bra84b]. Parallel-transported [HLBA^{+}91]. partial [Bra77a]. particle [BK69, Bra91]. path [BG96]. periodic [BFT85]. perturbation [Bra79, Bra81a]. physics [Bra05]. Planar [RSB10]. Poiseuille [BG69]. Poisson [BB83, Bra66]. potential [BLB^{+}95, RLM^{+}00]. Potts [ABJS95a, ABJS95b, KDB89]. predictions [BHD^{+}71]. principle [Bra69a, Bra69b].

Principles [Bra10, Bra73b]. Problem [BIYS00, BI71, SRB06b, YVB98]. Problems [Bra77b, Bra73a, BI78, BD79, Bra79, Bra80b, Bra80c, Bra81a, BC83, BFT85, BRA86b, BT86, Bra87, BM95, BMxx, BBKL15b, BBKL15a, RB88, RBMM91a, RBMM91b, SRB08]. Proceedings [Gle87, MMD^{+}89, Ric77]. Processing [Bra84a, Bra84b]. profiles [ABBG70]. programming [BO84]. properties [LB06].

Quantitative [Bra94]. quasi [BT85]. quasi-elliptic [BT85]. Quotients [Bra66].

Radon [BMBG99, BMBG00]. random [Bra61]. ray [BL97, LB06]. recirculating [BY90, BY91b, BY93]. recombining [BM95]. Reconstruction [YYD^{+}12]. refinement [BB87]. region [BG66]. relativity [BL88]. Relaxation [RSB11, LB04]. Relaxation-Based [RSB11]. remarks [Bra82a]. Renormalization [BR01]. Report [Bra90b, BBKL15a]. Research [Bra90b, Ric77, Bra92b, Bra97]. resistive [ASB10]. resolution [ZSTB10]. results [BBKL15b]. review [Bra88, Bra02]. revisited [BG91]. Reynolds [ABBG70, BY91a, BY92, Bra92c, BY93]. Rigorous [Bra89, Bra94]. RMG [BR01]. roots [LB02b].

scale [Bra87]. scales [Bra85]. Schauder [Bra69b]. schemes [BT85, BY90, BY91b, LB04]. Schwarzschild [BL88]. Schwinger [HLBA^{+}91]. scientific [Bra97, Bra02]. scope [Bra90a]. second [Bra69a]. secular [LB02b]. semi [BDR80, RLM^{+}00, BLB^{+}95]. semi-implicit [BDR80]. semi-Lagrangian [RLM^{+}00, BLB^{+}95]. Set [YYD^{+}12]. shallow [BLB^{+}95, RLM^{+}00]. shallow-water [BLB^{+}95, RLM^{+}00]. simulation [BABH^{+}91, ZSTB10].

Simulations [KDR^{+}88, KDB89, TDB03]. Sinc [LB11]. Single [BK69]. singular [Bra79, Bra81a, BT86]. singular-perturbation [Bra81a]. slightly [BT86]. slowing [KDR^{+}88, KDB89]. small [BM95]. smooth [BV98b]. software [Bra77a, Ric77]. solids [ZSTB10]. Solution [BIYS00, SB93, BB91, BMR82, BC83, BL90a, BL90b, BY92, Bra92c, YVB98]. Solutions [Bra66, Bra77b, Bra73a, BD79, Bra80c, Bra82b, BT85]. Solver [LB12, BB83, RLM^{+}00]. solvers [Bra81b, Bra81a, BD92, BD94, BD99b, BR03, Bra05]. some [BY90, BY91b]. sonic [BD99b]. source [BBDBA71, BHD^{+}71]. spacetime [BL88]. Sparre [Bra61]. sparse [BMR84]. Special [MC92]. spectral [BFT85]. sphere [RLM^{+}00]. stability [Bra80c]. standing [BL97]. State [SB93, ABJS95a, ABJS95b, Bra81a, Bra82b, BRA86b, KDB89]. Statistically [BR01]. status [BBKL15a]. Steady [SB93, Bra81a, Bra82b]. Steady-State [SB93, Bra81a, Bra82b]. stochastic [BRA86b]. Stokes [Bra82b]. straight [BG66]. strategies [BR03]. strongly [ABDP81]. sum [SRB06b]. sums [Bra61]. Surface [YYD^{+}12]. symmetric [Bra86a]. symposium [Ric77]. systematic [Bra05, Bra10]. systems [BB91].

technique [Bra73a, Bra76]. Techniques [Bra84c, BB87, Bra77a, Bra79, BL11]. Textbook [TDB03, ASB10, TDBS02]. theorem [Bra61]. theoretical [BHD^{+}71]. theory [BK69, Bra86a]. thermodynamic [BGR94]. thin [RB88]. Three [ABJS95a, ABJS95b, BI71]. Three-state [ABJS95a, ABJS95b]. Transform [BMBG99, BMBG00, LB11]. transforms [Bra91, BV98b, BV98a]. transonic [SB77]. transportation [BI78]. transported [BABH^{+}91, HLBA^{+}91]. treatment [BMxx, MB91]. triangular [ABJS95a, ABJS95b]. trickle [BBDBA71]. tricle [BHD^{+}71]. turbulent [RBMM91a, RBMM91b]. Tutorial [SB96]. Two [Bra94, SB93]. Two-Dimensional [SB93]. Two-Level [Bra94]. Type [Bra66].

unification [BO84]. University [Ric77]. upscaling [Bra05, Bra10]. upwind [BY90, BY91b]. using [BABH^{+}91].

Value [Bra77b, BIYS00, Bra73a, Bra80c]. Variable [BG97]. Variable-Coupling [BG97]. variables [Bra61]. Variational [Bra80b]. Vectorized [BB83]. Velocity [ABBG70]. via [Bra69a, Bra69b, YYD^{+}12]. vorticity [BLB^{+}95, RLM^{+}00]. vorticity-based [RLM^{+}00].

water [BLB^{+}95, RLM^{+}00]. Wave [BL97, LB06]. Wave-ray [BL97, LB06]. weighted [SRB06a]. Weizmann [Bra90b]. Wisconsin [Ric77]. without [KDR^{+}88, KDB89]. Workshops [SB96].

zero [BABS90].

