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Volumn 274, Issue , 2014, Pages 208-229

The Monge-Ampère trajectory correction for semi-Lagrangian schemes

Author keywords

Incompressible flows; Magnetic reconnection; Magnetohydrodynamics; Monge Amp re equation; Newton Krylov methods; Nonlinear equations; Passive advection; Semi Lagrangian schemes

Indexed keywords

LAGRANGE MULTIPLIERS; MAGNETOHYDRODYNAMICS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; TRAJECTORIES;

EID: 84904621312     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2014.05.016     Document Type: Article
Times cited : (16)

References (73)
  • 1
    • 78650303012 scopus 로고    scopus 로고
    • On spontaneous formation of current sheets: untwisted magnetic fields
    • 112901
    • Bhattacharyya R., Low B.C., Smolarkiewicz P.K. On spontaneous formation of current sheets: untwisted magnetic fields. Phys. Plasmas 2010, 17. 112901.
    • (2010) Phys. Plasmas , vol.17
    • Bhattacharyya, R.1    Low, B.C.2    Smolarkiewicz, P.K.3
  • 2
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • Benamou J.-D., Brenier Y. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 2000, 84:375-393.
    • (2000) Numer. Math. , vol.84 , pp. 375-393
    • Benamou, J.-D.1    Brenier, Y.2
  • 3
    • 84891636802 scopus 로고    scopus 로고
    • Numerical solution of the optimal transportation problem using the Monge-Ampère equation
    • Benamou J.-D., Froese B.D., Oberman A.M. Numerical solution of the optimal transportation problem using the Monge-Ampère equation. J. Comput. Phys. 2014, 260:107-126.
    • (2014) J. Comput. Phys. , vol.260 , pp. 107-126
    • Benamou, J.-D.1    Froese, B.D.2    Oberman, A.M.3
  • 6
    • 0000474912 scopus 로고
    • Symmetries of the self-dual Einstein equations. 1. The infinite dimensional symmetry group and its low-dimensional subgroups
    • Boyer C.P., Winternitz P. Symmetries of the self-dual Einstein equations. 1. The infinite dimensional symmetry group and its low-dimensional subgroups. J. Math. Phys. 1989, 30:1081-1094.
    • (1989) J. Math. Phys. , vol.30 , pp. 1081-1094
    • Boyer, C.P.1    Winternitz, P.2
  • 7
    • 72649094597 scopus 로고    scopus 로고
    • Magnetic field evolution in simulations with Euler potentials
    • Brandenburg A. Magnetic field evolution in simulations with Euler potentials. Mon. Not. R. Astron. Soc. 2010, 401:347-354.
    • (2010) Mon. Not. R. Astron. Soc. , vol.401 , pp. 347-354
    • Brandenburg, A.1
  • 8
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Brenier Y. Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 1991, 44:375-417.
    • (1991) Commun. Pure Appl. Math. , vol.44 , pp. 375-417
    • Brenier, Y.1
  • 9
    • 0000977352 scopus 로고
    • Hybrid Krylov methods for nonlinear systems of equations
    • Brown P.N., Saad Y. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput. 1990, 11:450-481.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 450-481
    • Brown, P.N.1    Saad, Y.2
  • 10
    • 75749125433 scopus 로고    scopus 로고
    • Moving mesh generation using the parabolic Monge-Ampère equation
    • Budd C.J., Williams J.F. Moving mesh generation using the parabolic Monge-Ampère equation. SIAM J. Sci. Comput. 2009, 31:3438-3465.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 3438-3465
    • Budd, C.J.1    Williams, J.F.2
  • 11
    • 84871994880 scopus 로고    scopus 로고
    • Monge-Ampère based moving mesh methods for numerical weather prediction, with applications to the Eady Problem
    • Budd C.J., Cullen M.J.P., Walsh E.J. Monge-Ampère based moving mesh methods for numerical weather prediction, with applications to the Eady Problem. J. Comput. Phys. 2013, 236:247-270.
