## 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: 1,070 Publications (since 2003) References Indexed: 465 Publications with 18,288 References.
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### Latest Issues

 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 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 Spiliopoulos, Konstantinos V. 6 Bal, Guillaume 6 Du, Qiang 6 Holcman, David 6 Majda, Andrew J. 6 Mucha, Peter J. 6 Negulescu, Claudia 6 Qian, Jianliang 6 Sini, Mourad 6 Voigt, Axel 6 Weber, Marcus 6 Xin, Jack X. 6 Zhang, Pingwen 5 Bressloff, Paul C. 5 Caflisch, Russel E. 5 Fouque, Jean-Pierre 5 Galvis, Juan 5 Gunzburger, Max D. 5 Higham, Desmond J. 5 Le Bris, Claude 5 Legoll, Frédéric 5 Li, Guanglian 5 Målqvist, Axel 5 Ming, Pingbing 5 Movchan, Alexander B. 5 Najm, Habib N. 5 Ortiz, Michael 5 Owhadi, Houman 5 Pavliotis, Grigorios A. 5 Peterseim, Daniel 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 Burridge, Robert 4 Carrillo de la Plata, José Antonio 4 Chen, Huajie 4 Chen, Jingrun 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 Fackeldey, Konstantin 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 Li, Tiejun 4 Li, Xiantao 4 Lipton, Robert P. 4 Lötstedt, Per ...and 1,654 more Authors
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### Fields

 532 Numerical analysis (65-XX) 501 Partial differential equations (35-XX) 238 Fluid mechanics (76-XX) 207 Probability theory and stochastic processes (60-XX) 184 Statistical mechanics, structure of matter (82-XX) 167 Mechanics of deformable solids (74-XX) 130 Biology and other natural sciences (92-XX) 82 Optics, electromagnetic theory (78-XX) 75 Statistics (62-XX) 66 Ordinary differential equations (34-XX) 61 Computer science (68-XX) 58 Information and communication theory, circuits (94-XX) 57 Dynamical systems and ergodic theory (37-XX) 50 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) 29 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) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Operator theory (47-XX) 12 Combinatorics (05-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 6 Potential theory (31-XX) 6 Global analysis, analysis on manifolds (58-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

888 Publications have been cited 10,784 times in 7,338 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
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
Optimal local approximation spaces for generalized finite element methods with application to multiscale problems. Zbl 1229.65195
Babuska, Ivo; Lipton, Robert
2011
A nonlocal vector calculus with application to nonlocal boundary value problems. Zbl 1210.35057
Gunzburger, Max; Lehoucq, R. B.
2010
A posteriori control of modeling errors and discretization errors. Zbl 1050.65100
Braack, Malte; Ern, Alexandre
2003
Multiscale modeling of granular flows with application to crowd dynamics. Zbl 1221.35232
Cristiani, Emiliano; Piccoli, Benedetto; Tosin, Andrea
2011
Mixed generalized multiscale finite element methods and applications. Zbl 1317.65204
Chung, Eric T.; Efendiev, Yalchin; Lee, Chak Shing
2015
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
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
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
Bayesian numerical homogenization. Zbl 1322.35002
2015
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
Analysis of the recovery of edges in images and signals by minimizing nonconvex regularized least-squares. Zbl 1091.94007
Nikolova, Mila
2005
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
A multiscale finite element method for numerical homogenization. Zbl 1093.35007
Allaire, Grégoire; Brizzi, Robert
2005
The discontinuity set of solutions of the TV denoising problem and some extensions. Zbl 1145.49024
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2007
Gas pipeline models revisited: model hierarchies, nonisothermal models, and simulations of networks. Zbl 1254.76124
Brouwer, Jens; Gasser, Ingenuin; Herty, Michael
2011
A multiscale image representation using hierarchical $$(BV,L^2)$$ decompositions. Zbl 1146.68472
Tadmor, Eitan; Nezzar, Suzanne; Vese, Luminita
2004
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
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
Generalized multiscale finite element methods for wave propagation in heterogeneous media. Zbl 1315.65085
Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat
2014
Peridynamics as an upscaling of molecular dynamics. Zbl 1375.82073
Seleson, Pablo; Parks, Michael L.; Gunzburger, Max; Lehoucq, Richard B.
