메뉴 건너뛰기




Volumn 15, Issue 3, 2008, Pages 277-309

A Survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism

Author keywords

[No Author keywords available]

Indexed keywords

MAGNETIZATION PATTERNS; MATHEMATICAL PROPERTIES; MICROMAGNETISM; NONCONVEX; NONLOCAL CHARACTERS; NUMERICAL APPROXIMATIONS; PHYSICAL QUANTITIES; RECENT DEVELOPMENTS; STRONG SOLUTIONS; STRONGLY NONLINEAR; WEAK SOLUTIONS;

EID: 56949098941     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11831-008-9021-2     Document Type: Article
Times cited : (121)

References (55)
  • 1
    • 33748362404 scopus 로고    scopus 로고
    • Recent developments in the modeling, analysis, and numerics of ferromagnetism
    • M Kružík A Prohl 2006 Recent developments in the modeling, analysis, and numerics of ferromagnetism SIAM Rev 48 439 483
    • (2006) SIAM Rev , vol.48 , pp. 439-483
    • Kružík, M.1    Prohl, A.2
  • 3
    • 0000060534 scopus 로고
    • On the theory of the dispersion of magnetic permeability in ferromagnetic bodies
    • L Landau E Lifshitz 1935 On the theory of the dispersion of magnetic permeability in ferromagnetic bodies Phys Z Sowjetunion 8 153 169
    • (1935) Phys Z Sowjetunion , vol.8 , pp. 153-169
    • Landau, L.1    Lifshitz, E.2
  • 4
    • 0001038170 scopus 로고
    • A Lagrangian formulation of gyromagnetic equation of the magnetization field
    • T Gilbert 1955 A Lagrangian formulation of gyromagnetic equation of the magnetization field Phys Rev 100 1243 1255
    • (1955) Phys Rev , vol.100 , pp. 1243-1255
    • Gilbert, T.1
  • 5
    • 21444450553 scopus 로고    scopus 로고
    • Geometrical integration of Landau-Lifshitz-Gilbert equation based on the mid-point rule
    • M d'Aquino C Serpico G Miano 2005 Geometrical integration of Landau-Lifshitz-Gilbert equation based on the mid-point rule J Comput Phys 209 730 753
    • (2005) J Comput Phys , vol.209 , pp. 730-753
    • D'Aquino, M.1    Serpico, C.2    Miano, G.3
  • 7
    • 26644438806 scopus 로고    scopus 로고
    • Error estimates for a semi-implicit numerical scheme solving the Landau-Lifshitz equation with an exchange field
    • I Cimrák 2005 Error estimates for a semi-implicit numerical scheme solving the Landau-Lifshitz equation with an exchange field IMA J Numer Anal 25 611 634
    • (2005) IMA J Numer Anal , vol.25 , pp. 611-634
    • Cimrák, I.1
  • 8
    • 0041470137 scopus 로고    scopus 로고
    • On dissipation mechanisms in micromagnetics
    • P Podio-Guidugli 2001 On dissipation mechanisms in micromagnetics Eur Phys J B 19 417 424
    • (2001) Eur Phys J B , vol.19 , pp. 417-424
    • Podio-Guidugli, P.1
  • 9
    • 0035919582 scopus 로고    scopus 로고
    • Accurate discretization of a non-linear micromagnetic problem
    • P Monk O Vacus 2001 Accurate discretization of a non-linear micromagnetic problem Comput Methods Appl Mech Eng 190 5243 5269
    • (2001) Comput Methods Appl Mech Eng , vol.190 , pp. 5243-5269
    • Monk, P.1    Vacus, O.2
  • 10
    • 55349113267 scopus 로고    scopus 로고
    • A convergent implicit discretization of the Maxwell-Landau-Lifshitz- Gilbert equation
    • accepted
    • Baňas L, Bartels S, Prohl A. (2008) A convergent implicit discretization of the Maxwell-Landau-Lifshitz-Gilbert equation. SIAM J Numer Anal (accepted). http://na.uni-tuebingen.de/pub/prohl/papers/mllg.pdf
    • (2008) SIAM J Numer Anal
    • Baňas, L.1    Bartels, S.2    Prohl, A.3
  • 11
    • 34547926842 scopus 로고    scopus 로고
    • Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation
    • S Bartels A Prohl 2006 Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation SIAM J Numer Anal 44 1405 1419
    • (2006) SIAM J Numer Anal , vol.44 , pp. 1405-1419
    • Bartels, S.1    Prohl, A.2
  • 12
    • 36149026446 scopus 로고
    • Thermal fluctuations of a single domain particle
