## Multiscale Modeling & Simulation

### A SIAM Interdisciplinary Journal

 Short Title: Multiscale Model. Simul. Publisher: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA ISSN: 1540-3459; 1540-3467/e Online: http://epubs.siam.org/loi/mmsubt Comments: Indexed cover-to-cover
 Documents Indexed: 1,092 Publications (since 2003) References Indexed: 487 Publications with 19,280 References.
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### Latest Issues

 20, No. 3 (2022) 20, No. 2 (2022) 20, No. 1 (2022) 19, No. 4 (2021) 19, No. 3 (2021) 19, No. 2 (2021) 19, No. 1 (2021) 18, No. 4 (2020) 18, No. 3 (2020) 18, No. 2 (2020) 18, No. 1 (2020) 17, No. 4 (2019) 17, No. 3 (2019) 17, No. 2 (2019) 17, No. 1 (2019) 16, No. 4 (2018) 16, No. 3 (2018) 16, No. 2 (2018) 16, No. 1 (2018) 15, No. 4 (2017) 15, No. 2 (2017) 15, No. 1 (2017) 14, No. 4 (2016) 14, No. 3 (2016) 14, No. 2 (2016) 14, No. 1 (2016) 13, No. 4 (2015) 13, No. 3 (2015) 13, No. 2 (2015) 13, No. 1 (2015) 12, No. 4 (2014) 12, No. 3 (2014) 12, No. 2 (2014) 12, No. 1 (2014) 11, No. 4 (2013) 11, No. 3 (2013) 11, No. 2 (2013) 11, No. 1 (2013) 10, No. 4 (2012) 10, No. 3 (2012) 10, No. 2 (2012) 10, No. 1 (2012) 9, No. 4 (2011) 9, No. 3 (2011) 9, No. 2 (2011) 9, No. 1 (2011) 8, No. 5 (2010) 8, No. 4 (2010) 8, No. 3 (2010) 8, No. 2 (2010) 8, No. 1 (2009) 7, No. 4 (2009) 7, No. 3 (2008/2009) 7, No. 2 (2008) 7, No. 1 (2008) 6, No. 4 (2008) 6, No. 3 (2007) 6, No. 2 (2007) 6, No. 1 (2007) 5, No. 4 (2006) 5, No. 3 (2006) 5, No. 2 (2006) 5, No. 1 (2006) 4, No. 4 (2005/2006) 4, No. 3 (2005) 4, No. 2 (2005) 4, No. 1 (2005) 3, No. 4 (2005) 3, No. 3 (2005) 3, No. 2 (2005) 3, No. 1 (2004/2005) 2, No. 4 (2004) 2, No. 3 (2004) 2, No. 2 (2004) 2, No. 1 (2004) 1, No. 4 (2003) 1, No. 3 (2003) 1, No. 2 (2003) 1, No. 1 (2003)
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### Authors

 21 Ying, Lexing 18 Efendiev, Yalchin R. 17 Garnier, Josselin 15 Schütte, Christof 14 Hou, Thomas Yizhao 14 Sølna, Knut 13 Degond, Pierre 13 Luskin, Mitchell 12 Ortner, Christoph 11 Abdulle, Assyr 11 Borcea, Liliana 11 Osher, Stanley Joel 10 Ammari, Habib M. 10 Chung, Tsz Shun Eric 10 Lu, Jianfeng 9 Jin, Shi 9 Margetis, Dionisios 9 Vanden-Eijnden, Eric 8 Caselles Costa, Vicent 8 Forest, Mark Gregory 8 Kevrekidis, Ioannis George 8 Weinstein, Michael I. 8 Wheeler, Mary Fanett 7 Bal, Guillaume 7 Cao, Liqun 7 Engquist, Bjorn E. 7 Horenko, Illia 7 Jiang, Lijian 7 Li, Qin 7 Lin, Lin 7 Mikelić, Andro 7 Noé, Frank 7 Papanicolaou, George C. 7 Shapeev, Alexander V. 7 Sini, Mourad 7 Spiliopoulos, Konstantinos V. 6 Bressloff, Paul C. 6 Du, Qiang 6 Holcman, David 6 Le Bris, Claude 6 Legoll, Frédéric 6 Majda, Andrew J. 6 Målqvist, Axel 6 Mucha, Peter J. 6 Negulescu, Claudia 6 Peterseim, Daniel 6 Qian, Jianliang 6 Voigt, Axel 6 Weber, Marcus 6 Xin, Jack X. 6 Zhang, Pingwen 5 Caflisch, Russel E. 5 Chen, Huajie 5 Chen, Jingrun 5 Fackeldey, Konstantin 5 Fouque, Jean-Pierre 5 Galvis, Juan 5 Gunzburger, Max D. 5 Higham, Desmond J. 5 Li, Guanglian 5 Ming, Pingbing 5 Movchan, Alexander B. 5 Najm, Habib N. 5 Ortiz, Michael 5 Owhadi, Houman 5 Pavliotis, Grigorios A. 5 Salloum, Maher 5 Sargsyan, Khachik V. 5 Shen, Zuowei 5 Stuart, Andrew M. 5 Tsai, Yen-Hsi Richard 5 Ward, Michael J. 5 Yang, Haizhao 5 Zhang, Zhiwen 4 Aarnes, Jørg E. 4 Aristoff, David 4 Aujol, Jean-François 4 Brown, Donald L. 4 Burger, Martin 4 Burridge, Robert 4 Carrillo de la Plata, José Antonio 4 Chen, Ke 4 Craster, Richard V. 4 Cushman, John H. 4 Dagan, Gedeon 4 Damle, Anil 4 Debusschere, Bert J. 4 Deluzet, Fabrice 4 Dimarco, Giacomo 4 Fiori, Aldo 4 Friesecke, Gero 4 Ho, Kenneth L. 4 Jankovic, Igor 4 Kang, Hyeonbae 4 Kutz, J. Nathan 4 Lawley, Sean D. 4 Lehoucq, Richard B. 4 Leung, Wingtat 4 Li, Ruo 4 Li, Tiejun ...and 1,696 more Authors
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### Fields

 545 Numerical analysis (65-XX) 516 Partial differential equations (35-XX) 242 Fluid mechanics (76-XX) 208 Probability theory and stochastic processes (60-XX) 186 Statistical mechanics, structure of matter (82-XX) 168 Mechanics of deformable solids (74-XX) 134 Biology and other natural sciences (92-XX) 84 Optics, electromagnetic theory (78-XX) 75 Statistics (62-XX) 68 Ordinary differential equations (34-XX) 63 Computer science (68-XX) 57 Dynamical systems and ergodic theory (37-XX) 57 Information and communication theory, circuits (94-XX) 51 Calculus of variations and optimal control; optimization (49-XX) 41 Quantum theory (81-XX) 34 Operations research, mathematical programming (90-XX) 31 Mechanics of particles and systems (70-XX) 30 Systems theory; control (93-XX) 26 Geophysics (86-XX) 23 Harmonic analysis on Euclidean spaces (42-XX) 23 Classical thermodynamics, heat transfer (80-XX) 16 Approximations and expansions (41-XX) 16 Integral equations (45-XX) 13 Operator theory (47-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Combinatorics (05-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Potential theory (31-XX) 5 Astronomy and astrophysics (85-XX) 4 Real functions (26-XX) 4 Functional analysis (46-XX) 4 Differential geometry (53-XX) 3 Measure and integration (28-XX) 3 Functions of a complex variable (30-XX) 3 Integral transforms, operational calculus (44-XX) 2 General and overarching topics; collections (00-XX) 2 Algebraic geometry (14-XX) 1 Difference and functional equations (39-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

911 Publications have been cited 11,278 times in 7,661 Documents Cited by Year
Signal recovery by proximal forward-backward splitting. Zbl 1179.94031
Combettes, Patrick L.; Wajs, Valérie R.