    • (2013) J. Comput. Phys. , vol.236 , pp. 247-270
    • Budd, C.J.1    Cullen, M.J.P.2    Walsh, E.J.3
  • 13
    • 14844323740 scopus 로고    scopus 로고
    • Parametric Bäcklund transformations I: phenomenology
    • Clelland J.N., Ivey T.A. Parametric Bäcklund transformations I: phenomenology. Trans. Am. Math. Soc. 2005, 357:1061-1093.
    • (2005) Trans. Am. Math. Soc. , vol.357 , pp. 1061-1093
    • Clelland, J.N.1    Ivey, T.A.2
  • 15
    • 79954917207 scopus 로고    scopus 로고
    • A Monge-Ampère enhancement for semi-Lagrangian methods
    • Cossette J.-F., Smolarkiewicz P.K. A Monge-Ampère enhancement for semi-Lagrangian methods. Comput. Fluids 2011, 46:180-185.
    • (2011) Comput. Fluids , vol.46 , pp. 180-185
    • Cossette, J.-F.1    Smolarkiewicz, P.K.2
  • 18
    • 0026112879 scopus 로고
    • Generalised Lagrangian solutions for atmospheric and oceanic flows
    • Cullen M.J.P., Norbury J., Purser R.J. Generalised Lagrangian solutions for atmospheric and oceanic flows. SIAM J. Appl. Math. 1991, 51:20-31.
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 20-31
    • Cullen, M.J.P.1    Norbury, J.2    Purser, R.J.3
  • 19
    • 18244374488 scopus 로고    scopus 로고
    • MHD unstable modes in the 3D evolution of 2D MHD structures and the diminished role of coalescence instabilities
    • Dahlburg R.B., Einaudi G. MHD unstable modes in the 3D evolution of 2D MHD structures and the diminished role of coalescence instabilities. Phys. Lett. A 2002, 294:101-107.
    • (2002) Phys. Lett. A , vol.294 , pp. 101-107
    • Dahlburg, R.B.1    Einaudi, G.2
  • 20
    • 19944414954 scopus 로고    scopus 로고
    • An explanation for the 'switch-on' nature of magnetic energy release and its application to coronal heating
    • Dahlburg R.B., Klimchuk J.A., Antiochos S.K. An explanation for the 'switch-on' nature of magnetic energy release and its application to coronal heating. Astrophys. J. 2005, 622:1191-1201.
    • (2005) Astrophys. J. , vol.622 , pp. 1191-1201
    • Dahlburg, R.B.1    Klimchuk, J.A.2    Antiochos, S.K.3
  • 21
    • 53349146583 scopus 로고    scopus 로고
    • An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization
    • Delzanno G.L., Chacón L., Finn J.M., Chung Y., Lapenta G. An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization. J. Comput. Phys. 2008, 227:9841-9864.
    • (2008) J. Comput. Phys. , vol.227 , pp. 9841-9864
    • Delzanno, G.L.1    Chacón, L.2    Finn, J.M.3    Chung, Y.4    Lapenta, G.5
  • 22
    • 0038804645 scopus 로고    scopus 로고
    • A balanced approach to modelling rotating stably stratified geophysical flows
    • Dritschel D.G., Viúdez Á. A balanced approach to modelling rotating stably stratified geophysical flows. J. Fluid Mech. 2003, 488:123-150.
    • (2003) J. Fluid Mech. , vol.488 , pp. 123-150
    • Dritschel, D.G.1    Viúdez, Á.2
  • 23
    • 0000011239 scopus 로고
    • Variational iterative methods for nonsymmetric systems of linear equations
    • Eisenstat S.C., Elman H.C., Schultz M.H. Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 1983, 20:345-357.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 345-357
    • Eisenstat, S.C.1    Elman, H.C.2    Schultz, M.H.3
  • 24
    • 0000504721 scopus 로고    scopus 로고
    • Convergence analysis for a class of high-order semi-Lagrangian advection schemes
    • Falcone M., Ferretti R. Convergence analysis for a class of high-order semi-Lagrangian advection schemes. SIAM J. Numer. Anal. 1998, 35:909-940.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 909-940
    • Falcone, M.1    Ferretti, R.2
  • 25
    • 21844523098 scopus 로고
    • On the Monge-Ampère equivalent of the sine-Gordon equation
    • Ferapontov E.V., Nutku Y. On the Monge-Ampère equivalent of the sine-Gordon equation. J. Phys. A, Math. Gen. 1994, 27:7831-7834.