References

Abarbanel:1970:VPF

[ABBG70] S. Abarbanel, S. Bennett, A. Brandt, and J. Gillis. Velocity profiles of flow at low Reynolds numbers. J. Appl. Mech, 37:2–4, 1970.

Alcouffe:1981:MGM

[ABDP81] R. E. Alcouffe, A. Brandt, J. E. Dendy, Jr., and J. W. Painter. The multi-grid methods for the diffusion equation with strongly discontinuous coefficients. SIAM J. Sci. Stat. Comput., 2(4):430– 454, ???? 1981. CODEN SI-JCD4. ISSN 0196-5204.

Adler:1995:TPA

[ABJS95a] J. Adler, A. Brandt, W. Janke, and S. Shmulyian. Threestate Potts antiferromagnet on the triangular lattice. Journal of Physics A (Mathematical and General), 28(18):5117– 5129, September 1995. CO-DEN JPHAC5. ISSN 0305-4470 (print), 1361-6447 (electronic).

Adler:1995:TSP

[ABJS95b] J. Adler, A. Brandt, W. Janke, and S. Shmulyian. Threestate Potts antiferromagnet on the triangular lattice. Journal of Physics A (Mathematical and General), 28(18):5117– 5129, 1995. CODEN JPHAC5. ISSN 0305-4470 (print), 1361-6447 (electronic).

Adams:2010:TTM

[ASB10] Mark F. Adams, Ravi Samtaney, and Achi Brandt. Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics. Journal of Computational Physics, 229(18): 6208–6219, September 1, 2010. CODEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/S0021999110002007.

Ben-Av:1991:FSU

[BABH^{+}91] R. Ben-Av, A. Brandt, M. Harmatz, E. Katznelson, P. G. Lauwers, S. Solomon, and K. Wolowesky. Fermion simulation using parallel transported multigrid. Phys. Lett. B, 253 (1–2):185–192, January 3, 1991. CODEN PYLBAJ. ISSN 0370-2693 (print), 1873-2445 (electronic).

Ben-Av:1990:FMI

[BABS90] R. Ben-Av, A. Brandt, and S. Solomon. The fermionic matrix, instantons, zero modes and multigrid. Nucl. Phys. B, B329: 193, 1990. CODEN NUPBBO. ISSN 0550-3213 (print), 1873-1562 (electronic).

Barkai:1983:VMP

[BB83] D. Barkai and A. Brandt. Vectorized multigrid Poisson solver for the CDC Cyber 205. Applied Math. Comp., 13(3–4):215– 227, November 1983. CODEN AMHCBQ. ISSN 0096-3003 (print), 1873-5649 (electronic).

Bai:1987:LMR

[BB87] D. Bai and A. Brandt. Local mesh refinement multilevel techniques. SIAM J. Sci. Stat. Comput., 8(2):109–134, March 1987. CODEN SIJCD4. ISSN 0196-5204.

Balsara:1991:MMF

[BB91] Dinshaw S. Balsara and Achi Brandt. Multilevel methods for fast solution of N-body and hybrid systems. In W. Hackbusch and U. Trottenberg, editors, Multigrid methods, III (Bonn, 1990), Internat. Ser. Numer. Math., pages 131–142 (of ix + 394). Birkhäuser Verlag, Basel, 1991. ISBN 0-8176-2632-8. LCCN QA377.C7628 1991.

Bolten:2011:BAM

[BBB^{+}11] Matthias Bolten, Achi Brandt, James Brannick, Andreas Frommer, Karsten Kahl, and Ira Livshits. A bootstrap algebraic multilevel method for Markov chains. SIAM Journal on Scientific Computing, 33(6): 3425–3446, ???? 2011. CO-DEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (elec-

tronic). URL http://epubs.
siam.org/sisc/resource/1/
sjoce3/v33/i6/p3425_s1.

Brandt:1971:ITS

[BBDBA71] A. Brandt, E. Bresler, N. Dinar, and I. Ben-Asher. Infiltration from a trickle source. I. mathematical models. Soil Sci. Soc. Amer. Proc., 35:675–682, 1971.

Brandt:2011:BA

[BBKL11] A. Brandt, J. Brannick, K. Kahl, and I. Livshits. Bootstrap AMG. SIAM Journal on Scientific Computing, 33(2): 612–632, ???? 2011. CO-DEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (elec-

tronic). URL http://epubs.
siam.org/sisc/resource/1/
sjoce3/v33/i2/p612_s1.

Brandt:2015:BAM

[BBKL15a] Achi Brandt, James Brannick, Karsten Kahl, and Ira Livshits. Bootstrap algebraic multigrid: status report, open problems, and outlook. Numerical Mathematics. Theory, Methods and Applications, 8(1):

112–135, 2015. ISSN 1004-8979 (print), 2079-7338 (electronic).

Brandt:2015:ADA

[BBKL15b] Achi Brandt, James Brannick, Karsten Kahl, and Irene Livshits. Algebraic distance for anisotropic diffusion problems: multilevel results. Electronic Transactions on Numerical Analysis (ETNA), 44:472– 496, 2015. ISSN 1068-9613 (print), 1097-4067 (electronic).

Brandt:1983:MAS

[BC83] Achi Brandt and Colin W. Cryer. Multigrid algorithms for the solution of linear complementarity problems arising from free boundary problems. SIAM J. Sci. Stat. Comput., 4(4):655– 684, December 1983. CODEN SIJCD4. ISSN 0196-5204.

Brandt:1979:MGS

[BD79] A. Brandt and N. Dinar. Multigrid solutions to elliptic flow problems. In S. Parter, editor, Numerical Methods for Partial Differential Equations, pages 53–147 (of ix + 332). Academic Press, New York, NY, USA, 1979. ISBN 0-12-546050-3. LCCN QA374 .A38 1978.

Brandt:1992:MSD

[BD92] A. Brandt and B. Diskin. Multigrid solvers on decomposed domains. In A. Quarteroni, editor, Proc. Sixth Int. Conf. on Domain Decomposition Methods, pages ??–?? (of xxii + 484). Amer. Math. Soc., Providence, RI, USA, 1992. ISBN 0-8218-5158-6. LCCN QA402.2 .I55 1992.

Brandt:1994:MSD

[BD94] Achi Brandt and Boris Diskin.