2005
A review of image denoising algorithms, with a new one. Zbl 1108.94004
Buades, A.; Coll, B.; Morel, J. M.
2005
Nonlocal operators with applications to image processing. Zbl 1181.35006
Gilboa, Guy; Osher, Stanley
2008
An iterative regularization method for total variation-based image restoration. Zbl 1090.94003
Osher, Stanley; Burger, Martin; Goldfarb, Donald; Xu, Jinjun; Yin, Wotao
2005
Split Bregman methods and frame based image restoration. Zbl 1189.94014
Cai, Jian-Feng; Osher, Stanley; Shen, Zuowei
2010
Image decomposition and restoration using total variation minimization and the $$H^{-1}$$ norm. Zbl 1051.49026
Osher, Stanley; Solé, Andrés; Vese, Luminita
2003
A multiscale mortar mixed finite element method. Zbl 1322.76039
Arbogast, Todd; Pencheva, Gergina; Wheeler, Mary F.; Yotov, Ivan
2007
Fast discrete curvelet transforms. Zbl 1122.65134
Candès, Emmanuel; Demanet, Laurent; Donoho, David; Ying, Lexing
2006
Domain decomposition preconditioners for multiscale flows in high-contrast media. Zbl 1206.76042
Galvis, Juan; Efendiev, Yalchin
2010
Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers. Zbl 1228.65234
Engquist, Björn; Ying, Lexing
2011
Nonlocal linear image regularization and supervised segmentation. Zbl 1140.68517
Gilboa, Guy; Osher, Stanley
2007
Domain decomposition preconditioners for multiscale flows in high contrast media: reduced dimension coarse spaces. Zbl 1381.65029
Galvis, Juan; Efendiev, Yalchin
2010
On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Zbl 1181.76125
Aarnes, Jørg E.
2004
Deblurring and denoising of images by nonlocal functionals. Zbl 1161.68827
Kindermann, Stefan; Osher, Stanley; Jones, Peter W.
2005
Ground states and dynamics of multicomponent Bose-Einstein condensates. Zbl 1062.82034
Bao, Weizhu
2004
Multiscale stochastic volatility asymptotics. Zbl 1074.91015
Fouque, Jean-Pierre; Papanicolaou, George; Sircar, Ronnie; Solna, Knut
2004
Optimal local approximation spaces for generalized finite element methods with application to multiscale problems. Zbl 1229.65195
Babuska, Ivo; Lipton, Robert
2011
Adaptive multiscale finite-volume method for multiphase flow and transport in porous media. Zbl 1160.76372
Jenny, P.; Lee, S. H.; Tchelepi, H. A.
2004
Mixed generalized multiscale finite element methods and applications. Zbl 1317.65204
Chung, Eric T.; Efendiev, Yalchin; Lee, Chak Shing
2015
A nonlocal vector calculus with application to nonlocal boundary value problems. Zbl 1210.35057
Gunzburger, Max; Lehoucq, R. B.
2010
A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium. Zbl 1317.74028
Mikelić, Andro; Wheeler, Mary F.; Wick, Thomas
2015
Oversampling for the multiscale finite element method. Zbl 1297.65155
Henning, Patrick; Peterseim, Daniel
2013
Multiscale modeling of granular flows with application to crowd dynamics. Zbl 1221.35232
Cristiani, Emiliano; Piccoli, Benedetto; Tosin, Andrea
2011
A posteriori control of modeling errors and discretization errors. Zbl 1050.65100
Braack, Malte; Ern, Alexandre
2003
On a priori error analysis of fully discrete heterogeneous multiscale FEM. Zbl 1092.65093
Abdulle, Assyr
2005
Extinction times for birth-death processes: Exact results, continuum asymptotics, and the failure of the Fokker-Planck approximation. Zbl 1072.60092
Doering, Charles R.; Sargsyan, Khachik V.; Sander, Leonard M.