    • (1994) J. Phys. A, Math. Gen. , vol.27 , pp. 7831-7834
    • Ferapontov, E.V.1    Nutku, Y.2
  • 27
    • 78649322125 scopus 로고    scopus 로고
    • Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation
    • Froese B.D., Oberman A.M. Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation. J. Comput. Phys. 2011, 230:818-834.
    • (2011) J. Comput. Phys. , vol.230 , pp. 818-834
    • Froese, B.D.1    Oberman, A.M.2
  • 30
    • 84891678258 scopus 로고    scopus 로고
    • Particle acceleration and transport in reconnecting twisted loops in a stratified atmosphere
    • Gordovskyy M., Browning P.K., Kontar E.P., Bian N.H. Particle acceleration and transport in reconnecting twisted loops in a stratified atmosphere. Astron. Astrophys. 2014, 561:A72.
    • (2014) Astron. Astrophys. , vol.561
    • Gordovskyy, M.1    Browning, P.K.2    Kontar, E.P.3    Bian, N.H.4
  • 34
    • 77957737271 scopus 로고    scopus 로고
    • Topological complexity and tangential discontinuity in magnetic fields
    • 092901
    • Janse Å.M., Low B.C., Parker E.N. Topological complexity and tangential discontinuity in magnetic fields. Phys. Plasmas 2010, 17. 092901.
    • (2010) Phys. Plasmas , vol.17
    • Janse Å, M.1    Low, B.C.2    Parker, E.N.3
  • 36
    • 84889807732 scopus 로고    scopus 로고
    • Magnetohydrodynamic modeling of the solar eruption on 2010 April 8
    • Kliem B., Su Y.N., van Ballegooijen A.A., DeLuca E.E. Magnetohydrodynamic modeling of the solar eruption on 2010 April 8. Astrophys. J. 2013, 779:129.
    • (2013) Astrophys. J. , vol.779 , pp. 129
    • Kliem, B.1    Su, Y.N.2    van Ballegooijen, A.A.3    DeLuca, E.E.4
  • 37
    • 0348198275 scopus 로고    scopus 로고
    • Jacobian-free Newton-Krylov methods: a survey of approaches and applications
    • Knoll D.A., Keyes D.E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 2004, 193:357-397.
    • (2004) J. Comput. Phys. , vol.193 , pp. 357-397
    • Knoll, D.A.1    Keyes, D.E.2
  • 38
  • 39
    • 0001125804 scopus 로고
    • A class of semi-Lagrangian integrated-mass (SLIM) numerical transport algorithms
    • René Laprise J.P., Plante A. A class of semi-Lagrangian integrated-mass (SLIM) numerical transport algorithms. Mon. Weather Rev. 1995, 123:553-565.
    • (1995) Mon. Weather Rev. , vol.123 , pp. 553-565
    • René Laprise, J.P.1    Plante, A.2
  • 40
    • 13844310722 scopus 로고    scopus 로고
    • Numerical solution of the Monge-Ampère equation by a Newton's algorithm
    • Loeper G., Rapetti F. Numerical solution of the Monge-Ampère equation by a Newton's algorithm. C. R. Acad. Sci. Paris, Ser I 2005, 340:319-324.
    • (2005) C. R. Acad. Sci. Paris, Ser I , vol.340 , pp. 319-324
    • Loeper, G.1    Rapetti, F.2
  • 41
    • 33748090243 scopus 로고    scopus 로고
    • Magnetic helicity in a two-flux partitioning of an ideal hydromagnetic fluid
    • Low B.C. Magnetic helicity in a two-flux partitioning of an ideal hydromagnetic fluid. Astrophys. J. 2006, 646:1288-1302.