Multigrid solvers on decomposed domains. In Domain decomposition methods in science and engineering (Como, 1992), volume 157 of Contemp. Math., pages 135–155. Amer. Math. Soc., Providence, RI, USA, 1994.

Brandt:1999:FCM

[BD99a] A. Brandt and J. Dym. Fast calculation of multiple line integrals. SIAM Journal on Scientific Computing, 20(4):1417– 1429, 1999. CODEN SJOCE3. ISSN 1095-7197.

Brandt:1999:MSN

[BD99b] Achi Brandt and Boris Diskin.

Multigrid solvers for nonaligned sonic flows. SIAM Journal on Scientific Computing, 21(2):473– 501, 1999. CODEN SJOCE3. ISSN 1095-7197.

Brandt:1980:MMS

[BDR80] Achi Brandt, J. E. Dendy, Jr., and Hans Ruppel. The multigrid method for semi-implicit hydrodynamics codes. Journal of Computational Physics, 34(3): 348–370, March 1, 1980. CO-DEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/0021999180900947.

Brandt:1985:ISM

[BFT85] Achi Brandt, Scott R. Fulton, and G. D. Taylor. Improved spectral multigrid methods for periodic elliptic problems. Journal of Computational Physics, 58 (1):96–112, March 1985. CO-DEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/0021999185901597.

Brandt:1966:MFI

[BG66] A. Brandt and J. Gillis. Magnetohydrodynamic flow in the inlet region of a straight channel. Phys. of Fluids, 9:690–699, 1966. CODEN PHFLE6. ISSN 1070-6631.

Brandt:1969:AAH

[BG69] A. Brandt and J. Gillis. Asymptotic approach to Hartmann– Poiseuille flows. Journal of Computational Physics, 3(4): 523–538, April 1969. CO-DEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/0021999169900606.

Brandt:1991:PMR

[BG91] Achi Brandt and Joseph Greenwald. Parabolic multigrid revisited. In W. Hackbusch and U. Trottenberg, editors, Multigrid methods, III (Bonn, 1990), Internat. Ser. Numer. Math., pages 143–154 (of ix + 394). Birkhäuser Verlag, Basel, 1991.

ISBN 0-8176-2632-8. LCCN QA377.C7628 1991.

Brandt:1996:OMA

[BG96] A. Brandt and M. Galun. Optimal multigrid algorithms for the massive Gaussian model and path integrals. Journal of Statistical Physics, 82 (5–6):1503–1518, March 1996. CODEN JSTPSB. ISSN 0022-4715 (print), 1572-9613 (electronic). URL http://

link.springer.com/article/
10.1007/BF02183393.

Brandt:1997:OMA

[BG97] A. Brandt and M. Galun.

Optimal multigrid algorithms for variable-coupling isotropic Gaussian models. Journal of Statistical Physics, 88 (3–4):637–664, August 1997. CODEN JSTPSB. ISSN 0022-4715 (print), 1572-9613 (electronic). URL http://

link.springer.com/article/
10.1023/B%3AJOSS.0000015166.
92664.d8.

Brandt:2003:MAD

[BG03] Achi Brandt and Rima Gandlin.

Multigrid for atmospheric data assimilation: analysis. In Hyperbolic problems: theory, numerics, applications, pages 369–376. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2003.

Brandt:1994:OMA

[BGR94] A. Brandt, M. Galun, and D. Ron. Optimal multigrid algorithms for calculating thermodynamic limits. Journal of Statistical Physics, 74 (1–2):313–348, January 1994. CODEN JSTPSB. ISSN 0022-4715 (print), 1572-9613 (electronic). URL http://

                                        link.springer.com/article/
                                        10.1007/BF02186816.

Bressler:1971:ITS

[BHD^{+}71] E. Bressler, J. Heller, N. Dinar, I. Ben-Asher, A. Brandt, and D. Goldberg. Infiltration from a tricle source. II. experimental data and theoretical predictions. Soil Sci. Soc. Amer. Proc., 35: 683–689, 1971.

Brandt:1971:APT

[BI71] A. Brandt and Y. Intrator. The assignment problem with three job categories. Cas. Pest. Mat., 96:8–11, 1971. CODEN CPMTA8. ISSN 0008-7394, 0528-2195.

Brandt:1978:FAL

[BI78] A. Brandt and J. Intrator. Fast algorithms for long transportation problems. Computers and Operations Research, 5:263–271, 1978. CODEN CMORAP. ISSN 0305-0548 (print), 1873-765X (electronic).

Brandt:2009:DDA

[BIW09] Achi Brandt, Oleg Iliev, and Joerg Willems. A domain decomposition approach for calculating the graph corresponding to a fibrous geometry. In Domain decomposition methods in science and engineering XVIII, volume 70 of Lect. Notes Comput.

Sci. Eng., pages 3–14. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2009.

Brandt:2000:MSE

[BIYS00] Achi Brandt, Moshe Israeli, Irad Yavneh, and Andrew Siegel. Multigrid solution of an elliptic boundary-value problem with integral constraints. SIAM Journal on Scientific Computing, 21 (4):1357–1369, July 2000. CO-DEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic).

URL http://epubs.siam.org/
sam-bin/dbq/article/33181.

Brandt:1969:SPT

[BK69] A. Brandt and I. Kelson. Single particle theory of fission. Phys. Ref., 183:1025–1054, 1969.

Brandt:1988:MGR

[BL88] A. Brandt and A. Lanza. Multigrid in general relativity: I. Schwarzschild spacetime. Class. Quantum Grav., 5:713–732, 1988. CODEN CQGRDG. ISSN 0264-9381 (print), 1361-6382 (electronic).

Brandt:1990:MMMa

[BL90a] A. Brandt and A. A. Lubrecht.

Multilevel matrix multiplication and fast solution of integral equations. Journal of Computational Physics, 87(2):494, April 1990. CODEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (electronic). URL http://www.

sciencedirect.com/science/
article/pii/0021999190902642.

Brandt:1990:MMMb

[BL90b] A. Brandt and A. A. Lubrecht. Multilevel matrix multiplication and fast solution of integral equations. Journal of Computational Physics, 90(2): 348–370, October 1990. CO-DEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (elec-

                                        tronic).  URL http://www.
                                        sciencedirect.com/science/
                                        article/pii/002199919090171V.

