# zbMATH — the first resource for mathematics

## 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: 1,039 Publications (since 2003) References Indexed: 434 Publications with 16,970 References.
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#### Latest Issues

 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 17 Efendiev, Yalchin R. 17 Garnier, Josselin 14 Schütte, Christof 14 Sølna, Knut 13 Degond, Pierre 13 Hou, Thomas Yizhao 13 Luskin, Mitchell 12 Ortner, Christoph 11 Abdulle, Assyr 11 Borcea, Liliana 11 Osher, Stanley Joel 10 Ammari, Habib M. 10 Lu, Jianfeng 9 Jin, Shi 9 Margetis, Dionisios 9 Vanden-Eijnden, Eric 8 Caselles Costa, Vicent 8 Chung, Tsz Shun Eric 8 Kevrekidis, Ioannis George 8 Wheeler, Mary Fanett 7 Engquist, Bjorn E. 7 Forest, M. Gregory 7 Horenko, Illia 7 Jiang, Lijian 7 Li, Qin 7 Lin, Lin 7 Mikelić, Andro 7 Papanicolaou, George C. 7 Shapeev, Alexander V. 7 Weinstein, Michael I. 6 Bal, Guillaume 6 Cao, Liqun 6 Du, Qiang 6 Holcman, David 6 Majda, Andrew J. 6 Negulescu, Claudia 6 Noé, Frank 6 Qian, Jianliang 6 Sini, Mourad 6 Spiliopoulos, Konstantinos V. 6 Voigt, Axel 6 Weber, Marcus 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 Målqvist, Axel 5 Ming, Pingbing 5 Movchan, Alexander B. 5 Mucha, Peter J. 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 Xin, Jack X. 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 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, Guanglian 4 Li, Tiejun 4 Li, Xiantao 4 Lipton, Robert P. 4 Lötstedt, Per 4 Lu, Wangtao 4 Méhats, Florian ...and 1,599 more Authors
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#### Fields

 513 Numerical analysis (65-XX) 487 Partial differential equations (35-XX) 234 Fluid mechanics (76-XX) 199 Probability theory and stochastic processes (60-XX) 180 Statistical mechanics, structure of matter (82-XX) 166 Mechanics of deformable solids (74-XX) 128 Biology and other natural sciences (92-XX) 78 Optics, electromagnetic theory (78-XX) 71 Statistics (62-XX) 66 Ordinary differential equations (34-XX) 58 Dynamical systems and ergodic theory (37-XX) 58 Computer science (68-XX) 56 Information and communication theory, circuits (94-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 40 Quantum theory (81-XX) 33 Operations research, mathematical programming (90-XX) 29 Mechanics of particles and systems (70-XX) 29 Systems theory; control (93-XX) 26 Geophysics (86-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 22 Classical thermodynamics, heat transfer (80-XX) 16 Integral equations (45-XX) 15 Approximations and expansions (41-XX) 14 Operator theory (47-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Combinatorics (05-XX) 10 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

830 Publications have been cited 9,585 times in 6,512 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
Fast discrete curvelet transforms. Zbl 1122.65134
Candès, Emmanuel; Demanet, Laurent; Donoho, David; Ying, Lexing
2006
A multiscale mortar mixed finite element method. Zbl 1322.76039
Arbogast, Todd; Pencheva, Gergina; Wheeler, Mary F.; Yotov, Ivan
2007
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
Ground states and dynamics of multicomponent Bose-Einstein condensates. Zbl 1062.82034
Bao, Weizhu
2004
Deblurring and denoising of images by nonlocal functionals. Zbl 1161.68827
Kindermann, Stefan; Osher, Stanley; Jones, Peter W.
2005
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
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
A nonlocal vector calculus with application to nonlocal boundary value problems. Zbl 1210.35057
Gunzburger, Max; Lehoucq, R. B.