2009
High-dimensional finite elements for elliptic problems with multiple scales. Zbl 1074.65135
Viet Ha Hoang; Schwab, Christoph
2005
Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics. Zbl 1262.60072
Anderson, David F.; Higham, Desmond J.
2012
Randomized oversampling for generalized multiscale finite element methods. Zbl 1337.65148
Calo, Victor M.; Efendiev, Yalchin; Galvis, Juan; Li, Guanglian
2016
A multiple scale model for tumor growth. Zbl 1107.92019
Alarcón, T.; Byrne, H. M.; Maini, P. K.
2005
Analysis of a two-scale Cahn-Hilliard model for binary image inpainting. Zbl 1149.35309
Bertozzi, Andrea; Esedoḡlu, Selim; Gillette, Alan
2007
Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. Zbl 1316.35235
Luo, Guo; Hou, Thomas Y.
2014
A fast butterfly algorithm for the computation of Fourier integral operators. Zbl 1184.65125
Candès, Emmanuel; Demanet, Laurent; Ying, Lexing
2009
From the microscale to collective crowd dynamics. Zbl 1280.90019
Bellomo, Nicola; Bellouquid, Abdelghani; Knopoff, Damian
2013
Learning multiscale sparse representations for image and video restoration. Zbl 1194.49041
Mairal, Julien; Sapiro, Guillermo; Elad, Michael
2008
Capturing small scales in elliptic problems using a residual-free bubbles finite element method. Zbl 1032.65131
Sangalli, Giancarlo
2003
Crystal precipitation and dissolution in a porous medium: Effective equations and numerical experiments. Zbl 1176.35020
van Noorden, T. L.
2009
Strong convergence rate for two-time-scale jump-diffusion stochastic differential systems. Zbl 1144.60038
Givon, Dror
2007
On atomistic-to-continuum coupling by blending. Zbl 1160.65338
Badia, Santiago; Parks, Michael; Bochev, Pavel; Gunzburger, Max; Lehoucq, Richard
2008
Localized bases for finite-dimensional homogenization approximations with nonseparated scales and high contrast. Zbl 1244.65140
2011
Locating multiple multiscale acoustic scatterers. Zbl 1328.35135
Li, Jingzhi; Liu, Hongyu; Zou, Jun
2014
Boundary problems for the fractional and tempered fractional operators. Zbl 1391.60104
Deng, Weihua; Li, Buyang; Tian, Wenyi; Zhang, Pingwen
2018
A rate-independent model for inelastic behavior of shape-memory alloys. Zbl 1183.74207
Mielke, Alexander; Roubíček, Tomáš
2003
Numerical homogenization of nonlinear random parabolic operators. Zbl 1181.76113
Efendiev, Y.; Pankov, A.
2004
Reduced-basis approach for homogenization beyond the periodic setting. Zbl 1156.74358
Boyaval, Sébastien
2008
Fast and slow dynamics for the computational singular perturbation method. Zbl 1065.34049
Zagaris, Antonios; Kaper, Hans G.; Kaper, Tasso J.
2004
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
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
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
Eigenfracture: an eigendeformation approach to variational fracture. Zbl 1173.74040
Schmidt, Bernd; Fraternali, Fernando; Ortiz, Michael
2009
Binary interaction algorithms for the simulation of flocking and swarming dynamics. Zbl 1274.92053
Albi, G.; Pareschi, L.