Brandt:1997:WRM

[BL97] A. Brandt and I. Livshits. Waveray multigrid method for standing wave equations. Electronic Transactions on Numerical Analysis (ETNA), 6(Dec.): 162–181, 1997. CODEN ???? ISSN 1068-9613 (print), 1097-4067 (electronic). URL http:

                                        //etna.mcs.kent.edu/vol.6.
                                        1997/pp162-181.dir/pp162-

181.pdf. Special issue on multilevel methods (Copper Mountain, CO, 1997).

Brandt:2011:MTG

[BL11] Achi Brandt and Oren E. Livne. Multigrid techniques — 1984 guide with applications to fluid dynamics, volume 67 of Classics in Applied Mathematics. SIAM, Philadelphia, PA, USA, 2011. ISBN 1-61197-074-1. xx + 218 pp. Revised edition of the 1984 original [MR0772748].

Bates:1995:GSN

[BLB^{+}95] J. R. Bates, Y. Li, A. Brandt, S. F. McCormick, and J. Ruge.

A global shallow-water numerical model based on the semi-Lagrangian advection of potential vorticity. Quart. J. Roy. Met. Soc., 121(528):1981– ??, 1995. Submitted.

Brandt:1995:RIM

[BM95] A. Brandt and V. Mikulinsky. On recombining iterants in multigrid algorithms and problems with small islands. SIAM Journal on Scientific Computing, 16(1):20–28, January 1995. CODEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic).

Brandt:19xx:MTP

[BMxx] A. Brandt and V. Mikulinsky.

Multigrid treatment of problems with highly oscillating boundary and boundary conditions. SIAM J. Sci. Stat. Comput., ??(??):??, ???? 19xx. CODEN SIJCD4. ISSN 0196-5204. Submitted.

Brandt:1999:FAM

[BMBG99] Achi Brandt, Jordan Mann, Matvei Brodski, and Meirav Galun. A fast and accurate multilevel inversion of the radon transform. SIAM Journal on Applied Mathematics, 60 (2):437–462, 1999. CODEN SMJMAP. ISSN 0036-1399 (print), 1095-712X (electronic).

URL http://epubs.siam.org/
sam-bin/dbq/article/32425.

Brandt:2000:FAM

[BMBG00] Achi Brandt, Jordan Mann, Matvei Brodski, and Meirav Galun. A fast and accurate multilevel inversion of the Radon transform. SIAM Journal on Applied Mathematics, 60 (2):437–462, 2000. CODEN SMJMAP. ISSN 1095-712X.

Brandt:1982:AMA

[BMR82] A. Brandt, S. McCormick, and J. Ruge. Algebraic multigrid (AMG) for automatic multigrid solution with application to geodetic computations. Technical report, Institute for Computational Studies, Fort Collins, CO, POB 1852, 1982.

Brandt:1983:MMD

[BMR83] A. Brandt, S. McCormick, and J. Ruge. Multigrid methods for differential eigenproblems. SIAM J. Sci. Stat. Comput., 4 (2):244–260, June 1983. CODEN SIJCD4. ISSN 0196-5204.

Brandt:1984:AMA

[BMR84] A. Brandt, S. McCormick, and J. Ruge. Algebraic multigrid (AMG) for sparse matrix equations. In D. J. Evans, editor, Sparsity and its Applications, pages 257–284 (of x + 338). Cambridge University Press, Cambridge, UK, 1984. ISBN 0-521-26272-0. LCCN QA188.S58 1985.

Brandt:1984:GTU

[BO84] A. Brandt and D. Ophir. GRID-PACK: Toward unification of general grid programming. In B. Engquist and T. Smedsaas, editors, PDE Software:

Modules Interfaces and Systems, pages 269–288 (of ix + 453). North-Holland, Amsterdam, The Netherlands, 1984. ISBN 0-444-87620-0. LCCN QA377 .I44 1983.

Brandt:2001:RMR

[BR01] Achi Brandt and Dorit Ron.

Renormalization multigrid (RMG): Statistically optimal renormalization group flow and coarseto-fine Monte Carlo acceleration. Journal of Statistical Physics, 102(1–2):231–257, January 2001. CODEN JSTPSB. ISSN 0022-4715 (print), 1572-9613 (electronic). URL http://

link.springer.com/article/
10.1023/A%3A1026520927784.

Brandt:2003:MSM

[BR03] Achi Brandt and Dorit Ron.

Multigrid solvers and multilevel optimization strategies. In Multilevel optimization in VLSI-CAD, volume 14 of Comb. Optim., pages 1–69. Kluwer Acad. Publ., Dordrecht, 2003.

Brandt:1961:GCT

[Bra61] A. Brandt. A generalization of a combinatorial theorem of Sparre Andersen about sums of random variables. Math. Scand, 9:325– 358, 1961. CODEN MTSCAN. ISSN 0025-5521 (print), 1903-1807 (electronic).

Brandt:1966:EDQ

[Bra66] Achi Brandt. Estimates for difference quotients of solutions of Poisson type difference equations. Math. Comp., 20(96): 473–499, October 1966. CO-DEN MCMPAF. ISSN 0025-5718 (print), 1088-6842 (electronic).

Brandt:1969:IES

[Bra69a] A. Brandt. Interior estimates for second order elliptic differential (or finite-difference) equations via the maximum principle. Israel J. Math, 7:95–121, 1969.

Brandt:1969:ISE

[Bra69b] A. Brandt. Interior schauder estimates for parabolic differential equations via the maximum principle. Israel J. Math, 7:254– 262, 1969.

Brandt:1973:MLA

[Bra73a] A. Brandt. Multi-level adaptive technique (MLAT) for fast numerical solutions to boundary value problems. In H. Cabannes and R. Temam, editors, Lecture Notes in Physics 18, pages 82– 89. Proc. 3rd Int. Conf. Numerical Methods in Fluid Mechanics, Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 1973. ISBN 0-387-06170-3. LCCN QA901 .I471 1972.

Brandt:1973:GLM

[Bra73b] Achi Brandt. Generalized local maximum principles for finitedifference operators. Math. Comp., 27(124):685–718, October 1973. CODEN MCMPAF. ISSN 0025-5718 (print), 1088-6842 (electronic).