    • (2006) Astrophys. J. , vol.646 , pp. 1288-1302
    • Low, B.C.1
  • 42
    • 84861891851 scopus 로고    scopus 로고
    • A hybrid method of semi-Lagrangian and additive semi-implicit Runge-Kutta schemes for gyrokinetic Vlasov simulations
    • Maeyama S., Ishizawa A., Watanabe T.-H., Nakajima N., Tsuji-lio S., Tsutsui H. A hybrid method of semi-Lagrangian and additive semi-implicit Runge-Kutta schemes for gyrokinetic Vlasov simulations. J. Comput. Phys. 2012, 183:1986-1992.
    • (2012) J. Comput. Phys. , vol.183 , pp. 1986-1992
    • Maeyama, S.1    Ishizawa, A.2    Watanabe, T.-H.3    Nakajima, N.4    Tsuji-lio, S.5    Tsutsui, H.6
  • 43
    • 0035618489 scopus 로고    scopus 로고
    • Polar factorization of maps on Riemannian manifolds
    • McCann R.J. Polar factorization of maps on Riemannian manifolds. Geom. Funct. Anal. 2001, 11:589-608.
    • (2001) Geom. Funct. Anal. , vol.11 , pp. 589-608
    • McCann, R.J.1
  • 44
    • 0014441553 scopus 로고
    • The degree of knottedness of tangled vortex lines
    • Moffatt H.K. The degree of knottedness of tangled vortex lines. J. Fluid Mech. 1969, 35:117-129.
    • (1969) J. Fluid Mech. , vol.35 , pp. 117-129
    • Moffatt, H.K.1
  • 48
    • 0000373540 scopus 로고
    • Nanoflares and the solar X-ray corona
    • Parker E.N. Nanoflares and the solar X-ray corona. Astrophys. J. 1988, 330:474-479.
    • (1988) Astrophys. J. , vol.330 , pp. 474-479
    • Parker, E.N.1
  • 49
    • 0010676675 scopus 로고
    • Translated from the first Russian edition by F. Leo Boron with the assistance of Albert L. Rabenstein, C. Richard, and P. Bollinger, Noordhoff Ltd., Groningen
    • Pogorelov A.V. Monge-Ampère equations of elliptic type 1964, Translated from the first Russian edition by F. Leo Boron with the assistance of Albert L. Rabenstein, C. Richard, and P. Bollinger, Noordhoff Ltd., Groningen.
    • (1964) Monge-Ampère equations of elliptic type
    • Pogorelov, A.V.1
  • 50
    • 0001580414 scopus 로고
    • Coalescence of magnetic islands
    • Pritchett P.L., Wu C.C. Coalescence of magnetic islands. Phys. Fluids 1979, 22:2140-2146.
    • (1979) Phys. Fluids , vol.22 , pp. 2140-2146
    • Pritchett, P.L.1    Wu, C.C.2
  • 51
    • 0141626774 scopus 로고    scopus 로고
    • An all-scale anelastic model for geophysical flows: dynamic grid deformation
    • Prusa J.M., Smolarkiewicz P.K. An all-scale anelastic model for geophysical flows: dynamic grid deformation. J. Comput. Phys. 2003, 190:601-622.
    • (2003) J. Comput. Phys. , vol.190 , pp. 601-622
    • Prusa, J.M.1    Smolarkiewicz, P.K.2
  • 53
    • 42649139227 scopus 로고    scopus 로고
    • Nonlinear dynamics of the Parker scenario for coronal heating
    • Rappazzo A.F., Velli M., Einaudi G., Dahlburg R.B. Nonlinear dynamics of the Parker scenario for coronal heating. Astrophys. J. 2008, 677:1348-1366.
    • (2008) Astrophys. J. , vol.677 , pp. 1348-1366
    • Rappazzo, A.F.1    Velli, M.2    Einaudi, G.3    Dahlburg, R.B.4
  • 54
    • 0030268964 scopus 로고    scopus 로고
    • A synchronous and iterative flux-correction formalism for coupled transport equations
    • Schär C., Smolarkiewicz P.K. A synchronous and iterative flux-correction formalism for coupled transport equations. J. Comput. Phys. 1996, 128:101-120.