2005
Bayesian numerical homogenization. Zbl 1322.35002
2015
Multiscale representations for manifold-valued data. Zbl 1236.65166
Rahman, Inam Ur; Drori, Iddo; Stodden, Victoria C.; Donoho, David L.; Schröder, Peter
2005
A fast total variation minimization method for image restoration. Zbl 1172.94316
Huang, Yumei; Ng, Michael K.; Wen, You-Wei
2008
A multiscale finite element method for numerical homogenization. Zbl 1093.35007
Allaire, Grégoire; Brizzi, Robert
2005
Analysis of the recovery of edges in images and signals by minimizing nonconvex regularized least-squares. Zbl 1091.94007
Nikolova, Mila
2005
From signal transduction to spatial pattern formation in E. coli: A paradigm for multiscale modeling in biology. Zbl 1073.35205
2005
A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids. Zbl 1124.76022
Aarnes, Jørg E.; Krogstad, Stein; Lie, Knut-Andreas
2006
The discontinuity set of solutions of the TV denoising problem and some extensions. Zbl 1145.49024
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2007
A MUSIC algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency. Zbl 1075.35101
Ammari, Habib; Iakovleva, Ekaterina; Lesselier, Dominique
2005
Generalized multiscale finite element methods for wave propagation in heterogeneous media. Zbl 1315.65085
Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat
2014
A multiscale image representation using hierarchical $$(BV,L^2)$$ decompositions. Zbl 1146.68472
Tadmor, Eitan; Nezzar, Suzanne; Vese, Luminita
2004
Gas pipeline models revisited: model hierarchies, nonisothermal models, and simulations of networks. Zbl 1254.76124
Brouwer, Jens; Gasser, Ingenuin; Herty, Michael
2011
Analysis of a geometrical multiscale model based on the coupling of ODEs and PDEs for blood flow simulations. Zbl 1060.35003
Quarteroni, Alfio; Veneziani, Alessandro
2003
Diffuse interface models on graphs for classification of high dimensional data. Zbl 1259.68215
Bertozzi, Andrea L.; Flenner, Arjuna
2012
Peridynamics as an upscaling of molecular dynamics. Zbl 1375.82073
Seleson, Pablo; Parks, Michael L.; Gunzburger, Max; Lehoucq, Richard B.
2009
Crystal precipitation and dissolution in a porous medium: Effective equations and numerical experiments. Zbl 1176.35020
van Noorden, T. L.
2009
Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235
Luo, Guo; Hou, Thomas Y.
2014
Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics. Zbl 1262.60072
Anderson, David F.; Higham, Desmond J.
2012
Analysis of a two-scale Cahn-Hilliard model for binary image inpainting. Zbl 1149.35309
Bertozzi, Andrea; Esedoḡlu, Selim; Gillette, Alan
2007
High-dimensional finite elements for elliptic problems with multiple scales. Zbl 1074.65135
Viet Ha Hoang; Schwab, Christoph
2005
An asymptotic analysis of the mean first passage time for narrow escape problems. I: Two-dimensional domains. Zbl 1203.35023
Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T.
2010
Randomized oversampling for generalized multiscale finite element methods. Zbl 1337.65148
Calo, Victor M.; Efendiev, Yalchin; Galvis, Juan; Li, Guanglian
2016
From the microscale to collective crowd dynamics. Zbl 1280.90019
Bellomo, Nicola; Bellouquid, Abdelghani; Knopoff, Damian
2013
A multiple scale model for tumor growth. Zbl 1107.92019
Alarcón, T.; Byrne, H. M.; Maini, P. K.
2005
Learning multiscale sparse representations for image and video restoration. Zbl 1194.49041
Mairal, Julien; Sapiro, Guillermo; Elad, Michael
2008
A fast butterfly algorithm for the computation of Fourier integral operators. Zbl 1184.65125
Candès, Emmanuel; Demanet, Laurent; Ying, Lexing
2009
Localized bases for finite-dimensional homogenization approximations with nonseparated scales and high contrast. Zbl 1244.65140
2011
Boundary problems for the fractional and tempered fractional operators. Zbl 1391.60104
Deng, Weihua; Li, Buyang; Tian, Wenyi; Zhang, Pingwen
2018
Strong convergence rate for two-time-scale jump-diffusion stochastic differential systems. Zbl 1144.60038
Givon, Dror
2007
Capturing small scales in elliptic problems using a residual-free bubbles finite element method. Zbl 1032.65131
Sangalli, Giancarlo
2003
Binary interaction algorithms for the simulation of flocking and swarming dynamics. Zbl 1274.92053
Albi, G.; Pareschi, L.
2013
Locating multiple multiscale acoustic scatterers. Zbl 1328.35135
Li, Jingzhi; Liu, Hongyu; Zou, Jun
2014
On atomistic-to-continuum coupling by blending. Zbl 1160.65338
Badia, Santiago; Parks, Michael; Bochev, Pavel; Gunzburger, Max; Lehoucq, Richard
2008
Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems. Zbl 1175.60058
Coifman, R. R.; Kevrekidis, I. G.; Lafon, S.; Maggioni, M.; Nadler, B.
2008
Numerical homogenization of nonlinear random parabolic operators. Zbl 1181.76113
Efendiev, Y.; Pankov, A.
2004
Fast and slow dynamics for the computational singular perturbation method. Zbl 1065.34049
Zagaris, Antonios; Kaper, Hans G.; Kaper, Tasso J.
2004
A rate-independent model for inelastic behavior of shape-memory alloys. Zbl 1183.74207
Mielke, Alexander; Roubíček, Tomáš
2003
A BDDC algorithm with enriched coarse spaces for two-dimensional elliptic problems with oscillatory and high contrast coefficients. Zbl 1317.65090
Kim, Hyea Hyun; Chung, Eric T.
2015
An asymptotic analysis of the mean first passage time for narrow escape problems. II: The sphere. Zbl 1204.35030
Cheviakov, Alexei F.; Ward, Michael J.; Straube, Ronny
2010
Reduced-basis approach for homogenization beyond the periodic setting. Zbl 1156.74358
Boyaval, Sébastien
2008
Transition path theory for Markov jump processes. Zbl 1185.60086
Metzner, Philipp; Schütte, Christof; Vanden-Eijnden, Eric
2009
Eigenfracture: an eigendeformation approach to variational fracture. Zbl 1173.74040
Schmidt, Bernd; Fraternali, Fernando; Ortiz, Michael
2009
A Lagrangian particle-wavelet method. Zbl 1122.65085
Bergdorf, Michael; Koumoutsakos, Petros
2006
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
2008
Multilevel adaptive particle methods for convection-diffusion equations. Zbl 1088.76055
Bergdorf, Michael; Cottet, Georges-Henri; Koumoutsakos, Petros
2005
Numerical homogenization of elliptic multiscale problems by subspace decomposition. Zbl 1352.65521
Kornhuber, Ralf; Yserentant, Harry
2016
Phase transitions in a kinetic flocking model of Cucker-Smale type. Zbl 1356.35260
Barbaro, Alethea B. T.; Cañizo, José A.; Carrillo, José A.; Degond, Pierre
2016
Homogenization of Maxwell’s equations in a split ring geometry. Zbl 1228.35028
Bouchitté, Guy; Schweizer, Ben
2010
A framework for adaptive multiscale methods for elliptic problems. Zbl 1160.65342
Nolen, James; Papanicolaou, George; Pironneau, Olivier
2008
Well modeling in the multiscale finite volume method for subsurface flow simulation. Zbl 1205.76175
Wolfsteiner, Christian; Lee, Seong H.; Tchelepi, Hamdi A.