Brandt:1976:MLA

[Bra76] A. Brandt. Multi-level adaptive technique (MLAT). I. the multigrid method. IBM Research Report RC-6026, IBM T. J. Watson Research Center, Yorktown Heights, NY, 1976.

Brandt:1977:MLAb

[Bra77a] A. Brandt. Multi-level adaptive techniques (MLAT) for partial differential equations: ideas and software. In Rice [Ric77], pages 273–314 (of ix + 388). ISBN 0-12-587260-7. LCCN QA297 .M36 1977. URL

https://www.sciencedirect.
com/book/9780125872607/mathematical-
software.

Brandt:1977:MLAa

[Bra77b] Achi Brandt. Multi-level adaptive solutions to boundary-value problems. Math. Comp., 31 (138):333–390, April 1977. CO-DEN MCMPAF. ISSN 0025-5718 (print), 1088-6842 (electronic).

Brandt:1979:MLA

[Bra79] A. Brandt. Multi-level adaptive techniques (MLAT) for singular perturbation problems. In P. W. Hemker and J. J. H. Miller, editors, Numerical analysis of singular perturbation problems, pages 53–142 (of xi + 499). Academic Press, New York, NY, USA, 1979. ISBN 0-12-340250-6. LCCN QA371 .N79 1978.

Brandt:1980:MLAb

[Bra80a] A. Brandt. Multi-level adaptive finite-element computations in fluid dynamics. AIAA Journal, 18:1165–1172, 1980.

Brandt:1980:MLAa

[Bra80b] A. Brandt. Multi-level adaptive finite elements methods: I. variational problems. In D. Pallaschke J. Frehse and U. Trottenberg, editors, Special Topics of Applied Mathematics, pages 91–128 (of viii + 248). North-Holland, Amsterdam, The Netherlands, 1980. ISBN 0-444-86035-5. LCCN QA320 .S62 1979.

Brandt:1980:NSF

[Bra80c] A. Brandt. Numerical stability and fast solutions to boundary value problems. In J. J. H. Miller, editor, Boundary and Interior Layers - Computational and Asymptotic Methods, pages 29–49 (of xi + 425). Boole Press, Dublin, Ireland, 1980. ISBN 0-906783-01-1. LCCN QA913 .B68 1980.

Brandt:1981:MGSb

[Bra81a] A. Brandt. Multi-grid solvers for non-elliptic and singularperturbation steady-state problems. Technical report, Weizmann Institute of Science, 1981.

Brandt:1981:MGSa

[Bra81b] A. Brandt. Multi-grid solvers on parallel computers. In M. Schultz, editor, Elliptic Problem Solvers, pages 39–84 (of xiii + 444). Academic Press, New York, NY, USA, 1981. ISBN 0-12-632620-7. LCCN QA377 .E53 1980.

Brandt:1982:IRM

[Bra82a] A. Brandt. Introductory remarks on multigrid methods. In K. W. Morton and M. J. Baines, editors, Numerical Methods for Fluid Dynamics, pages 127–134 (of xiv + 517). Academic Press, New York, NY, USA, 1982. ISBN 0-12-508360-2. LCCN TA357.N87 1982.

Brandt:1982:MGS

[Bra82b] A. Brandt. Multi-grid solutions to steady-state compressible Navier–Stokes equations. I. In R. Glowinsky and J. L. Lions, editors, Computing Methods in Applied Sciences and Engineering, V, pages 407–422 (of x + 668). North-Holland, Amsterdam, The Netherlands, 1982. ISBN 0-444-86450-4. LCCN QA297 .E53 1981.

Brandt:1984:LMLa

[Bra84a] A. Brandt. Local and multi-level parallel processing mill. Technical report, Department of Applied Mathematics, Weizmann Institute, Rehovot, Israel, 1984.

Brandt:1984:LMLb

[Bra84b] A. Brandt. Local and multilevel parallel processing mill. In U. Trottenberg and P. Wypior, editors, Rechnerarchiteckturen fur die Numerische Simulation auf der Basis Superschneller Losungsverfahren I, pages 31–40. GMD-Studien 88, 1984.

Brandt:1984:MTG

[Bra84c] A. Brandt. Multigrid techniques: 1984 guide, with applications to fluid dynamics. Gmd studien nr. 85, GMD, GMD-AIW, Postfach 1240, D-5205, St. Augustin 1, Germany, 1984. ISBN 3-88457-081-1. 191 pages.

Brandt:1985:ILS

[Bra85] A. Brandt. Introduction – levels and scales. In D. Paddon and H. Holstein, editors, Multigrid Methods for Integral and Differential Problems, pages 1–10 (of xii + 323). Clarendon Press, Oxford, UK, 1985. ISBN 0-19-853606-2. LCCN QA431 .M751 1985. US$36.40.

Brandt:1986:AMT

[Bra86a] A. Brandt. Algebraic multigrid theory: The symmetric case. Appl. Math. Comp., 19:23–56, 1986. Preliminary proceedings of the International Multigrid Conference, April 6–8, 1983, Copper Mountain, CO.

Brandt:1986:MLA

[BRA86b] A. Brandt, D. Ron, and D. J. Amit. Multi-level approaches to discrete-state and stochastic problems. In W. Hackbusch and U. Trottenberg, editors, Multigrid Methods II, pages 66–99 (of vi + 335). Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1986. ISBN 0-387-16491-X. LCCN QA3 .L35 v.1228. DM50.00.

Brandt:1987:MLA

[Bra87] A. Brandt. Multi-level approaches to large scale problems. In Gleason [Gle87], pages 1319–1334. ISBN 0-8218-0110-4. LCCN QA1 .I8 1986 v. 1-2. Two volumes.

Brandt:1988:MCR

[Bra88] A. Brandt. Multilevel computations: review and recent developments. In S. F. McCormick, editor, Multigrid Methods: Theory, Applications and Supercomputing, pages 35–62 (of xiv + 644). Marcel Dekker, New York, NY, USA, 1988. ISBN 0-8247-7979-7. LCCN QA377 .M9431 1988.

Brandt:1989:RLM

[Bra89] A. Brandt. Rigorous local mode analysis of multigrid. In Mandel et al. [MMD^{+}89], page 438. ISBN 0-89871-248-3. LCCN QA377 .C767 1989. US$39.50.