    • (1996) J. Comput. Phys. , vol.128 , pp. 101-120
    • Schär, C.1    Smolarkiewicz, P.K.2
  • 55
    • 0031249990 scopus 로고    scopus 로고
    • Coalescence of magnetic islands including anomalous resistivity
    • Schumacher J., Kliem B. Coalescence of magnetic islands including anomalous resistivity. Phys. Plasmas 1997, 4:3533-3543.
    • (1997) Phys. Plasmas , vol.4 , pp. 3533-3543
    • Schumacher, J.1    Kliem, B.2
  • 56
    • 84873129383 scopus 로고    scopus 로고
    • EULAG, a computational model for multiscale flows: an MHD extension
    • Smolarkiewicz P.K., Charbonneau P. EULAG, a computational model for multiscale flows: an MHD extension. J. Comput. Phys. 2013, 236:608-623.
    • (2013) J. Comput. Phys. , vol.236 , pp. 608-623
    • Smolarkiewicz, P.K.1    Charbonneau, P.2
  • 57
    • 33645523038 scopus 로고    scopus 로고
    • Multidimensional positive definite advection transport algorithm: an overview
    • Smolarkiewicz P.K. Multidimensional positive definite advection transport algorithm: an overview. Int. J. Numer. Methods Fluids 2006, 50:1123-1144.
    • (2006) Int. J. Numer. Methods Fluids , vol.50 , pp. 1123-1144
    • Smolarkiewicz, P.K.1
  • 58
    • 0027010079 scopus 로고
    • A class of semi-Lagrangian approximations for fluids
    • Smolarkiewicz P.K., Pudykiewicz J.A. A class of semi-Lagrangian approximations for fluids. J. Atmos. Sci. 1992, 49:2082-2096.
    • (1992) J. Atmos. Sci. , vol.49 , pp. 2082-2096
    • Smolarkiewicz, P.K.1    Pudykiewicz, J.A.2
  • 59
    • 0000686029 scopus 로고
    • A class of monotone interpolation schemes
    • Smolarkiewicz P.K., Grell G.A. A class of monotone interpolation schemes. J. Comput. Phys. 1992, 101:431-440.
    • (1992) J. Comput. Phys. , vol.101 , pp. 431-440
    • Smolarkiewicz, P.K.1    Grell, G.A.2
  • 60
    • 39549091901 scopus 로고    scopus 로고
    • Aspects of the dynamical core of a nonhydrostatic, deep-atmosphere, unified weather and climate-prediction model
    • Staniforth A., Wood N. Aspects of the dynamical core of a nonhydrostatic, deep-atmosphere, unified weather and climate-prediction model. J. Comput. Phys. 2008, 227:3445-3464.
    • (2008) J. Comput. Phys. , vol.227 , pp. 3445-3464
    • Staniforth, A.1    Wood, N.2
  • 61
    • 0026291228 scopus 로고
    • Semi-Lagrangian integration schemes for atmospheric models - A review
    • Staniforth A., CÔté J. Semi-Lagrangian integration schemes for atmospheric models - A review. Month. Weather Rev. 1991, 119:2206-2223.
    • (1991) Month. Weather Rev. , vol.119 , pp. 2206-2223
    • Staniforth, A.1    Côté, J.2
  • 62
    • 0346156219 scopus 로고    scopus 로고
    • Semi-Lagrangian methods for level set equations
    • Strain J. Semi-Lagrangian methods for level set equations. J. Comput. Phys. 1999, 151:498-533.
    • (1999) J. Comput. Phys. , vol.151 , pp. 498-533
    • Strain, J.1
  • 63
    • 79952444448 scopus 로고    scopus 로고
    • Optimal mass transport for higher dimensional adaptive grid generation
    • Sulman M., Williams J.F., Russell R.D. Optimal mass transport for higher dimensional adaptive grid generation. J. Comput. Phys. 2011, 230:3302-3330.
    • (2011) J. Comput. Phys. , vol.230 , pp. 3302-3330
    • Sulman, M.1    Williams, J.F.2    Russell, R.D.3
  • 64
    • 0031446633 scopus 로고    scopus 로고
    • On the second boundary value problem for equations of Monge-Ampère type
    • Urbas J. On the second boundary value problem for equations of Monge-Ampère type. J. Reine Angew. Math. 1997, 487:115-124.