2006
Hybrid multiscale methods. II: Kinetic equations. Zbl 1185.65198
Dimarco, Giacomo; Pareschi, Lorenzo
2008
Implicit-explicit variational integration of highly oscillatory problems. Zbl 1185.65227
Stern, Ari; Grinspun, Eitan
2009
Heterogeneous multiscale FEM for diffusion problems on rough surfaces. Zbl 1160.65337
Abdulle, Assyr; Schwab, Christoph
2005
Multiscale two-dimensional modeling of a motile simple-shaped cell. Zbl 1068.92005
Rubinstein, B.; Jacobson, K.; Mogilner, A.
2005
A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems. Zbl 1090.65128
Ohlberger, Mario
2005
A fourth-order variational image registration model and its fast multigrid algorithm. Zbl 1218.65022
Chumchob, N.; Chen, K.; Brito-Loeza, Carlos
2011
Nonintrusive and structure preserving multiscale integration of stiff ODEs, SDEs, and Hamiltonian systems with hidden slow dynamics via flow averaging. Zbl 1215.65187
Tao, Molei; Owhadi, Houman; Marsden, Jerrold E.
2010
An MsFEM type approach for perforated domains. Zbl 1316.35021
Le Bris, Claude; Legoll, Frédéric; Lozinski, Alexei
2014
Analysis of explicit tau-leaping schemes for simulating chemically reacting systems. Zbl 1145.92041
Li, Tiejun
2007
Analysis of a geometrical multiscale blood flow model based on the coupling of ODEs and hyperbolic PDEs. Zbl 1085.35095
Fernández, Miguel Ángel; Milisic, Vuk; Quarteroni, Alfio
2005
Image decomposition using total variation and $$\text{div}(\text{BMO})$$. Zbl 1093.94006
Le, Triet M.; Vese, Luminita A.
2005
Finite element heterogeneous multiscale method for the wave equation. Zbl 1298.65145
Abdulle, Assyr; Grote, Marcus J.
2011
An asymptotic preserving scheme for strongly anisotropic elliptic problems. Zbl 1190.35216
Degond, Pierre; Deluzet, Fabrice; Negulescu, Claudia
2010
Existence of global weak solutions to some regularized kinetic models for dilute polymers. Zbl 1228.76004
Barrett, John W.; Süli, Endre
2007
Matching of asymptotic expansions for wave propagation in media with thin slots I: The asymptotic expansion. Zbl 1132.35347
Joly, Patrick; Tordeux, Sébastien
2006
Bloch-wave homogenization on large time scales and dispersive effective wave equations. Zbl 1320.35043
Dohnal, T.; Lamacz, A.; Schweizer, B.
2014
Homogenization of immiscible compressible two-phase flow in porous media: application to gas migration in a nuclear waste repository. Zbl 1215.35024
Amaziane, B.; Antontsev, S.; Pankratov, L.; Piatnitski, A.
2010
Blow-up of solutions to a $$p$$-Laplace equation. Zbl 1261.35137
Gorb, Yuliya; Novikov, Alexei
2012
Finite element heterogeneous multiscale method for the wave equation: long-time effects. Zbl 1315.65084
Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian
2014
The total variation regularized $$L^1$$ model for multiscale decomposition. Zbl 1355.49037
Yin, Wotao; Goldfarb, Donald; Osher, Stanley
2007
Consistent energy-based atomistic/continuum coupling for two-body potentials in one and two dimensions. Zbl 1246.74065
Shapeev, Alexander V.
2011
Two-dimensional bulk microflow simulations based on regularized grad’s 13-moment equations. Zbl 1388.76340
Torrilhon, Manuel
2006
An analytical framework for the numerical homogenization of monotone elliptic operators and quasiconvex energies. Zbl 1119.74038
Gloria, Antoine
2006
The TVL1 model: a geometric point of view. Zbl 1187.94010
Duval, Vincent; Aujol, Jean-François; Gousseau, Yann
2009
On asymptotic preserving schemes for a class of stochastic differential equations in averaging and diffusion approximation regimes. Zbl 1481.65019
Bréhier, Charles-Edouard; Rakotonirina-Ricquebourg, Shmuel
2022
Upscaling errors in heterogeneous multiscale methods for the Landau-Lifshitz equation. Zbl 1482.65168
Leitenmaier, Lena; Runborg, Olof
2022
A semi-Lagrangian computation of front speeds of G-equation in ABC and Kolmogorov flows with estimation via ballistic orbits. Zbl 1482.76064
Kao, Chou; Liu, Yu-Yu; Xin, Jack
2022
Analysis and optimization of certain parallel Monte Carlo methods in the low temperature limit. Zbl 1484.60030
Dupuis, Paul; Wu, Guo-Jhen
2022
Approximative policy iteration for exit time feedback control problems driven by stochastic differential equations using tensor train format. Zbl 07540470
Fackeldey, Konstantin; Oster, Mathias; Sallandt, Leon; Schneider, Reinhold
2022
Enriched nonconforming multiscale finite element method for Stokes flows in heterogeneous media based on high-order weighting functions. Zbl 1487.65179
Feng, Qingqing; Allaire, Gregoire; Omnes, Pascal
2022
Multiscale invariants of Floquet topological insulators. Zbl 1487.35337
Bal, Guillaume; Massatt, Daniel
2022
Optimal local approximation spaces for parabolic problems. Zbl 1487.65157
Schleuß, Julia; Smetana, Kathrin
2022
Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity. Zbl 1461.65067
Schäfer, Florian; Sullivan, T. J.; Owhadi, Houman
2021
Uniform error bounds of an exponential wave integrator for the long-time dynamics of the nonlinear Klein-Gordon equation. Zbl 07382150
Feng, Yue; Yi, Wenfan
2021
Exponential convergence for multiscale linear elliptic PDEs via adaptive edge basis functions. Zbl 1473.65296
Chen, Yifan; Hou, Thomas Y.; Wang, Yixuan
2021
A hybrid finite-volume, discontinuous Galerkin discretization for the radiative transport equation. Zbl 1453.82099
Heningburg, Vincent; Hauck, Cory D.