Brandt:1990:SMI

[Bra90a] A. Brandt. The scope of multiresolution iterative computations. SIAM News, 23:8–9, 1990. ISSN 0036-1437.

Brandt:1990:WIR

[Bra90b] A. Brandt. The weizmann institute research in multilevel computation: 1988 report. In J. Mandel et al., editors, Proc. 4th Copper Mountain Conference on Multigrid Methods, pages 13–53. SIAM, Philadelphia, PA, USA, 1990. ISBN 0-89871-248-3. LCCN QA377 .C767 1989. US$39.50.

Brandt:1991:MCI

[Bra91] Achi Brandt. Multilevel computations of integral transforms and particle interactions with oscillatory kernels. Computer Physics Communications, 65(1– 3):24–38, April 2, 1991. CO-DEN CPHCBZ. ISSN 0010-4655 (print), 1879-2944 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/001046559190151A.

Brandt:1992:MML

[Bra92a] A. Brandt. Multigrid methods in lattice field computations. Nucl. Phys. B, 26:137–180, 1992. CO-DEN NUPBBO. ISSN 0550-3213 (print), 1873-1562 (electronic). Proc. Suppl.

Brandt:1992:MCM

[Bra92b] A. Brandt. Multiscale computational methods: research activities. In T. Chan and Z.-C. Shi, editors, Proc. 1991 Hang Zhou International Conference on Scientific Computation, pages 1–7. World Scientific Publishing Co., Singapore, Philadelphia, River Edge, NJ, 1992.

Brandt:1992:MSHb

[Bra92c] A. Brandt. On multigrid solution of high-Reynolds incompressible entering flows. Journal of Computational Physics, 99(2):352, April 1992. CO-DEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/002199919290226O.

Brandt:1994:RQA

[Bra94] Achi Brandt. Rigorous quantitative analysis of multigrid, I: Constant coefficients two-level cycle with L_{2}-norm. SIAM Journal on Numerical Analysis, 31(6): 1695–1730, December 1994. CO-DEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Brandt:1997:GCR

[Bra97] Achi Brandt. The Gauss Center research in multiscale scientific computation. Electronic Transactions on Numerical Analysis (ETNA), 6(Dec.):1–34, 1997. CODEN ???? ISSN 1068-9613 (print), 1097-4067 (electronic).

URL http://etna.mcs.kent.
edu/vol.6.1997/pp1-34.dir/

pp1-34.pdf. Special issue on multilevel methods (Copper Mountain, CO, 1997).

Brandt:2000:GHA

[Bra00] Achi Brandt. General highly accurate algebraic coarsening. Electronic Transactions on Numerical Analysis (ETNA), 10: 1–20, 2000. CODEN ???? ISSN 1068-9613 (print), 1097-4067 (electronic). URL http:/

/etna.mcs.kent.edu/vol.10.
2000/pp1-20.dir/pp1-20.pdf.

Multilevel methods (Copper Mountain, CO, 1999).

Brandt:2002:MSC

[Bra02] Achi Brandt. Multiscale scientific computation: review 2001. In Multiscale and multiresolution methods, volume 20 of Lect. Notes Comput. Sci. Eng., pages 3–95. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2002.

Brandt:2005:MSS

[Bra05] A. Brandt. Multiscale solvers and systematic upscaling in computational physics. Computer Physics Communications, 169 (1–3):438–441, July 1, 2005. CO-DEN CPHCBZ. ISSN 0010-4655 (print), 1879-2944 (elec-

                                        tronic).  URL http://www.
                                        sciencedirect.com/science/
                                        article/pii/S0010465505001943.

Brandt:2010:PSU

[Bra10] Achi Brandt. Principles of systematic upscaling. In Jacob Fish, editor, Multiscale methods. Bridging the scales in science and engineering, pages 193–215. Oxford University Press, Walton Street, Oxford OX2 6DP, UK, 2010. ISBN 0-19-923385-3. LCCN TA335 .M85 2010.

Brandt:1985:MSQ

[BT85] A. Brandt and S. Ta’asan. Multigrid solutions to quasielliptic schemes. In E. M. Murman and S. S. Abarbanel, editors, Progress and Supercomputing in Computational Fluid Dynamics, pages 235–255 (of ix + 403). Birkhäuser Verlag, Basel, 1985. ISBN 0-8176-3321-9. LCCN QA911 .U21 1984.

Brandt:1986:MMN

[BT86] A. Brandt and S. Ta’asan.

Multigrid method for nearly singular and slightly indefinite problems. In W. Hackbusch and U. Trottenberg, editors, Multigrid Methods II, pages 100–122 (of vi + 335). Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1986. ISBN 0-387-16491-X. LCCN QA3 .L35 v.1228. DM50.00.

Brandt:1998:MEIb

[BV98a] A. Brandt and C. H. Venner.

Multilevel evaluation of integral transforms on adaptive grids. In Multigrid methods V (Stuttgart, 1996), volume 3 of Lect. Notes Comput. Sci. Eng., pages 21– 44. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 1998.

Brandt:1998:MEI

[BV98b] A. Brandt and C. H. Venner.

Multilevel evaluation of integral transforms with asymptotically smooth kernels. SIAM Journal on Scientific Computing, 19 (2):468–492, 1998. CODEN SJOCE3. ISSN 1095-7197.

Brandt:1990:IFO

[BY90] A. Brandt and Irad Yavneh.

Inadequacy of first-order upwind difference schemes for some recirculating flows. Journal of Computational Physics, 89(1):251, July 1990. CO-DEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/002199919090127M.

Brandt:1991:ICG

[BY91a] A. Brandt and I. Yavneh. Improved coarse-grid correction for high-Reynolds flows. In Mandel and Carey [MC92], page ?? ISBN ???? LCCN ???? Two volumes.

Brandt:1991:IFO

[BY91b] A. Brandt and I. Yavneh. Inadequacy of first-order upwind difference schemes for some recirculating flows. Journal of Computational Physics, 93(1): 128–143, 1991. CODEN JCT-PAH. ISSN 0021-9991 (print), 1090-2716 (electronic).