2013
A Lagrangian particle-wavelet method. Zbl 1122.65085
Bergdorf, Michael; Koumoutsakos, Petros
2006
Multilevel adaptive particle methods for convection-diffusion equations. Zbl 1088.76055
Bergdorf, Michael; Cottet, Georges-Henri; Koumoutsakos, Petros
2005
A framework for adaptive multiscale methods for elliptic problems. Zbl 1160.65342
Nolen, James; Papanicolaou, George; Pironneau, Olivier
2008
Homogenization of Maxwell’s equations in a split ring geometry. Zbl 1228.35028
Bouchitté, Guy; Schweizer, Ben
2010
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
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
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
2008
Hybrid multiscale methods. II: Kinetic equations. Zbl 1185.65198
Dimarco, Giacomo; Pareschi, Lorenzo
2008
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
Transition path theory for Markov jump processes. Zbl 1185.60086
Metzner, Philipp; Schütte, Christof; Vanden-Eijnden, Eric
2009
Well modeling in the multiscale finite volume method for subsurface flow simulation. Zbl 1205.76175
Wolfsteiner, Christian; Lee, Seong H.; Tchelepi, Hamdi A.
2006
Analysis of explicit tau-leaping schemes for simulating chemically reacting systems. Zbl 1145.92041
Li, Tiejun
2007
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
Numerical homogenization of elliptic multiscale problems by subspace decomposition. Zbl 1352.65521
Kornhuber, Ralf; Yserentant, Harry
2016
Existence of global weak solutions to some regularized kinetic models for dilute polymers. Zbl 1228.76004
Barrett, John W.; Süli, Endre
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
Matching of asymptotic expansions for wave propagation in media with thin slots I: The asymptotic expansion. Zbl 1132.35347
Joly, Patrick; Tordeux, Sébastien
2006
An MsFEM type approach for perforated domains. Zbl 1316.35021
Le Bris, Claude; Legoll, Frédéric; Lozinski, Alexei
2014
Consistent energy-based atomistic/continuum coupling for two-body potentials in one and two dimensions. Zbl 1246.74065
Shapeev, Alexander V.
2011
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
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
Bloch-wave homogenization on large time scales and dispersive effective wave equations. Zbl 1320.35043
Dohnal, T.; Lamacz, A.; Schweizer, B.
2014
Finite element heterogeneous multiscale method for the wave equation: long-time effects. Zbl 1315.65084
Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian
2014
Implicit-explicit variational integration of highly oscillatory problems. Zbl 1185.65227
Stern, Ari; Grinspun, Eitan
2009
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
Bandelet image approximation and compression. Zbl 1091.94006
Le Pennec, E.; Mallat, S.
2005
Blow-up of solutions to a $$p$$-Laplace equation. Zbl 1261.35137
Gorb, Yuliya; Novikov, Alexei
2012
Importance sampling for multiscale diffusions. Zbl 1250.60031
Dupuis, Paul; Spiliopoulos, Konstantinos; Wang, Hui
2012
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
Analysis and optimization of certain parallel Monte Carlo methods in the low temperature limit. Zbl 07490841
Dupuis, Paul; Wu, Guo-Jhen
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
A hybrid finite-volume, discontinuous Galerkin discretization for the radiative transport equation. Zbl 1453.82099
Heningburg, Vincent; Hauck, Cory D.
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 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
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
Exponential convergence for multiscale linear elliptic PDEs via adaptive edge basis functions. Zbl 1473.65296
Chen, Yifan; Hou, Thomas Y.; Wang, Yixuan
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
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
Optimal convergence rates for elliptic homogenization problems in nondivergence-form: analysis and numerical illustrations. Zbl 1475.35030
Sprekeler, Timo; Tran, Hung V.
2021
Weak SINDy: Galerkin-based data-driven model selection. Zbl 07411447
Messenger, Daniel A.; Bortz, David M.