2021
Weak SINDy: Galerkin-based data-driven model selection. Zbl 07411447
Messenger, Daniel A.; Bortz, David M.
2021
Wavelet-based edge multiscale finite element method for Helmholtz problems in perforated domains. Zbl 1478.65124
Fu, Shubin; Li, Guanglian; Craster, Richard; Guenneau, Sebastien
2021
Homogenization of two-phase flow in porous media from pore to Darcy scale: a phase-field approach. Zbl 1462.35045
Metzger, Stefan; Knabner, Peter
2021
An asymptotic representation formula for scattering by thin tubular structures and an application in inverse scattering. Zbl 1470.35128
Capdeboscq, Yves; Griesmaier, Roland; Knöller, Marvin
2021
Mixed finite element approximation of periodic Hamilton-Jacobi-Bellman problems with application to numerical homogenization. Zbl 07382143
Gallistl, Dietmar; Sprekeler, Timo; Süli, Endre
2021
An inverse random source problem for Maxwell’s equations. Zbl 1453.78006
Li, Peijun; Wang, Xu
2021
Singular limit for reactive diffusive transport through an array of thin channels in case of critical diffusivity. Zbl 1481.35033
2021
High contrast elliptic operators in honeycomb structures. Zbl 1481.35291
Cassier, Maxence; Weinstein, Michael I.
2021
Hierarchical model reduction techniques for flow modeling in a parametrized setting. Zbl 1468.65209
Zancanaro, Matteo; Ballarin, Francesco; Perotto, Simona; Rozza, Gianluigi
2021
Sharp error estimates on a stochastic structure-preserving scheme In computing effective diffusivity of 3D chaotic flows. Zbl 07382148
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen
2021
Approximate optimal controls via instanton expansion for low temperature free energy computation. Zbl 1475.49027
Ferré, Grégoire; Grafke, Tobias
2021
Optimal convergence rates for elliptic homogenization problems in nondivergence-form: analysis and numerical illustrations. Zbl 1475.35030
Sprekeler, Timo; Tran, Hung V.
2021
Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs. Zbl 1480.92096
Kostré, Margarita; Schütte, Christof; Noé, Frank; del Razo, Mauricio J.
2021
Explicit and energy-conserving constraint energy minimizing generalized multiscale discontinuous Galerkin method for wave propagation in heterogeneous media. Zbl 1478.65083
Cheung, Siu Wun; Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat
2021
On continuum approximations of discrete-state Markov processes of large system size. Zbl 1465.60068
Lunz, Davin
2021
Variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system. Zbl 1467.82071
Carrillo, Jose A.; Wang, Li; Xu, Wuzhe; Yan, Ming
2021
Mathematical proof of the Mandel-Cryer effect in poroelasticity. Zbl 1464.35344
van Duijn, Cornelis J.; Mikelic, Andro
2021
Diffusive limit of a two-dimensional well-balanced scheme for the free Klein-Kramers equation. Zbl 1462.35400
Gosse, Laurent
2021
Multiscale control of generic second order traffic models by driver-assist vehicles. Zbl 1470.35372
Chiarello, Felisia Angela; Piccoli, Benedetto; Tosin, Andrea
2021
Asymptotic analysis of target fluxes in the three-dimensional narrow capture problem. Zbl 1465.35027
Bressloff, Paul C.
2021
Effective coupling conditions for arbitrary flows in Stokes-Darcy systems. Zbl 1470.35280
Eggenweiler, Elissa; Rybak, Iryna
2021
Estimation of the Koopman generator by Newton’s extrapolation. Zbl 1470.60216
Sechi, Renata; Sikorski, Alexander; Weber, Marcus
2021
Mathematical study of a Lagrange-multiplier technique for stiff transport problems. Zbl 1465.35033
Negulescu, Claudia
2021
A modified split Bregman algorithm for computing microstructures through Young measures. Zbl 1466.49013
Jaramillo, Gabriela; Venkataramani, Shankar C.
2021
Wave packets in the fractional nonlinear Schrödinger equation with a honeycomb potential. Zbl 1470.35299
Xie, Peng; Zhu, Yi
2021
Kernel analog forecasting: multiscale test problems. Zbl 1487.60088
Burov, Dmitry; Giannakis, Dimitrios; Manohar, Krithika; Stuart, Andrew
2021
Analysis of the acoustic waves reflected by a cluster of small holes in the time-domain and the equivalent mass density. Zbl 1471.35088
Sini, Mourad; Wang, Haibing; Yao, Qingyun
2021
Multiflocks: emergent dynamics in systems with multiscale collective behavior. Zbl 1470.92403
2021
Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Zbl 1447.65077
Hong, Qingguo; Kraus, Johannes; Lymbery, Maria; Wheeler, Mary F.
2020
Phase field modeling of precipitation and dissolution processes in porous media: upscaling and numerical experiments. Zbl 1446.35119
Bringedal, Carina; von Wolff, Lars; Pop, Iuliu Sorin
2020
A hybrid multiscale model for cancer invasion of the extracellular matrix. Zbl 1443.92080
Sfakianakis, Nikolaos; Madzvamuse, Anotida; Chaplain, Mark A. J.
2020
The equivalent media generated by bubbles of high contrasts: volumetric metamaterials and metasurfaces. Zbl 1439.35555
2020
Multiscale variance reduction methods based on multiple control variates for kinetic equations with uncertainties. Zbl 1433.76150
Dimarco, Giacomo; Pareschi, Lorenzo
2020
Efficient approximation of flow problems with multiple scales in time. Zbl 1446.65065
Frei, S.; Richter, T.
2020
Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism. Zbl 1446.82064
Hudson, Thomas; Li, Xingjie H.