Brandt:1992:MSHa

[BY92] A. Brandt and I. Yavneh. On multigrid solution of high-Reynolds incompressible entering flows. Journal of Computational Physics, 101(1): 151–164, July 1992. CO-DEN JCTPAH. ISSN 0021-9991 (print), 1090-2716 (elec-

tronic).  URL http://www.
sciencedirect.com/science/
article/pii/0021999192900495.

Brandt:1993:AMC

[BY93] A. Brandt and I. Yavneh. Accelerated multigrid convergence and high-Reynolds recirculating flows. SIAM Journal on Scientific Computing, 14(3):607– 626, 1993. CODEN SJOCE3.

ISSN 1064-8275 (print), 1095-7197 (electronic).

Brandt:1997:MAA

[BZ97] Achi Brandt and Leonid Yu. Zaslavsky. Multiscale algorithm for atmospheric data assimilation. SIAM Journal on Scientific Computing, 18(3):949– 956, 1997. CODEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic).

Gleason:1987:PIC

[Gle87] Andrew M. Gleason, editor.

Proceedings of the International Congress of Mathematicians, 1986: August 3–11, 1986, Berkeley. Amer. Math. Soc., Providence, RI, USA, 1987. ISBN 0-8218-0110-4. LCCN QA1 .I8 1986 v. 1-2. Two volumes.

Harmatz:1991:PTM

[HLBA^{+}91] M. Harmatz, P. G. Lauwers, R. Ben-Av, A. Brandt, E. Katznelson, S. Solomon, and K. Wolowesky. Paralleltransported multigrid and its application to the Schwinger model. Nucl. Phys. B, 20, 1991. CODEN NUPBBO. ISSN 0550-3213 (print), 1873-1562 (electronic). (Proc. Suppl.).

Kandel:1989:SCS

[KDB89] D. Kandel, E. Domany, and A. Brandt. Simulations without critical slowing down — Ising and 3-state Potts models. Physical Review B: Condensed Matter and Materials Physics, 40:330– 344, 1989. CODEN PRBMDO. ISSN 1098-0121.

Kandel:1988:SCS

[KDR^{+}88] D. Kandel, E. Domany, D. Ron, A. Brandt, and E. Loh, Jr. Simulations without critical slowing down. Phys. Rev. Lett., 60:1591– 1594, 1988. CODEN PRLTAO. ISSN 0031-9007 (print), 1079-7114 (electronic), 1092-0145.

Livne:2002:MEC

[LB02a] Oren E. Livne and Achi Brandt. Multiscale eigenbasis calculations: N eigenfunctions in O(N log N). In Multiscale and multiresolution methods, volume 20 of Lect. Notes Comput. Sci. Eng., pages 347–357. Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2002.

Livne:2002:RSE

[LB02b] Oren E. Livne and Achi Brandt. N roots of the secular equation in O(N) operations. SIAM Journal on Matrix Analysis and Applications, 24(2):439–453, 2002. CODEN SJMAEL. ISSN 1095-7162.

Livne:2004:LMA

[LB04] O. E. Livne and A. Brandt. Local mode analysis of multicolor and composite relaxation schemes. Computers and Mathematics with Applications, 47(2– 3):301–317, January/February 2004. CODEN CMAPDK. ISSN 0898-1221 (print), 1873-7668 (electronic).

Livshits:2006:APW

[LB06] Irene Livshits and Achi Brandt.

Accuracy properties of the waveray multigrid algorithm for Helmholtz equations. SIAM Journal on Scientific Computing, 28(4):1228–1251, 2006. CO-DEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic).

Livne:2011:MMS

[LB11] Oren E. Livne and Achi E.

Brandt. MuT: The Multilevel Sinc Transform. SIAM Journal on Scientific Computing, 33 (4):1726–1738, ???? 2011. CO-DEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (elec-

tronic). URL http://epubs.
siam.org/sisc/resource/1/
sjoce3/v33/i4/p1726_s1.

Livne:2012:LAM

[LB12] Oren E. Livne and Achi Brandt. Lean Algebraic Multigrid (LAMG): Fast graph Laplacian linear solver. SIAM Journal on Scientific Computing, 34 (4):B499–B522, ???? 2012. CO-DEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic).

Mikulinsky:1991:MTF

[MB91] V. Mikulinsky and A. Brandt.

Multigrid treatment of free boundary conditions. In W. Hackbusch and U. Trottenberg, editors, Multigrid methods: special topics and applications, II (Bonn, 1990), volume 189, pages 940–949. Gesellsch. Math. Datenverarbeitung, St. Augustin, 1991. GMD-Studien.

Mandel:1992:SIM

[MC92] Jan Mandel and Graham F. Carey, editors. Special issue on multigrid methods: from the Fifth Copper Mountain Conference on Multigrid Methods, Colorado, April 1991, volume 9(9– 10) of Communications in applied numerical methods. John Wiley and Sons, Inc., Chichester, UK, 1992. ISBN ???? LCCN ???? Two volumes.

Mandel:1989:PFC

[MMD^{+}89] J. Mandel, S. F. McCormick, J. E. Dendy, C. Farhat, G. Lonsdale, S. V. Parter, J. W. Ruge, and K. Stüben, editors. Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods. SIAM, Philadelphia, PA, USA, 1989. ISBN 0-89871-248-3. LCCN QA377 .C767 1989. US$39.50.

Ruge:1988:MAE

[RB88] J. Ruge and A. Brandt. A multigrid approach for elasticity problems on thin domains. In S. F. McCormick, editor, Multigrid Methods: Theory, Applications and Supercomputing, pages 541–555 (of xiv + 644). Marcel Dekker, New York, NY, USA, 1988. ISBN 0-8247-7979-7. LCCN QA377 .M9431 1988.

Ruge:1991:MMA

[RBMM91a] J. Ruge, A. Brandt, J. McWilliams, and R. Milliff. Multigrid methods applied to turbulent flow problems. In W. Hackbusch and T. Trottenberg, editors, Multigrid Methods III, pages 91–103 (of ix + 394). Birkhäuser Verlag, Basel, 1991. ISBN 0-8176-2632-

8. LCCN QA377.C7628 1991.

Ruge:1991:MMT

[RBMM91b] John Ruge, Achi Brandt, Jim McWilliams, and Ralph Milliff. Multigrid methods for turbulent flow problems. In Multigrid methods, III (Bonn, 1990), volume 98 of Internat. Ser. Numer. Math., pages 91–103. Birkhäuser Verlag, Basel, 1991.