2021
An inverse random source problem for Maxwell’s equations. Zbl 1453.78006
Li, Peijun; Wang, Xu
2021
Kernel analog forecasting: multiscale test problems. Zbl 07382142
Burov, Dmitry; Giannakis, Dimitrios; Manohar, Krithika; Stuart, Andrew
2021
Multiflocks: emergent dynamics in systems with multiscale collective behavior. Zbl 1470.92403
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
Hierarchical model reduction techniques for flow modeling in a parametrized setting. Zbl 1468.65209
Zancanaro, Matteo; Ballarin, Francesco; Perotto, Simona; Rozza, Gianluigi
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
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
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
Singular limit for reactive diffusive transport through an array of thin channels in case of critical diffusivity. Zbl 1481.35033
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
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
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
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 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
A kinetic approach to active rods dynamics in confined domains. Zbl 1439.35478
Berlyand, Leonid; Jabin, Pierre-Emmanuel; Potomkin, Mykhailo; Ratajczyk, Elżbieta
2020
The equivalent media generated by bubbles of high contrasts: volumetric metamaterials and metasurfaces. Zbl 1439.35555
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
Wavelet sparse regularization for manifold-valued data. Zbl 1457.94026
Storath, Martin; Weinmann, Andreas
2020
Asymptotic and numerical analysis of a stochastic PDE model of volume transmission. Zbl 1445.35346
Lawley, Sean D.; Shankar, Varun
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
Ensemble Kalman filter for multiscale inverse problems. Zbl 1453.65393
Abdulle, Assyr; Garegnani, Giacomo; Zanoni, Andrea
2020
Multiscale asymptotic analysis for portfolio optimization under stochastic environment. Zbl 1458.91193
Fouque, Jean-Pierre; Hu, Ruimeng
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
A cascadic adaptive finite element method for nonlinear eigenvalue problems in quantum physics. Zbl 1435.65212
Xu, Fei
2020
Multiscale variance reduction methods based on multiple control variates for kinetic equations with uncertainties. Zbl 1433.76150
Dimarco, Giacomo; Pareschi, Lorenzo
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
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
Randomized sampling for basis function construction in generalized finite element methods. Zbl 1446.65162
Chen, Ke; Li, Qin; Lu, Jianfeng; Wright, Stephen J.
2020
An embedded corrector problem for homogenization. I: Theory. Zbl 1446.35015
Cancès, Eric; Ehrlacher, Virginie; Legoll, Frédéric; Stamm, Benjamin; Xiang, Shuyang
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
Close-to-touching acoustic subwavelength resonators: eigenfrequency separation and gradient blow-up. Zbl 1459.35091
Ammari, Habib; Davies, Bryn; Yu, Sanghyeon
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
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
Importance sampling for slow-fast diffusions based on moderate deviations. Zbl 1440.60024
Spiliopoulos, Konstantinos; Morse, Matthew R.
2020
Anisotropic nonlocal diffusion operators for normal and anomalous dynamics. Zbl 1448.60192
Deng, Weihua; Wang, Xudong; Zhang, Pingwen
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
Multiscale finite elements for transient advection-diffusion equations through advection-induced coordinates. Zbl 1451.65204
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
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
Boundary conditions for kinetic theory based models I: lattice Boltzmann models. Zbl 1421.76185
Zhao, Weifeng; Huang, Juntao; Yong, Wen-An
2019
Asymptotics of the gradient of solutions to the perfect conductivity problem. Zbl 1426.78022
Li, Haigang; Li, Yanyan; Yang, Zhuolun
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
A multiscale neural network based on hierarchical matrices. Zbl 1435.65181
Fan, Yuwei; Lin, Lin; Ying, Lexing; Zepeda-Núñez, Leonardo
2019
Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates. Zbl 1422.60133
Lelievre, Tony; Zhang, Wei
2019
Hybrid models for simulating blood flow in microvascular networks. Zbl 1433.76200
Vidotto, Ettore; Koch, Timo; Köppl, Tobias; Helmig, Rainer; Wohlmuth, Barbara
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
The Foldy-Lax approximation for the full electromagnetic scattering by small conductive bodies of arbitrary shapes. Zbl 1409.35065
2019
Nonlocal models with heterogeneous localization and their application to seamless local-nonlocal coupling. Zbl 1447.45001
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang
2019
Wave propagation and imaging in moving random media. Zbl 1409.76014
Borcea, Liliana; Garnier, Josselin; Solna, Knut
2019
Renormalized reduced order models with memory for long time prediction. Zbl 1412.65178
Price, Jacob; Stinis, Panos
2019
A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition. Zbl 1455.65053
Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun
2019
Asymptotic-preserving scheme for the resolution of evolution equations with stiff transport terms. Zbl 1412.35331
Fedele, Baptiste; Negulescu, Claudia; Possanner, Stefan
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
Relaxation-based coarsening for multilevel hypergraph partitioning. Zbl 1419.05160
Shaydulin, Ruslan; Chen, Jie; Safro, Ilya
2019
Effective properties of fibrous Composites and cluster convergence. Zbl 1421.74086
2019
Multiscale finite element methods for advection-dominated problems in perforated domains. Zbl 1423.35022
Le Bris, Claude; Legoll, FreDeRic; Madiot, FrancOis
2019
Raster grid pathology and the cure. Zbl 1426.78015
Fannjiang, Albert
2019
On constrained Langevin equations and (bio)chemical reaction networks. Zbl 1481.60146
Anderson, David F.; Higham, Desmond J.; Leite, Saul C.; Williams, Ruth J.