2010
On a priori error analysis of fully discrete heterogeneous multiscale FEM. Zbl 1092.65093
Abdulle, Assyr
2005
Oversampling for the multiscale finite element method. Zbl 1297.65155
Henning, Patrick; Peterseim, Daniel
2013
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
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
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
From signal transduction to spatial pattern formation in E. coli: A paradigm for multiscale modeling in biology. Zbl 1073.35205
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
The discontinuity set of solutions of the TV denoising problem and some extensions. Zbl 1145.49024
Caselles, Vicent; Chambolle, Antonin; Novaga, Matteo
2007
Mixed generalized multiscale finite element methods and applications. Zbl 1317.65204
Chung, Eric T.; Efendiev, Yalchin; Lee, Chak Shing
2015
Peridynamics as an upscaling of molecular dynamics. Zbl 1375.82073
Seleson, Pablo; Parks, Michael L.; Gunzburger, Max; Lehoucq, Richard B.
2009
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
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
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
Diffuse interface models on graphs for classification of high dimensional data. Zbl 1259.68215
Bertozzi, Andrea L.; Flenner, Arjuna
2012
A multiple scale model for tumor growth. Zbl 1107.92019
Alarcón, T.; Byrne, H. M.; Maini, P. K.
2005
Gas pipeline models revisited: model hierarchies, nonisothermal models, and simulations of networks. Zbl 1254.76124
Brouwer, Jens; Gasser, Ingenuin; Herty, Michael
2011
High-dimensional finite elements for elliptic problems with multiple scales. Zbl 1074.65135
Viet Ha Hoang; Schwab, Christoph
2005
A multiscale image representation using hierarchical $$(BV,L^2)$$ decompositions. Zbl 1146.68472
Tadmor, Eitan; Nezzar, Suzanne; Vese, Luminita
2004
Multilevel Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics. Zbl 1262.60072
Anderson, David F.; Higham, Desmond J.
2012
Capturing small scales in elliptic problems using a residual-free bubbles finite element method. Zbl 1032.65131
Sangalli, Giancarlo
2003
Randomized oversampling for generalized multiscale finite element methods. Zbl 1337.65148
Calo, Victor M.; Efendiev, Yalchin; Galvis, Juan; Li, Guanglian
2016
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
On atomistic-to-continuum coupling by blending. Zbl 1160.65338
Badia, Santiago; Parks, Michael; Bochev, Pavel; Gunzburger, Max; Lehoucq, Richard
2008
Analysis of a two-scale Cahn-Hilliard model for binary image inpainting. Zbl 1149.35309
Bertozzi, Andrea; Esedoḡlu, Selim; Gillette, Alan
2007
From the microscale to collective crowd dynamics. Zbl 1280.90019
Bellomo, Nicola; Bellouquid, Abdelghani; Knopoff, Damian
2013
Localized bases for finite-dimensional homogenization approximations with nonseparated scales and high contrast. Zbl 1244.65140
2011
A rate-independent model for inelastic behavior of shape-memory alloys. Zbl 1183.74207
Mielke, Alexander; Roubíček, Tomáš
2003
Learning multiscale sparse representations for image and video restoration. Zbl 1194.49041
Mairal, Julien; Sapiro, Guillermo; Elad, Michael
2008
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
Bayesian numerical homogenization. Zbl 1322.35002
2015
Numerical homogenization of nonlinear random parabolic operators. Zbl 1181.76113
Efendiev, Y.; Pankov, A.
2004
Locating multiple multiscale acoustic scatterers. Zbl 1328.35135
Li, Jingzhi; Liu, Hongyu; Zou, Jun
2014
Strong convergence rate for two-time-scale jump-diffusion stochastic differential systems. Zbl 1144.60038
Givon, Dror
2007
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
Crystal precipitation and dissolution in a porous medium: Effective equations and numerical experiments. Zbl 1176.35020
van Noorden, T. L.
2009
Eigenfracture: an eigendeformation approach to variational fracture. Zbl 1173.74040
Schmidt, Bernd; Fraternali, Fernando; Ortiz, Michael
2009
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
Multilevel adaptive particle methods for convection-diffusion equations. Zbl 1088.76055
Bergdorf, Michael; Cottet, Georges-Henri; Koumoutsakos, Petros
2005
Generalized multiscale finite element methods for wave propagation in heterogeneous media. Zbl 1315.65085
Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat
2014
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
Fast and slow dynamics for the computational singular perturbation method. Zbl 1065.34049
Zagaris, Antonios; Kaper, Hans G.; Kaper, Tasso J.