    • W Brown 1963 Thermal fluctuations of a single domain particle Phys Rev 130 1677 1686
    • (1963) Phys Rev , vol.130 , pp. 1677-1686
    • Brown, W.1
  • 15
    • 0006681755 scopus 로고    scopus 로고
    • Langevin-dynamics study of the dynamical properties of small magnetic particles
    • L Garcia-Palacios FJ Lazaro 1998 Langevin-dynamics study of the dynamical properties of small magnetic particles Phys Rev B 58 14937 14958
    • (1998) Phys Rev B , vol.58 , pp. 14937-14958
    • Garcia-Palacios, L.1    Lazaro, F.J.2
  • 16
    • 0035425886 scopus 로고    scopus 로고
    • Micromagnetic simulation of thermally activated switching in fine particles
    • W Scholz T Schrefl J Fidler 2001 Micromagnetic simulation of thermally activated switching in fine particles J Magn Magn Mater 233 296 304
    • (2001) J Magn Magn Mater , vol.233 , pp. 296-304
    • Scholz, W.1    Schrefl, T.2    Fidler, J.3
  • 17
    • 33144479177 scopus 로고    scopus 로고
    • Mapping the Monte-Carlo scheme to Langevin dynamics: A Fokker-Planck approach
    • XZ Cheng MBA Jalil HK Lee Y Okabe 2006 Mapping the Monte-Carlo scheme to Langevin dynamics: A Fokker-Planck approach Phys Rev Lett 96 067208
    • (2006) Phys Rev Lett , vol.96 , pp. 067208
    • Cheng, X.Z.1    Jalil, M.B.A.2    Lee, H.K.3    Okabe, Y.4
  • 19
    • 33947381078 scopus 로고    scopus 로고
    • Sensitivity analysis framework for micromagnetism with application to optimal shape design of MRAM memories
    • I Cimrák V Melicher 2007 Sensitivity analysis framework for micromagnetism with application to optimal shape design of MRAM memories Inverse Probl 23 563 588
    • (2007) Inverse Probl , vol.23 , pp. 563-588
    • Cimrák, I.1    Melicher, V.2
  • 20
    • 56949091726 scopus 로고    scopus 로고
    • The Landau-Lifshitz model for shape optimization of MRAM memories
    • I Cimrák V Melicher 2006 The Landau-Lifshitz model for shape optimization of MRAM memories PAMM 6 23 26
    • (2006) PAMM , vol.6 , pp. 23-26
    • Cimrák, I.1    Melicher, V.2
  • 21
    • 24644508476 scopus 로고    scopus 로고
    • A survey on multipole level set methods with applications for identifying piecewise constant functions
    • X Tai T Chan 2004 A survey on multipole level set methods with applications for identifying piecewise constant functions Int J Numer Anal Model 1 25 47
    • (2004) Int J Numer Anal Model , vol.1 , pp. 25-47
    • Tai, X.1    Chan, T.2
  • 22
    • 37349038483 scopus 로고    scopus 로고
    • Level Set Method for optimal shape design of MRAM core. Micromagnetic approach
    • V Melicher I Cimrák R Van Keer 2008 Level Set Method for optimal shape design of MRAM core. Micromagnetic approach Physica B: Condens Matter 403 308 311
    • (2008) Physica B: Condens Matter , vol.403 , pp. 308-311
    • Melicher, V.1    Cimrák, I.2    Van Keer, R.3
  • 23
    • 0010533619 scopus 로고    scopus 로고
    • Regular solutions for Landau-Lifshitz Equation in a bounded domain
    • G Carbou P Fabrie 2001 Regular solutions for Landau-Lifshitz Equation in a bounded domain Diff Integral Equ 14 213 229
    • (2001) Diff Integral Equ , vol.14 , pp. 213-229
    • Carbou, G.1    Fabrie, P.2
  • 24
    • 85174220879 scopus 로고    scopus 로고
    • Neumann problem for the Landau-Lifshitz-Maxwell system in two dimensions
    • B Guo S Ding 2001 Neumann problem for the Landau-Lifshitz-Maxwell system in two dimensions Chin Ann Math Ser B 22 529 540
    • (2001) Chin Ann Math ser B , vol.22 , pp. 529-540
    • Guo, B.1    Ding, S.2
  • 25
    • 0037293461 scopus 로고    scopus 로고
    • Geometric integration on spheres and some interesting applications
    • D Lewis N Nigam 2003 Geometric integration on spheres and some interesting applications J Comput Appl Math 151 141 170
    • (2003) J Comput Appl Math , vol.151 , pp. 141-170
    • Lewis, D.1    Nigam, N.2
  • 26
    • 0034547805 scopus 로고    scopus 로고