2019
A two-dimensional “flea on the elephant” phenomenon and its numerical visualization. Zbl 1408.35110
Bianchini, Roberta; Gosse, Laurent; Zuazua, Enrique
2019
Variational formulation for Wannier functions with entangled band structure. Zbl 1412.82041
Damle, Anil; Levitt, Antoine; Lin, Lin
2019
Numerical homogenization and model order reduction for multiscale inverse problems. Zbl 1412.65195
Abdulle, Assyr; Blasio, Andrea Di
2019
Online adaptive basis enrichment for mixed CEM-GMsFEM. Zbl 1435.65196
Chung, Eric T.; Pun, Sai-Mang
2019
A two field iterated asymptotic-preserving method for highly anisotropic elliptic equations. Zbl 1426.65173
Deluzet, Fabrice; Narski, Jacek
2019
Intrinsic complexity and scaling laws: from random fields to random vectors. Zbl 1428.62206
Bryson, Jennifer; Zhao, Hongkai; Zhong, Yimin
2019
Numerical methods for computing an averaged matrix field. Application to the asymptotic analysis of a parabolic problem with stiff transport terms. Zbl 1426.65143
Blanc, Thomas
2019
A multiscale domain decomposition algorithm for boundary value problems for eikonal equations. Zbl 1426.65198
Martin, Lindsay; Tsai, Yen-Hsi R.
2019
Globally constructed adaptive local basis set for spectral projectors of second order differential operators. Zbl 1409.65118
Li, Yingzhou; Lin, Lin
2019
Optimized sampling for multiscale dynamics. Zbl 07033871
Manohar, Krithika; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan
2019
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### Cited by 9,614 Authors

 90 Chung, Tsz Shun Eric 64 Efendiev, Yalchin R. 45 Abdulle, Assyr 39 Garnier, Josselin 37 Degond, Pierre 37 Lu, Jianfeng 36 Shen, Zuowei 32 Osher, Stanley Joel 31 Jin, Shi 30 Ortner, Christoph 30 Wheeler, Mary Fanett 30 Ying, Lexing 29 Ammari, Habib M. 29 Vasilyeva, Maria V. 28 Carrillo de la Plata, José Antonio 28 Chen, Ke 28 Du, Qiang 27 Wick, Thomas 25 Leung, Wingtat 25 Peterseim, Daniel 25 Tai, Xuecheng 24 Huang, Ting-Zhu 23 Hou, Thomas Yizhao 22 Bao, Weizhu 22 Bellomo, Nicola 22 Burger, Martin 22 Gunzburger, Max D. 22 Qian, Jianliang 21 Bal, Guillaume 21 Bostan, Mihai 21 Pareschi, Lorenzo 21 Park, Won-Kwang 21 Schütte, Christof 20 Cui, Junzhi 20 Fu, Shubin 20 Ha, Seung-Yeal 20 Jiang, Lijian 20 Kevrekidis, Ioannis George 20 Le Bris, Claude 20 Luskin, Mitchell 20 Valentin, Frédéric 20 Wu, Boying 20 Zeng, Tie Yong 19 Bertozzi, Andrea Louise 19 Galvis, Juan 19 Henning, Patrick 19 Quarteroni, Alfio M. 19 Shen, Lixin 19 Yang, Haizhao 18 Dimarco, Giacomo 18 Pavliotis, Grigorios A. 18 Steidl, Gabriele 18 Zhang, Xiaoqun 17 Combettes, Patrick L. 17 Gander, Martin Jakob 17 Jenny, Patrick 17 Kang, Hyeonbae 17 Karniadakis, George Em 17 Lawley, Sean D. 17 Owhadi, Houman 17 Peyré, Gabriel 17 Schönlieb, Carola-Bibiane 17 Schweizer, Ben 17 Sølna, Knut 16 Bressloff, Paul C. 16 Chambolle, Antonin 16 Hajibeygi, Hadi 16 Holcman, David 16 Ohlberger, Mario 16 Samaey, Giovanni 16 Spiliopoulos, Konstantinos V. 16 Süli, Endre E. 16 Wu, Chunlin 16 Zanella, Mattia 15 Borcea, Liliana 15 Feng, Xiangchu 15 Grohs, Philipp 15 Hauck, Cory D. 15 Herty, Michael Matthias 15 Holm, Darryl D. 15 Liu, Jianguo 15 Mikelić, Andro 15 Soize, Christian 15 Stuart, Andrew M. 15 Yang, Xu 15 Yao, Jen-Chih 14 Aujol, Jean-François 14 Cai, Jian-Feng 14 Cholamjiak, Prasit 14 Dong, Bin 14 Klawonn, Axel 14 Koumoutsakos, Petros D. 14 Li, Guanglian 14 Li, Qin 14 Lin, Guang 14 Lv, Xiaoguang 14 Majda, Andrew J. 14 Nordbotten, Jan Martin 14 Sini, Mourad 14 Stefanelli, Ulisse ...and 9,514 more Authors