2004
A framework for adaptive multiscale methods for elliptic problems. Zbl 1160.65342
Nolen, James; Papanicolaou, George; Pironneau, Olivier
2008
Reduced-basis approach for homogenization beyond the periodic setting. Zbl 1156.74358
Boyaval, Sébastien
2008
Analysis of explicit tau-leaping schemes for simulating chemically reacting systems. Zbl 1145.92041
Li, Tiejun
2007
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
A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems. Zbl 1090.65128
Ohlberger, Mario
2005
Well modeling in the multiscale finite volume method for subsurface flow simulation. Zbl 1205.76175
Wolfsteiner, Christian; Lee, Seong H.; Tchelepi, Hamdi A.
2006
A Lagrangian particle-wavelet method. Zbl 1122.65085
Bergdorf, Michael; Koumoutsakos, Petros
2006
An asymptotic preserving scheme for strongly anisotropic elliptic problems. Zbl 1190.35216
Degond, Pierre; Deluzet, Fabrice; Negulescu, Claudia
2010
Multiscale modeling of chemical kinetics via the master equation. Zbl 1153.60370
Macnamara, Shev; Burrage, Kevin; Sidje, Roger B.
2008
Finite element heterogeneous multiscale method for the wave equation. Zbl 1298.65145
Abdulle, Assyr; Grote, Marcus J.
2011
Homogenization of Maxwell’s equations in a split ring geometry. Zbl 1228.35028
Bouchitté, Guy; Schweizer, Ben
2010
A fourth-order variational image registration model and its fast multigrid algorithm. Zbl 1218.65022
Chumchob, N.; Chen, K.; Brito-Loeza, Carlos
2011
An analytical framework for the numerical homogenization of monotone elliptic operators and quasiconvex energies. Zbl 1119.74038
Gloria, Antoine
2006
Transition path theory for Markov jump processes. Zbl 1185.60086
Metzner, Philipp; Schütte, Christof; Vanden-Eijnden, Eric
2009
Gyrokinetic Vlasov equation in three dimensional setting. Second order approximation. Zbl 1220.35176
Bostan, Mihai
2010
Bandelet image approximation and compression. Zbl 1091.94006
Le Pennec, E.; Mallat, S.
2005
Hybrid multiscale methods. II: Kinetic equations. Zbl 1185.65198
Dimarco, Giacomo; Pareschi, Lorenzo
2008
Boundary problems for the fractional and tempered fractional operators. Zbl 1391.60104
Deng, Weihua; Li, Buyang; Tian, Wenyi; Zhang, Pingwen
2018
Analysis of a one-dimensional nonlocal quasi-continuum method. Zbl 1177.74169
Ming, Pingbing; Yang, Jerry Zhijian
2009
Existence of global weak solutions to some regularized kinetic models for dilute polymers. Zbl 1228.76004
Barrett, John W.; Süli, Endre
2007
An operator formulation of the multiscale finite-volume method with correction function. Zbl 1404.65222
Lunati, Ivan; Lee, Seong H.
2009
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
Binary interaction algorithms for the simulation of flocking and swarming dynamics. Zbl 1274.92053
Albi, G.; Pareschi, L.
2013
Matching of asymptotic expansions for wave propagation in media with thin slots I: The asymptotic expansion. Zbl 1132.35347
Joly, Patrick; Tordeux, Sébastien
2006
Mountain waves and Gaussian beams. Zbl 1149.41014
Tanushev, Nicolay M.; Qian, Jianliang; Ralston, James V.
2007
FENE dumbbell model and its several linear and nonlinear closure approximations. Zbl 1108.76006
Du, Qiang; Liu, Chun; Yu, Peng
2005
Consistency and stability of tau-leaping schemes for chemical reaction systems. Zbl 1089.60516
Rathinam, Muruhan; Petzold, Linda R.; Cao, Yang; Gillespie, Daniel T.