    • Numerical methods for the Landau-Lifshitz equation
    • W E X-P Wang 2000 Numerical methods for the Landau-Lifshitz equation SIAM J Numer Anal 38 1647 1665
    • (2000) SIAM J Numer Anal , vol.38 , pp. 1647-1665
    • E, W.1    Wang, X.-P.2
  • 27
    • 0035575745 scopus 로고    scopus 로고
    • Cayley transforms in micromagnetics
    • P Krishnaprasad X Tan 2001 Cayley transforms in micromagnetics Physica B 306 195 199
    • (2001) Physica B , vol.306 , pp. 195-199
    • Krishnaprasad, P.1    Tan, X.2
  • 29
    • 0004378032 scopus 로고    scopus 로고
    • Error estimates for a numerical scheme for ferromagnetic problems
    • P Monk O Vacus 1999 Error estimates for a numerical scheme for ferromagnetic problems SIAM J Numer Anal 36 696 718
    • (1999) SIAM J Numer Anal , vol.36 , pp. 696-718
    • Monk, P.1    Vacus, O.2
  • 30
    • 0035356823 scopus 로고    scopus 로고
    • Numerical technique for integration of the Landau-Lifshitz equation
    • C Serpico I Mayergoyz G Bertotti 2001 Numerical technique for integration of the Landau-Lifshitz equation J Appl Phys 89 6991 6993
    • (2001) J Appl Phys , vol.89 , pp. 6991-6993
    • Serpico, C.1    Mayergoyz, I.2    Bertotti, G.3
  • 31
    • 34548405051 scopus 로고    scopus 로고
    • Error analysis of numerical scheme for 3D Maxwell-Landau-Lifshitz system
    • I Cimrák 2007 Error analysis of numerical scheme for 3D Maxwell-Landau-Lifshitz system Math Methods Appl Sci 30 1667 1683
    • (2007) Math Methods Appl Sci , vol.30 , pp. 1667-1683
    • Cimrák, I.1
  • 32
    • 33846564564 scopus 로고    scopus 로고
    • Existence, regularity and local uniqueness of the solutions to the Maxwell-Landau-Lifshitz system in three dimensions
    • I Cimrák 2007 Existence, regularity and local uniqueness of the solutions to the Maxwell-Landau-Lifshitz system in three dimensions J Math Anal Appl 329 1080 1093
    • (2007) J Math Anal Appl , vol.329 , pp. 1080-1093
    • Cimrák, I.1
  • 33
    • 40849121000 scopus 로고    scopus 로고
    • Regularity properties of the solutions to the 3D Maxwell-Landau-Lifshitz system in weighted Sobolev spaces
    • I Cimrák 2008 Regularity properties of the solutions to the 3D Maxwell-Landau-Lifshitz system in weighted Sobolev spaces J Comput Appl Math 215 320 327
    • (2008) J Comput Appl Math , vol.215 , pp. 320-327
    • Cimrák, I.1
  • 34
    • 0000914360 scopus 로고
    • On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness
    • F Alouges A Soyeur 1992 On global weak solutions for Landau-Lifshitz equations: Existence and nonuniqueness Nonlinear Anal 18 1071 1094
    • (1992) Nonlinear Anal , vol.18 , pp. 1071-1094
    • Alouges, F.1    Soyeur, A.2
  • 35
    • 0001473350 scopus 로고
    • The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
    • B Guo M Hong 1993 The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps Calc Var Partial Differ Equ 1 311 334
    • (1993) Calc Var Partial Differ Equ , vol.1 , pp. 311-334
    • Guo, B.1    Hong, M.2
  • 36
    • 0037503095 scopus 로고    scopus 로고
    • Numerical study of nonlinear ferromagnetic materials
    • M Slodička I Cimrák 2003 Numerical study of nonlinear ferromagnetic materials Appl Numer Math 46 95 111
    • (2003) Appl Numer Math , vol.46 , pp. 95-111
    • Slodička, M.1    Cimrák, I.2
  • 37
    • 3042554534 scopus 로고    scopus 로고
    • An iterative approximation scheme for the Landau-Lifshitz-Gilbert equation
    • I Cimrák M Slodička 2004 An iterative approximation scheme for the Landau-Lifshitz-Gilbert equation J Comput Appl Math 169 17 32
    • (2004) J Comput Appl Math , vol.169 , pp. 17-32
    • Cimrák, I.1    Slodička, M.2
  • 38
    • 0742304589 scopus 로고    scopus 로고
    • Optimal convergence rate for Maxwell-Landau-Lifshitz system
    • I Cimrák M Slodička 2004 Optimal convergence rate for Maxwell-Landau-Lifshitz system Physica B 343 236 240