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### Cited in 527 Journals

 554 Journal of Computational Physics 282 Multiscale Modeling & Simulation 274 Computer Methods in Applied Mechanics and Engineering 192 Journal of Scientific Computing 180 Journal of Computational and Applied Mathematics 160 SIAM Journal on Scientific Computing 143 Computers & Mathematics with Applications 138 Journal of Mathematical Imaging and Vision 136 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 136 SIAM Journal on Imaging Sciences 102 Applied and Computational Harmonic Analysis 90 Applied Mathematics and Computation 89 Journal of Statistical Physics 86 SIAM Journal on Numerical Analysis 85 Computational Geosciences 78 Journal of Mathematical Analysis and Applications 74 Archive for Rational Mechanics and Analysis 72 Inverse Problems and Imaging 71 Journal of Mathematical Biology 71 Journal of Differential Equations 71 SIAM Journal on Applied Mathematics 70 Inverse Problems 70 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 69 Physica D 68 SIAM Journal on Mathematical Analysis 67 Journal of Fluid Mechanics 67 Numerische Mathematik 64 Mathematics of Computation 64 Applied Numerical Mathematics 59 Journal of Nonlinear Science 57 Bulletin of Mathematical Biology 53 Advances in Computational Mathematics 51 Mathematical Problems in Engineering 50 Communications in Computational Physics 46 Computational Mechanics 45 Journal of Theoretical Biology 40 Applied Mathematical Modelling 38 International Journal for Numerical Methods in Engineering 38 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 37 Nonlinear Analysis. Real World Applications 35 Applicable Analysis 35 Numerical Algorithms 34 Kinetic and Related Models 33 Journal of Mathematical Physics 32 Journal of the Mechanics and Physics of Solids 32 Journal of Optimization Theory and Applications 32 Computational Optimization and Applications 32 Discrete and Continuous Dynamical Systems. Series B 32 SIAM/ASA Journal on Uncertainty Quantification 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 30 Foundations of Computational Mathematics 28 BIT 28 International Journal of Computer Vision 27 Mathematical Programming. Series A. Series B 27 Comptes Rendus. Mathématique. Académie des Sciences, Paris 26 Communications in Mathematical Physics 26 European Journal of Applied Mathematics 26 SIAM Journal on Optimization 26 Discrete and Continuous Dynamical Systems 26 Networks and Heterogeneous Media 25 Discrete and Continuous Dynamical Systems. Series S 24 Journal de Mathématiques Pures et Appliquées. Neuvième Série 24 Computational and Applied Mathematics 24 Abstract and Applied Analysis 23 SIAM Journal on Applied Dynamical Systems 22 Mathematical Biosciences 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 Multidimensional Systems and Signal Processing 20 Nonlinearity 20 Wave Motion 20 SIAM Journal on Control