2005
Two-dimensional bulk microflow simulations based on regularized grad’s 13-moment equations. Zbl 1388.76340
Torrilhon, Manuel
2006
Numerical homogenization of elliptic multiscale problems by subspace decomposition. Zbl 1352.65521
Kornhuber, Ralf; Yserentant, Harry
2016
Finite element heterogeneous multiscale method for the wave equation: long-time effects. Zbl 1315.65084
Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian
2014
Importance sampling for multiscale diffusions. Zbl 1250.60031
Dupuis, Paul; Spiliopoulos, Konstantinos; Wang, Hui
2012
Escape from subcellular domains with randomly switching boundaries. Zbl 1329.82092
Bressloff, Paul C.; Lawley, Sean D.
2015
Mixed multiscale finite element methods using limited global information. Zbl 1277.76036
Aarnes, J. E.; Efendiev, Y.; Jiang, L.
2008
A hybrid finite-volume, discontinuous Galerkin discretization for the radiative transport equation. Zbl 1453.82099
Heningburg, Vincent; Hauck, Cory D.
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
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
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
The equivalent media generated by bubbles of high contrasts: volumetric metamaterials and metasurfaces. Zbl 1439.35555
2020
A hybrid multiscale model for cancer invasion of the extracellular matrix. Zbl 1443.92080
Sfakianakis, Nikolaos; Madzvamuse, Anotida; Chaplain, Mark A. J.
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
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
Efficient approximation of flow problems with multiple scales in time. Zbl 1446.65065
Frei, S.; Richter, T.
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 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
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
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
Mathematical analysis of electromagnetic plasmonic metasurfaces. Zbl 1448.35491
Ammari, Habib; Li, Bowen; Zou, Jun
2020
Multiscale flux-based modeling of biofilm communities. Zbl 1448.92144
Zhang, T.; Parker, A.; Carlson, R. P.; Stewart, P. S.; Klapper, I.
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
Numerically modeling stochastic Lie transport in fluid dynamics. Zbl 1454.76064
Cotter, Colin; Crisan, Dan; Holm, Darryl D.; Pan, Wei; Shevchenko, Igor
2019
Asymptotics of the gradient of solutions to the perfect conductivity problem. Zbl 1426.78022
Li, Haigang; Li, Yanyan; Yang, Zhuolun
2019
Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles. Zbl 1428.35268
Tosin, Andrea; Zanella, Mattia
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
Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates. Zbl 1422.60133
Lelievre, Tony; Zhang, Wei
2019
The Foldy-Lax approximation for the full electromagnetic scattering by small conductive bodies of arbitrary shapes. Zbl 1409.35065
2019
On the convergence of the SINDy algorithm. Zbl 1437.37108
Zhang, Linan; Schaeffer, Hayden
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
Heterogeneous multiscale method for Maxwell’s equations. Zbl 1435.78019
Hochbruck, Marlis; Maier, Bernhard; Stohrer, Christian
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
Raster grid pathology and the cure. Zbl 1426.78015
Fannjiang, Albert
2019
A constraint energy minimizing generalized multiscale finite element method for parabolic equations. Zbl 1426.65200
Li, Mengnan; Chung, Eric; Jiang, Lijian
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
Renormalized reduced order models with memory for long time prediction. Zbl 1412.65178
Price, Jacob; Stinis, Panos
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
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
On the convergence rates of GMsFEMs for heterogeneous elliptic problems without oversampling techniques. Zbl 1426.65179
Li, Guanglian
2019
A multiscale domain decomposition algorithm for boundary value problems for eikonal equations. Zbl 1426.65198
Martin, Lindsay; Tsai, Yen-Hsi R.
2019
Effective properties of fibrous Composites and cluster convergence. Zbl 1421.74086
2019
Stochastic model reduction for slow-fast systems with moderate time scale separation. Zbl 1434.70056
Wouters, Jeroen; Gottwald, Georg A.