2020
A data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reduction. Zbl 1459.35194
Li, Sijing; Zhang, Zhiwen; Zhao, Hongkai
2020
Well-balanced finite-volume schemes for hydrodynamic equations with general free energy. Zbl 1434.82098
Carrillo, José A.; Kalliadasis, Serafim; Perez, Sergio P.; Shu, Chi-Wang
2020
On the conservation properties in multiple scale coupling and simulation for Darcy flow with hyperbolic-transport in complex flows. Zbl 1454.35271
Abreu, Eduardo; Díaz, Ciro; Galvis, Juan; Pérez, John
2020
A kinetic approach to active rods dynamics in confined domains. Zbl 1439.35478
Berlyand, Leonid; Jabin, Pierre-Emmanuel; Potomkin, Mykhailo; Ratajczyk, Elżbieta
2020
A cascadic adaptive finite element method for nonlinear eigenvalue problems in quantum physics. Zbl 1435.65212
Xu, Fei
2020
Asymptotic and numerical analysis of a stochastic PDE model of volume transmission. Zbl 1445.35346
Lawley, Sean D.; Shankar, Varun
2020
Randomized sampling for basis function construction in generalized finite element methods. Zbl 1446.65162
Chen, Ke; Li, Qin; Lu, Jianfeng; Wright, Stephen J.
2020
Ensemble Kalman filter for multiscale inverse problems. Zbl 1453.65393
Abdulle, Assyr; Garegnani, Giacomo; Zanoni, Andrea
2020
Generalized multiscale finite element method for the steady state linear Boltzmann equation. Zbl 1434.65244
Chung, Eric; Efendiev, Yalchin; Li, Yanbo; Li, Qin
2020
Wavelet sparse regularization for manifold-valued data. Zbl 1457.94026
Storath, Martin; Weinmann, Andreas
2020
A statistical framework for generating microstructures of two-phase random materials: application to fatigue analysis. Zbl 1435.82032
Khristenko, Ustim; Constantinescu, Andrei; Tallec, Patrick Le; Oden, J. Tinsley; Wohlmuth, Barbara
2020
The correspondence between Voigt and Reuss bounds and the decoupling constraint in a two-grid staggered algorithm for consolidation in heterogeneous porous media. Zbl 1433.74093
Dana, Saumik; Ita, Joel; Wheeler, Mary F.
2020
An embedded corrector problem for homogenization. I: Theory. Zbl 1446.35015
Cancès, Eric; Ehrlacher, Virginie; Legoll, Frédéric; Stamm, Benjamin; Xiang, Shuyang
2020
Close-to-touching acoustic subwavelength resonators: eigenfrequency separation and gradient blow-up. Zbl 1459.35091
Ammari, Habib; Davies, Bryn; Yu, Sanghyeon
2020
Multiscale asymptotic analysis for portfolio optimization under stochastic environment. Zbl 1458.91193
Fouque, Jean-Pierre; Hu, Ruimeng
2020
Mean field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods. Zbl 1453.35165
Gomes, S. N.; Pavliotis, G. A.; Vaes, U.
2020
Optimizing weighted ensemble sampling of steady states. Zbl 07205781
Aristoff, David; Zuckerman, Daniel M.
2020
A fast algorithm for multiresolution mode decomposition. Zbl 1440.42020
Tang, Gao; Yang, Haizhao
2020
Erratum to: “Spectral band degeneracies of $$\frac{\pi}{2}$$-rotationally invariant periodic Schrödinger operators”. Zbl 1470.35295
Keller, Rachael T.; Marzuola, Jeremy L.; Osting, Braxton; Weinstein, Michael I.
2020
Extracting structured dynamical systems using sparse optimization with very few samples. Zbl 07281460
Schaeffer, Hayden; Tran, Giang; Ward, Rachel; Zhang, Linan
2020
Simulation of multiscale hydrophobic lipid dynamics via efficient integral equation methods. Zbl 1436.35196
Fu, Szu-Pei P.; Ryham, Rolf; Klöckner, Andreas; Wala, Matt; Jiang, Shidong; Young, Yuan-Nan
2020
Fractal homogenization of multiscale interface problems. Zbl 1437.35204
Heida, Martin; Kornhuber, Ralf; Podlesny, Joscha
2020
Importance sampling for slow-fast diffusions based on moderate deviations. Zbl 1440.60024
Spiliopoulos, Konstantinos; Morse, Matthew R.
2020
Kinetic/fluid micro-macro numerical scheme for a two component gas mixture. Zbl 1446.65137
Crestetto, Anaïs; Klingenberg, Christian; Pirner, Marlies
2020
On the rotating nonlinear Klein-Gordon equation: nonrelativistic limit and numerical methods. Zbl 1446.65074
Mauser, Norbert J.; Zhang, Yong; Zhao, Xiaofei
2020
Multiscale flux-based modeling of biofilm communities. Zbl 1448.92144
Zhang, T.; Parker, A.; Carlson, R. P.; Stewart, P. S.; Klapper, I.
2020
Shape optimization for composite materials and scaffold structures. Zbl 1446.49035
Dambrine, Marc; Harbrecht, Helmut
2020
A low-rank approximated multiscale method for PDEs with random coefficients. Zbl 1453.65435
Ou, Na; Lin, Guang; Jiang, Lijian
2020
Efficiency of a micro-macro acceleration method for scale-separated stochastic differential equations. Zbl 1459.65015
Vandecasteele, Hannes; Zieliński, Przemysław; Samaey, Giovanni
2020
Anisotropic nonlocal diffusion operators for normal and anomalous dynamics. Zbl 1448.60192
Deng, Weihua; Wang, Xudong; Zhang, Pingwen
2020
Multiscale finite elements for transient advection-diffusion equations through advection-induced coordinates. Zbl 1451.65204
2020
Diffusive optical tomography in the Bayesian framework. Zbl 1440.62254
Newton, Kit; Li, Qin; Stuart, Andrew M.