and Optimization 20 Chaos 20 International Journal of Wavelets, Multiresolution and Information Processing 20 Statistics and Computing 19 Journal of Inequalities and Applications 18 Computer Physics Communications 18 Information Sciences 18 Quarterly of Applied Mathematics 18 Optimization 18 The Annals of Applied Probability 18 Communications in Partial Differential Equations 18 Pattern Recognition 18 SIAM Review 18 Continuum Mechanics and Thermodynamics 18 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 18 Mathematical Biosciences and Engineering 18 Computational & Mathematical Methods in Medicine 16 Numerical Functional Analysis and Optimization 16 Journal of Inverse and Ill-Posed Problems 16 ETNA. Electronic Transactions on Numerical Analysis 16 Research in the Mathematical Sciences 15 Mathematics and Computers in Simulation 15 Numerical Methods for Partial Differential Equations 15 Physics of Fluids 15 Communications on Pure and Applied Analysis ...and 427 more Journals
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### Cited in 60 Fields

 3,133 Numerical analysis (65-XX) 2,551 Partial differential equations (35-XX) 1,345 Fluid mechanics (76-XX) 911 Information and communication theory, circuits (94-XX) 854 Mechanics of deformable solids (74-XX) 794 Biology and other natural sciences (92-XX) 744 Probability theory and stochastic processes (60-XX) 690 Computer science (68-XX) 682 Statistical mechanics, structure of matter (82-XX) 569 Operations research, mathematical programming (90-XX) 532 Calculus of variations and optimal control; optimization (49-XX) 360 Statistics (62-XX) 306 Optics, electromagnetic theory (78-XX) 297 Operator theory (47-XX) 236 Ordinary differential equations (34-XX) 236 Dynamical systems and ergodic theory (37-XX) 200 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 178 Systems theory; control (93-XX) 169 Harmonic analysis on Euclidean spaces (42-XX) 146 Geophysics (86-XX) 143 Quantum theory (81-XX) 131 Integral equations (45-XX) 125 Classical thermodynamics, heat transfer (80-XX) 90 Approximations and expansions (41-XX) 89 Mechanics of particles and systems (70-XX) 87 Linear and multilinear algebra; matrix theory (15-XX) 77 Real functions (26-XX) 76 Functional analysis (46-XX) 49 Differential geometry (53-XX) 49 Global analysis, analysis on manifolds (58-XX) 47 Combinatorics (05-XX) 28 Integral transforms, operational calculus (44-XX) 22 General and overarching topics; collections (00-XX) 22 Special functions (33-XX) 20 Measure and integration (28-XX) 16 Potential theory (31-XX) 14 Convex and discrete geometry (52-XX) 13 Functions of a complex variable (30-XX) 13 Astronomy and astrophysics (85-XX) 12 Topological groups, Lie groups (22-XX) 11 Difference and functional equations (39-XX) 11 General topology (54-XX) 10 Manifolds and cell complexes (57-XX) 9 History and biography (01-XX) 9 Algebraic topology (55-XX) 5 Algebraic geometry (14-XX) 4 Abstract harmonic analysis (43-XX) 4 Relativity and gravitational theory (83-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Geometry (51-XX) 2 Mathematics education (97-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Sequences, series, summability (40-XX)