2019
A multiscale neural network based on hierarchical matrices. Zbl 1435.65181
Fan, Yuwei; Lin, Lin; Ying, Lexing; Zepeda-Núñez, Leonardo
2019
Estimation of the heat conducted by a cluster of small cavities and characterization of the equivalent heat conduction. Zbl 1439.35187
2019
Projection-based embedding theory for solving Kohn-Sham density functional theory. Zbl 1434.65325
Lin, Lin; Zepeda-Nunez, Leonardo
2019
On constrained Langevin equations and (bio)chemical reaction networks. Zbl 07033867
Anderson, David F.; Higham, Desmond J.; Leite, Saul C.; Williams, Ruth J.
2019
Wave propagation and imaging in moving random media. Zbl 1409.76014
Borcea, Liliana; Garnier, Josselin; Solna, Knut
2019
Globally constructed adaptive local basis set for spectral projectors of second order differential operators. Zbl 1409.65118
Li, Yingzhou; Lin, Lin
2019
A two-dimensional “flea on the elephant” phenomenon and its numerical visualization. Zbl 1408.35110
Bianchini, Roberta; Gosse, Laurent; Zuazua, Enrique
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
Boundary problems for the fractional and tempered fractional operators. Zbl 1391.60104
Deng, Weihua; Li, Buyang; Tian, Wenyi; Zhang, Pingwen
2018
Quaternions in collective dynamics. Zbl 1382.35310
Degond, Pierre; Frouvelle, Amic; Merino-Aceituno, Sara; Trescases, Ariane
2018
Phase-field modeling of two phase fluid filled fractures in a poroelastic medium. Zbl 1401.74084
Lee, Sanghyun; Mikelić, Andro; Wheeler, Mary F.; Wick, Thomas
2018
Hypocoercivity based sensitivity analysis and spectral convergence of the stochastic Galerkin approximation to collisional kinetic equations with multiple scales and random inputs. Zbl 1403.35197
Liu, Liu; Jin, Shi
2018
Erratum: “The interplay of curvature and vortices in flow on curved surfaces”. Zbl 1403.35243
Reuther, Sebastian; Voigt, Axel
2018
An adaptive generalized multiscale discontinuous Galerkin method for high-contrast flow problems. Zbl 1407.65257
Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat
2018
Boundary homogenization and capture time distributions of semipermeable membranes with periodic patterns of reactive sites. Zbl 1403.35030
Bernoff, Andrew J.; Lindsay, Alan E.; Schmidt, Daniel D.
2018
Bayesian inference using intermediate distribution based on coarse multiscale model for time fractional diffusion equations. Zbl 1393.65032
Jiang, Lijian; Ou, Na
2018
The multiscale hybrid-mixed method for the Maxwell equations in heterogeneous media. Zbl 1412.65188
Lanteri, Stéphane; Paredes, Diego; Scheid, Claire; Valentin, Frédéric
2018
Spectral band degeneracies of $$\frac{\pi}{2}$$-rotationally invariant periodic Schrödinger operators. Zbl 1412.35283
Keller, Rachael T.; Marzuola, J. L.; Osting, B.; Weinstein, M. I.
2018
Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime. Zbl 1397.35171
Feireisl, Eduard; Lukáčová-Medviďová, Mária; Nečasová, Šárka; Novotný, Antonín; She, Bangwei
2018
Heat generation with plasmonic nanoparticles. Zbl 1432.35241
Ammari, Habib; Romero, Francisco; Ruiz, Matias
2018
Langevin dynamics with general kinetic energies. Zbl 1392.82004
Stoltz, Gabriel; Trstanova, Zofia
2018
Stochastic unfolding and homogenization of spring network models. Zbl 1392.49014
Neukamm, Stefan; Varga, Mario
2018
Cloaking via mapping for the heat equation. Zbl 1401.35142
Craster, R. V.; Guenneau, Sebastien R. L.; Hutridurga, H. R.; Pavliotis, G. A.
2018
Extending Babich’s ansatz for point-source Maxwell’s equations using Hadamard’s method. Zbl 1448.65242
Lu, Wangtao; Qian, Jianliang; Burridge, Robert
2018
An efficient time-splitting method for the Ehrenfest dynamics. Zbl 1426.35194
Fang, Di; Jin, Shi; Sparber, Christof
2018
A new heterogeneous multiscale method for the Helmholtz equation with high contrast. Zbl 1445.35131
Ohlberger, Mario; Verfurth, Barbara
2018
A spectrally accurate algorithm and analysis for a Ginzburg-Landau model on superconducting surfaces. Zbl 1422.65451
Ganesh, M.; Thompson, T.