    • (2004) Physica B , vol.343 , pp. 236-240
    • Cimrák, I.1    Slodička, M.2
  • 39
    • 4544291644 scopus 로고    scopus 로고
    • A numerical scheme for a Maxwell-Landau-Lifshitz-Gilbert System
    • M Slodička L Baňas 2004 A numerical scheme for a Maxwell-Landau-Lifshitz-Gilbert System Appl Math Comput 158 79 99
    • (2004) Appl Math Comput , vol.158 , pp. 79-99
    • Slodička, M.1    Baňas, L.2
  • 40
    • 40849090931 scopus 로고    scopus 로고
    • Improved error estimates for a Maxwell-Landau-Lifshitz system
    • M Slodička I Cimrák 2004 Improved error estimates for a Maxwell-Landau-Lifshitz system PAMM 4 71 74
    • (2004) PAMM , vol.4 , pp. 71-74
    • Slodička, M.1    Cimrák, I.2
  • 41
    • 32644447749 scopus 로고    scopus 로고
    • Convergence of a finite element discretization for the Landau-Lifshitz equations in micromagnetism
    • F Alouges P Jaisson 2006 Convergence of a finite element discretization for the Landau-Lifshitz equations in micromagnetism Math Models Methods Appl Sci 16 299 316
    • (2006) Math Models Methods Appl Sci , vol.16 , pp. 299-316
    • Alouges, F.1    Jaisson, P.2
  • 42
    • 56949090309 scopus 로고    scopus 로고
    • Numerical approximation of the Landau-Lifshitz-Gilbert equation and finite time blow-up of weak solutions
    • accepted
    • Bartels S, Ko J, Prohl A (2007) Numerical approximation of the Landau-Lifshitz-Gilbert equation and finite time blow-up of weak solutions. Math Comput (accepted)
    • (2007) Math Comput
    • Bartels, S.1    Ko, J.2    Prohl, A.3
  • 43
    • 38349076060 scopus 로고    scopus 로고
    • A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres
    • J Barret X Bartels Feng A Prohl 2007 A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres SIAM J Numer Anal 45 905 927
    • (2007) SIAM J Numer Anal , vol.45 , pp. 905-927
    • Barret, J.1    Bartels, X.2    Feng3    Prohl, A.4
  • 44
    • 56949085608 scopus 로고    scopus 로고
    • Constraint preserving, inexact solution of implicit discretizations of Landau-Lifshitz-Gilbert equations and consequences for convergence
    • S Bartels 2006 Constraint preserving, inexact solution of implicit discretizations of Landau-Lifshitz-Gilbert equations and consequences for convergence PAMM 6 19 22
    • (2006) PAMM , vol.6 , pp. 19-22
    • Bartels, S.1
  • 45
    • 38349060008 scopus 로고    scopus 로고
    • Constraint preserving implicit finite element discretization of harmonic map heat flow into spheres
    • S Bartels A Prohl 2007 Constraint preserving implicit finite element discretization of harmonic map heat flow into spheres Math Comp 76 1847 1859
    • (2007) Math Comp , vol.76 , pp. 1847-1859
    • Bartels, S.1    Prohl, A.2
  • 46
    • 33644536096 scopus 로고    scopus 로고
    • Stability and convergence of finite element approximation schemes for harmonic maps
    • S Bartels 2004 Stability and convergence of finite element approximation schemes for harmonic maps SIAM J Numer Anal 43 220 238
    • (2004) SIAM J Numer Anal , vol.43 , pp. 220-238
    • Bartels, S.1
  • 50
    • 0001698420 scopus 로고    scopus 로고
    • Time average in micromagnetism
    • G Carbou P Fabrie 2001 Time average in micromagnetism J Differ Equ 147 383 409
    • (2001) J Differ Equ , vol.147 , pp. 383-409
    • Carbou, G.1    Fabrie, P.2
  • 52
    • 0000013815 scopus 로고    scopus 로고
    • Coupling between eddy currents and Landau-Lifshitz dynamics
    • I Mayergoyz C Serpico Y Shimizu 2000 Coupling between eddy currents and Landau-Lifshitz dynamics J Appl Phys 87 5529 5531
    • (2000) J Appl Phys , vol.87 , pp. 5529-5531
    • Mayergoyz, I.1    Serpico, C.2    Shimizu, Y.3
  • 53
    • 56949097218 scopus 로고    scopus 로고
    • Webpage address
    • Webpage address: http://www.ctcms.nist.gov/~rdm/mumag.org.html


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.