Rice:1977:MSI

[Ric77] John R. Rice, editor. Mathematical software III: Proceedings of a symposium conducted by the Mathematics Research Center, the University of Wisconsin– Madison, March 28–30, 1977, number 39 in Publication of the Mathematics Research Center, the University of Wisconsin, Madison. Academic Press, New York, NY, USA, 1977. ISBN 0-12-587260-7. LCCN QA3 .U45 no. 39; QA297 .M36 1977. URL

https://www.sciencedirect.
com/book/9780125872607/mathematical-
software.

Ruge:2000:NMS

[RLM^{+}00] John W. Ruge, Yong Li, Steve McCormick, Achi Brandt, and J. R. Bates. A nonlinear multigrid solver for a semi-Lagrangian potential vorticitybased shallow-water model on the sphere. SIAM Journal on Scientific Computing, 21(6):

2381–2395, 2000. CODEN SJOCE3. ISSN 1095-7197.

Ron:2010:FMA

[RSB10] Dorit Ron, Ilya Safro, and Achi Brandt. A fast multigrid algorithm for energy minimization under planar density constraints. Multiscale Modeling & Simulation, 8(5):1599– 1620, ???? 2010. CODEN MMSUBT. ISSN 1540-3459 (print), 1540-3467 (electronic).

                                        URL http://epubs.siam.org/
                                        mms/resource/1/mmsubt/v8/
                                        i5/p1599_s1.

Ron:2011:RBC

[RSB11] Dorit Ron, Ilya Safro, and Achi Brandt. Relaxation-based coarsening and multiscale graph organization. Multiscale Modeling & Simulation, 9(1):407– 423, ???? 2011. CODEN MMSUBT. ISSN 1540-3459 (print), 1540-3467 (electronic).

                                        URL http://epubs.siam.org/
                                        mms/resource/1/mmsubt/v9/
                                        i1/p407_s1.

South:1977:AML

[SB77] J. C. South and A. Brandt. Application of a multi-level grid method to transonic flow calculations. In T. C. Adamson, Jr. and M. F. Platzer, editors, Transonic flow problems in turbo machinery, pages 180–207. Hemisphere, Washington, DC, USA, 1977. ISBN 0-89116-069-8. LCCN TJ267 .P66 1976.

Sidilkover:1993:MSS

[SB93] David Sidilkover and Achi Brandt. Multigrid solution to steady-state two-dimensional conservation laws. SIAM Journal on Numerical Analysis, 30 (1):249–274, February 1993. CO-DEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Schlick:1996:CWM

[SB96] Tamar Schlick and Achi Brandt.

Conferences & workshops: A Multigrid Tutorial with Applications to Molecular Dynamics. IEEE Computational Science & Engineering, 3(3):78–79, 82, Fall 1996. CODEN ISCEE4. ISSN 1070-9924 (print), 1558-190X (electronic).

Safro:2006:GML

[SRB06a] Ilya Safro, Dorit Ron, and Achi Brandt. Graph minimum linear arrangement by multilevel weighted edge contractions. Journal of Algorithms, 60(1):24– 41, 2006. CODEN JOALDV. ISSN 0196-6774 (print), 1090-2678 (electronic).

Safro:2006:MAM

[SRB06b] Ilya Safro, Dorit Ron, and Achi Brandt. A multilevel algorithm for the minimum 2-sum problem. J. Graph Algorithms Appl., 10 (2):237–258, 2006. ISSN 1526-1719.

Safro:2008:MAL

[SRB08] Ilya Safro, Dorit Ron, and Achi Brandt. Multilevel algorithms for linear ordering problems. ACM Journal of Experimental Algorithmics, 13:20, 2008. ISSN 1084-6654.

Thomas:2003:TME

[TDB03] James L. Thomas, Boris Diskin, and Achi Brandt. Textbook multigrid efficiency for fluid simulations. In Annual review of fluid mechanics, Vol. 35, volume 35 of Annu. Rev. Fluid Mech., pages 317–340. Annual Reviews, Palo Alto, CA, 2003.

Thomas:2002:GFA

[TDBS02] James L. Thomas, Boris Diskin, Achi Brandt, and Jerry C. South, Jr. General framework for achieving textbook multigrid efficiency: one-dimensional Euler example. In Frontiers of computational fluid dynamics, 2002 (Half Moon Bay, CA, 2000), pages 61–80. World Sci. Publishing, River Edge, NJ, 2002.

Trottenberg:2001:M

[TOS01] U. Trottenberg, C. W. Oosterlee, and A. Schüller. Multigrid. Academic Press, New York, NY, USA, 2001. ISBN 0-12-701070-X. xvi + 631 pp. With contributions by A. Brandt, P. Oswald and K. Stüben.

Yavneh:1998:FMS

[YVB98] Irad Yavneh, Cornelis H. Venner, and Achi Brandt. Fast multigrid solution of the advection problem with closed characteristics. SIAM Journal on Scientific Computing, 19(1):111– 125, 1998. CODEN SJOCE3.

ISSN 1095-7197. Special issue on iterative methods (Copper Mountain, CO, 1996).

Ye:2012:MNB

[YYD^{+}12] Jian Ye, Igor Yanovsky, Bin Dong, Rima Gandlin, Achi Brandt, and Stanley Osher. Multigrid narrow band surface reconstruction via level set functions. Lecture Notes in Computer Science, 7431:61– 70, 2012. CODEN LNCSD9. ISSN 0302-9743 (print), 1611-3349 (electronic). URL http://

link.springer.com/chapter/
10.1007/978-3-642-33179-4_
7/;   http://link.springer.
com/content/pdf/10.1007/978-
3-642-33179-4_7.

Zhu:2010:EMM

[ZSTB10] Yongning Zhu, Eftychios Sifakis, Joseph Teran, and Achi Brandt. An efficient multigrid method for the simulation of high-resolution elastic solids. ACM Transactions on Graphics, 29(2):16:1– 16:18, March 2010. CODEN AT-GRDF. ISSN 0730-0301 (print), 1557-7368 (electronic).