2018
Kinetic modelling of strongly magnetized tokamak plasmas with mass disparate particles. The electron Boltzmann relation. Zbl 1417.35090
Negulescu, Claudia
2018
Accuracy of some approximate Gaussian filters for the Navier-Stokes equation in the presence of model error. Zbl 1408.93132
Branicki, M.; Majda, A. J.; Law, K. J. H.
2018
Identifying backbones in three-dimensional discrete fracture networks: a bipartite graph-based approach. Zbl 1457.76165
Hyman, Jeffrey D.; Hagberg, Aric; Osthus, Dave; Srinivasan, Shriram; Viswanathan, Hari; Srinivasan, Gowri
2018
Numerical homogenization of heterogeneous fractional Laplacians. Zbl 1426.65170
Brown, Donald L.; Gedicke, Joscha; Peterseim, Daniel
2018
Disentanglement via entanglement: a unified method for Wannier localization. Zbl 1448.65290
Damle, Anil; Lin, Lin
2018
Clustering nonstationary circadian rhythms using locally stationary wavelet representations. Zbl 1462.62665
Hargreaves, Jessica K.; Knight, Marina I.; Pitchford, Jon W.; Oakenfull, Rachael J.; Davis, Seth J.
2018
Harmonic extension on the point cloud. Zbl 06875724
Shi, Zuoqiang; Sun, Jian; Tian, Minghao
2018
Low-rank approximation to heterogeneous elliptic problems. Zbl 1448.65238
Li, Guanglian
2018
Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls. Zbl 1392.35201
Cristiani, Emiliano; Tosin, Andrea
2018
Continuum approximation of invasion probabilities. Zbl 1388.60135
Borchering, Rebecca K.; McKinley, Scott A.
2018
Six-dimensional adaptive simulation of the Vlasov equations using a hierarchical basis. Zbl 1393.65009
Deriaz, Erwan; Peirani, Sébastien
2018
An adaptive fast solver for a general class of positive definite matrices via energy decomposition. Zbl 1391.65066
Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, PengChuan
2018
Analysis of the residual-type and the gradient recovery-type a posteriori error estimators for a consistent atomistic-to-continuum coupling method in one-dimension. Zbl 1450.65138
Wang, Hao; Yang, Siyao
2018
On multiscale ADI methods for parabolic PDEs with a discontinuous coefficient. Zbl 1412.65083
Li, Zhilin; Chen, Xiaohong; Zhang, Zhengru
2018
Iterative solvers for elliptic problems with arbitrary anisotropy strengths. Zbl 1433.65259
Yang, Chang; Claustre, Jonathan; Deluzet, Fabrice
2018
Discrete-time statistical inference for multiscale diffusions. Zbl 1420.60035
Gailus, Siragan; Spiliopoulos, Konstantinos
2018
Nonlinear nonperturbative optics model enriched by evolution equation for polarization. Zbl 1400.78022
Lytova, Marianna; Lorin, Emmanuel; Bandrauk, André D.
2018
Computational complexity analysis for Monte Carlo approximations of classically scaled population processes. Zbl 1401.60130
Anderson, David F.; Higham, Desmond J.; Sun, Yu
2018
Residual-based variational multiscale modeling in a discontinuous Galerkin framework. Zbl 1433.65227
Stoter, Stein K. F.; Turteltaub, Sergio R.; Hulshoff, Steven J.; Schillinger, Dominik
2018
Compressing large-scale wave propagation models via phase-preconditioned rational Krylov subspaces. Zbl 1412.65139
Druskin, Vladimir; Remis, Rob F.; Zaslavsky, Mikhail; Zimmerling, Jörn T.
2018
Robustness of stochastic chemical reaction networks to extrinsic noise: the role of deficiency. Zbl 1400.92211
Levien, Ethan; Bressloff, Paul C.