2020
Quantum dynamics with the parallel transport gauge. Zbl 1440.65113
An, Dong; Lin, Lin
2020
Mathematical analysis of electromagnetic plasmonic metasurfaces. Zbl 1448.35491
Ammari, Habib; Li, Bowen; Zou, Jun
2020
Multiscale analysis of spectral broadening of acoustic waves by a turbulent shear layer. Zbl 1434.76113
Garnier, Josselin; Gay, Etienne; Savin, Eric
2020
Numerically modeling stochastic Lie transport in fluid dynamics. Zbl 1454.76064
Cotter, Colin; Crisan, Dan; Holm, Darryl D.; Pan, Wei; Shevchenko, Igor
2019
Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles. Zbl 1428.35268
Tosin, Andrea; Zanella, Mattia
2019
Asymptotics of the gradient of solutions to the perfect conductivity problem. Zbl 1426.78022
Li, Haigang; Li, Yanyan; Yang, Zhuolun
2019
On the convergence of the SINDy algorithm. Zbl 1437.37108
Zhang, Linan; Schaeffer, Hayden
2019
On the convergence rates of GMsFEMs for heterogeneous elliptic problems without oversampling techniques. Zbl 1426.65179
Li, Guanglian
2019
A multiscale neural network based on hierarchical matrices. Zbl 1435.65181
Fan, Yuwei; Lin, Lin; Ying, Lexing; Zepeda-Núñez, Leonardo
2019
A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083
Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen
2019
Boundary conditions for kinetic theory based models I: lattice Boltzmann models. Zbl 1421.76185
Zhao, Weifeng; Huang, Juntao; Yong, Wen-An
2019
Nonlocal models with heterogeneous localization and their application to seamless local-nonlocal coupling. Zbl 1447.45001
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang
2019
Hybrid models for simulating blood flow in microvascular networks. Zbl 1433.76200
Vidotto, Ettore; Koch, Timo; Köppl, Tobias; Helmig, Rainer; Wohlmuth, Barbara
2019
The Foldy-Lax approximation for the full electromagnetic scattering by small conductive bodies of arbitrary shapes. Zbl 1409.35065
2019
A perturbative approach to control variates in molecular dynamics. Zbl 1426.82080
Roussel, Julien; Stoltz, Gabriel
2019
Numerical homogenization of elliptic PDEs with similar coefficients. Zbl 1428.65085
Hellman, Fredrik; Målqvist, Axel
2019
A constraint energy minimizing generalized multiscale finite element method for parabolic equations. Zbl 1426.65200
Li, Mengnan; Chung, Eric; Jiang, Lijian
2019
Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates. Zbl 1422.60133
Lelievre, Tony; Zhang, Wei
2019
Heterogeneous multiscale method for Maxwell’s equations. Zbl 1435.78019
Hochbruck, Marlis; Maier, Bernhard; Stohrer, Christian
2019
Interface dynamics for an Allen-Cahn-type equation governing a matrix-valued field. Zbl 1439.35408
Wang, Dong; Osting, Braxton; Wang, Xiao-Ping
2019
Wave propagation and imaging in moving random media. Zbl 1409.76014
Borcea, Liliana; Garnier, Josselin; Solna, Knut
2019
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### Cited by 9,965 Authors

 96 Chung, Tsz Shun Eric 67 Efendiev, Yalchin R. 46 Abdulle, Assyr 39 Garnier, Josselin 38 Degond, Pierre 37 Lu, Jianfeng 36 Shen, Zuowei 33 Osher, Stanley Joel 31 Ammari, Habib M. 31 Jin, Shi 31 Ortner, Christoph 30 Carrillo de la Plata, José Antonio 30 Du, Qiang 30 Leung, Wingtat 30 Vasilyeva, Maria V. 30 Wheeler, Mary Fanett 30 Wick, Thomas 30 Ying, Lexing 28 Chen, Ke 27 Tai, Xuecheng 26 Peterseim, Daniel 24 Huang, Ting-Zhu 24 Pareschi, Lorenzo 23 Bao, Weizhu 23 Bellomo, Nicola 23 Burger, Martin 23 Dong, Bin 23 Fu, Shubin 23 Hou, Thomas Yizhao 23 Qian, Jianliang 23 Schütte, Christof 22 Bal, Guillaume 22 Gunzburger, Max D. 22 Park, Won-Kwang 21 Bostan, Mihai 21 Ha, Seung-Yeal 21 Kevrekidis, Ioannis George 21 Le Bris, Claude 20 Cui, Junzhi 20 Jiang, Lijian 20 Luskin, Mitchell 20 Quarteroni, Alfio M. 20 Valentin, Frédéric 20 Wu, Boying 20 Zeng, Tie Yong 19 Bertozzi, Andrea Louise 19 Galvis, Juan 19 Henning, Patrick 19 Shen, Lixin 19 Yang, Haizhao 19 Zhang, Xiaoqun 18 Combettes, Patrick L. 18 Dimarco, Giacomo 18 Gander, Martin Jakob 18 Owhadi, Houman 18 Pavliotis, Grigorios A. 18 Schweizer, Ben 18 Steidl, Gabriele 17 Bressloff, Paul C. 17 Chambolle, Antonin 17 Jenny, Patrick 17 Kang, Hyeonbae 17 Karniadakis, George Em 17 Lawley, Sean D. 17 Peyré, Gabriel 17 Schönlieb, Carola-Bibiane 17 Sini, Mourad 17 Sølna, Knut 17 Zanella, Mattia 16 Borcea, Liliana 16 Hajibeygi, Hadi 16 Hauck, Cory D. 16 Herty, Michael Matthias 16 Holcman, David 16 Holm, Darryl Dallas 16 Lin, Guang 16 Liu, Jianguo 16 Mikelić, Andro 16 Ohlberger, Mario 16 Samaey, Giovanni 16 Soize, Christian 16 Spiliopoulos, Konstantinos V. 16 Stuart, Andrew M. 16 Süli, Endre E. 16 Wu, Chunlin 15 Cai, Jian-Feng 15 Cholamjiak, Prasit 15 Feng, Xiangchu 15 Grohs, Philipp 15 Klawonn, Axel 15 Li, Qin 15 Tosin, Andrea 15 Yang, Xu 15 Yao, Jen-Chih 15 Zhu, Wei 14 Aujol, Jean-François 14 Cao, Liqun 14 Fadili, Jalal M. 14 Fouque, Jean-Pierre 14 Gloria, Antoine ...and 9,865 more Authors
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### Cited in 543 Journals