    • (1997) J. Reine Angew. Math. , vol.487 , pp. 115-124
    • Urbas, J.1
  • 65
    • 0242667030 scopus 로고    scopus 로고
    • Spectral preconditioners for nonhydrostatic atmospheric models
    • Thomas S.J., Hacker J.P., Smolarkiewicz P.K. Spectral preconditioners for nonhydrostatic atmospheric models. Month. Weather Rev. 2003, 131:2464-2478.
    • (2003) Month. Weather Rev. , vol.131 , pp. 2464-2478
    • Thomas, S.J.1    Hacker, J.P.2    Smolarkiewicz, P.K.3
  • 66
    • 66149192495 scopus 로고    scopus 로고
    • On the second boundary value problem for Monge-Ampère type equations and optimal transportation
    • Trudinger N.S., Wang X.-J. On the second boundary value problem for Monge-Ampère type equations and optimal transportation. Ann. Sc. Norm. Super. Pisa, Cl. Sci. 2009, 8:143-174.
    • (2009) Ann. Sc. Norm. Super. Pisa, Cl. Sci. , vol.8 , pp. 143-174
    • Trudinger, N.S.1    Wang, X.-J.2
  • 68
    • 84877698627 scopus 로고    scopus 로고
    • Propagation of plasmoids generated by fast reconnection in the geomagnetic tail
    • Ugai M. Propagation of plasmoids generated by fast reconnection in the geomagnetic tail. J. Atmos. Sol.-Terr. Phys. 2013, 99:47-52.
    • (2013) J. Atmos. Sol.-Terr. Phys. , vol.99 , pp. 47-52
    • Ugai, M.1
  • 69
    • 84861783562 scopus 로고    scopus 로고
    • A simple and conservative operator-splitting semi-Lagrangian volume-of-fluid advection scheme
    • Wang Z., Yang J., Stern F. A simple and conservative operator-splitting semi-Lagrangian volume-of-fluid advection scheme. J. Comput. Phys. 2012, 231:4981-4992.
    • (2012) J. Comput. Phys. , vol.231 , pp. 4981-4992
    • Wang, Z.1    Yang, J.2    Stern, F.3
  • 70
    • 0035922242 scopus 로고    scopus 로고
    • A semi-Lagrangian high-order method for Navier-Stokes equations
    • Xiu D.B., Karniadakis G.E. A semi-Lagrangian high-order method for Navier-Stokes equations. J. Comput. Phys. 2001, 172:658-684.
    • (2001) J. Comput. Phys. , vol.172 , pp. 658-684
    • Xiu, D.B.1    Karniadakis, G.E.2
  • 71
    • 84862858107 scopus 로고    scopus 로고
    • Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz
    • Yuan X., Jardin S.C., Keyes D.E. Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz. J. Comput. Phys. 2012, 231:5822-5853.
    • (2012) J. Comput. Phys. , vol.231 , pp. 5822-5853
    • Yuan, X.1    Jardin, S.C.2    Keyes, D.E.3
  • 72
    • 84866180020 scopus 로고    scopus 로고
    • A three-dimensional monotone and conservative semi-Lagrangian scheme (SLICE-3D) for transport problems
    • Zerroukat M., Allen T. A three-dimensional monotone and conservative semi-Lagrangian scheme (SLICE-3D) for transport problems. Q. J. R. Meteorol. Soc. 2012, 138:1640-1651.
    • (2012) Q. J. R. Meteorol. Soc. , vol.138 , pp. 1640-1651
    • Zerroukat, M.1    Allen, T.2
  • 73
    • 77952420856 scopus 로고    scopus 로고
    • The Monge-Ampère equation: various forms and numerical solution
    • Zheligovsky V., Podvigina O., Frisch U. The Monge-Ampère equation: various forms and numerical solution. J. Comput. Phys. 2010, 229:5043-5061.
    • (2010) J. Comput. Phys. , vol.229 , pp. 5043-5061
    • Zheligovsky, V.1    Podvigina, O.2    Frisch, U.3


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