 580 Journal of Computational Physics 298 Multiscale Modeling & Simulation 281 Computer Methods in Applied Mechanics and Engineering 209 Journal of Scientific Computing 185 Journal of Computational and Applied Mathematics 175 SIAM Journal on Scientific Computing 147 Computers & Mathematics with Applications 142 Journal of Mathematical Imaging and Vision 139 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 138 SIAM Journal on Imaging Sciences 102 Applied and Computational Harmonic Analysis 92 SIAM Journal on Numerical Analysis 91 Journal of Statistical Physics 91 Applied Mathematics and Computation 88 Computational Geosciences 79 Journal of Mathematical Analysis and Applications 76 Archive for Rational Mechanics and Analysis 75 SIAM Journal on Applied Mathematics 75 Inverse Problems and Imaging 73 Physica D 73 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 72 Journal of Mathematical Biology 72 Journal of Differential Equations 72 SIAM Journal on Mathematical Analysis 71 Numerische Mathematik 70 Inverse Problems 68 Journal of Fluid Mechanics 68 Mathematics of Computation 66 Applied Numerical Mathematics 61 Journal of Nonlinear Science 59 Bulletin of Mathematical Biology 55 Advances in Computational Mathematics 53 Communications in Computational Physics 51 Mathematical Problems in Engineering 48 Computational Mechanics 45 Journal of Theoretical Biology 42 Applicable Analysis 41 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 40 Applied Mathematical Modelling 39 Nonlinear Analysis. Real World Applications 38 International Journal for Numerical Methods in Engineering 36 Numerical Algorithms 35 SIAM/ASA Journal on Uncertainty Quantification 34 Discrete and Continuous Dynamical Systems. Series B 34 Kinetic and Related Models 33 Journal of Mathematical Physics 33 Journal of Optimization Theory and Applications 33 Computational Optimization and Applications 32 Journal of the Mechanics and Physics of Solids 32 Foundations of Computational Mathematics 31 Computers and Fluids 31 Mathematical Methods in the Applied Sciences 31 International Journal of Computer Mathematics 31 Calculus of Variations and Partial Differential Equations 28 BIT 28 Mathematical Programming. Series A. Series B 28 SIAM Journal on Optimization 28 International Journal of Computer Vision 28 Comptes Rendus. Mathématique. Académie des Sciences, Paris 28 Discrete and Continuous Dynamical Systems. Series S 27 Computational and Applied Mathematics 27 Networks and Heterogeneous Media 26 Communications in Mathematical Physics 26 European Journal of Applied Mathematics 26 Discrete and Continuous Dynamical Systems 25 Journal de Mathématiques Pures et Appliquées. Neuvième Série 25 SIAM Journal on Applied Dynamical Systems 24 Abstract and Applied Analysis 23 Mathematical Biosciences 23 Multidimensional Systems and Signal Processing 22 Applied Mathematics Letters 22 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 21 ZAMP. Zeitschrift für angewandte Mathematik und Physik 21 Mathematical Biosciences and Engineering 20 Nonlinearity 20 Wave Motion 20 SIAM Journal on Control and Optimization 20 Journal of Inequalities and Applications 20 Chaos 20 International Journal of Wavelets, Multiresolution and Information Processing 20 Statistics and Computing 19 Quarterly of Applied Mathematics 19 Optimization 19 Communications in Partial Differential Equations 19 ETNA. Electronic Transactions on Numerical Analysis 19 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 18 Computer Physics Communications 18 Information Sciences 18 The Annals of Applied Probability 18 Pattern Recognition 18 SIAM Review 18 Continuum Mechanics and Thermodynamics 18 Computational & Mathematical Methods in Medicine 17 Numerical Functional Analysis and Optimization 17 Research in the Mathematical Sciences 16 Chaos, Solitons and Fractals 16 Applied Mathematics and Optimization 16 Mathematics and Computers in Simulation 16 Journal of Inverse and Ill-Posed Problems 15 Physica A ...and 443 more Journals
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### Cited in 59 Fields

 3,299 Numerical analysis (65-XX) 2,670 Partial differential equations (35-XX) 1,402 Fluid mechanics (76-XX) 939 Information and communication theory, circuits (94-XX) 884 Mechanics of deformable solids (74-XX) 823 Biology and other natural sciences (92-XX) 777 Probability theory and stochastic processes (60-XX) 724 Computer science (68-XX) 710 Statistical mechanics, structure of matter (82-XX) 603 Operations research, mathematical programming (90-XX) 559 Calculus of variations and optimal control; optimization (49-XX) 381 Statistics (62-XX) 319 Operator theory (47-XX) 319 Optics, electromagnetic theory (78-XX) 246 Dynamical systems and ergodic theory (37-XX) 243 Ordinary differential equations (34-XX) 206 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 184 Systems theory; control (93-XX) 174 Harmonic analysis on Euclidean spaces (42-XX) 153 Geophysics (86-XX) 147 Quantum theory (81-XX) 138 Integral equations (45-XX) 130 Classical thermodynamics, heat transfer (80-XX) 97 Mechanics of particles and systems (70-XX) 94 Approximations and expansions (41-XX) 92 Linear and multilinear algebra; matrix theory (15-XX) 80 Real functions (26-XX) 80 Functional analysis (46-XX) 53 Combinatorics (05-XX) 51 Global analysis, analysis on manifolds (58-XX) 50 Differential geometry (53-XX) 29 Integral transforms, operational calculus (44-XX) 24 Special functions (33-XX) 23 Measure and integration (28-XX) 22 General and overarching topics; collections (00-XX) 16 Potential theory (31-XX) 15 Convex and discrete geometry (52-XX) 14 Functions of a complex variable (30-XX) 14 Astronomy and astrophysics (85-XX) 13 Topological groups, Lie groups (22-XX) 12 Difference and functional equations (39-XX) 10 General topology (54-XX) 9 Algebraic topology (55-XX) 9 Manifolds and cell complexes (57-XX) 8 History and biography (01-XX) 5 Algebraic geometry (14-XX) 4 Abstract harmonic analysis (43-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Relativity and gravitational theory (83-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 2 Geometry (51-XX) 2 Mathematics education (97-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Sequences, series, summability (40-XX)