2018
A tensor model for nematic phases of bent-core molecules based on molecular theory. Zbl 1401.76025
Xu, Jie; Ye, Fangfu; Zhang, Pingwen
2018
Mixed-integer programming for cycle detection in nonreversible Markov processes. Zbl 1391.60170
Witzig, Jakob; Beckenbach, Isabel; Eifler, Leon; Fackeldey, Konstantin; Gleixner, Ambros; Grever, Andreas; Weber, Marcus
2018
Incommensurate heterostructures in momentum space. Zbl 1434.82101
Massatt, Daniel; Carr, Stephen; Luskin, Mitchell; Ortner, Christoph
2018
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#### Cited by 8,641 Authors

 71 Chung, Tsz Shun Eric 52 Efendiev, Yalchin R. 42 Abdulle, Assyr 37 Degond, Pierre 36 Garnier, Josselin 35 Shen, Zuowei 34 Lu, Jianfeng 30 Osher, Stanley Joel 29 Ammari, Habib M. 29 Ortner, Christoph 29 Wheeler, Mary Fanett 29 Ying, Lexing 27 Chen, Ke 27 Du, Qiang 27 Jin, Shi 25 Carrillo de la Plata, José Antonio 24 Peterseim, Daniel 24 Tai, Xuecheng 23 Wick, Thomas 22 Huang, Ting-Zhu 22 Vasilyeva, Maria V. 21 Bal, Guillaume 21 Bostan, Mihai 21 Burger, Martin 21 Qian, Jianliang 20 Hou, Thomas Yizhao 20 Leung, Wingtat 20 Park, Won-Kwang 19 Bao, Weizhu 19 Bellomo, Nicola 19 Bertozzi, Andrea Louise 19 Galvis, Juan 19 Gunzburger, Max D. 19 Jiang, Lijian 19 Kevrekidis, Ioannis George 19 Le Bris, Claude 19 Pareschi, Lorenzo 19 Schütte, Christof 18 Luskin, Mitchell 18 Shen, Lixin 18 Valentin, Frédéric 17 Cui, Junzhi 17 Gander, Martin Jakob 17 Jenny, Patrick 17 Kang, Hyeonbae 17 Lawley, Sean D. 17 Peyré, Gabriel 17 Schweizer, Ben 17 Sølna, Knut 17 Wu, Boying 17 Zhang, Xiaoqun 16 Combettes, Patrick L. 16 Dimarco, Giacomo 16 Henning, Patrick 16 Pavliotis, Grigorios A. 16 Quarteroni, Alfio M. 16 Steidl, Gabriele 16 Süli, Endre E. 16 Yang, Haizhao 16 Zeng, Tie Yong 15 Bressloff, Paul C. 15 Chambolle, Antonin 15 Grohs, Philipp 15 Hajibeygi, Hadi 15 Holcman, David 15 Liu, Jianguo 15 Mikelić, Andro 15 Ohlberger, Mario 15 Samaey, Giovanni 15 Wu, Chunlin 14 Borcea, Liliana 14 Feng, Xiangchu 14 Ha, Seung-Yeal 14 Hauck, Cory D. 14 Holm, Darryl D. 14 Karniadakis, George Em 14 Klawonn, Axel 14 Koumoutsakos, Petros D. 14 Owhadi, Houman 14 Schönlieb, Carola-Bibiane 14 Sini, Mourad 14 Spiliopoulos, Konstantinos V. 14 Stefanelli, Ulisse 14 Yao, Jen-Chih 13 Aujol, Jean-François 13 Cai, Jian-Feng 13 Dong, Bin 13 Fadili, Jalal M. 13 Ji, Hui 13 Kružík, Martin 13 Majda, Andrew J. 13 Nordbotten, Jan Martin 13 Piccoli, Benedetto 13 Scianna, Marco 13 Yang, Xu 13 Zanella, Mattia 13 Zhu, Wei 12 Antoine, Xavier 12 Banks, Harvey Thomas 12 Bredies, Kristian ...and 8,541 more Authors
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#### Cited in 494 Journals

 484 Journal of Computational Physics 258 Multiscale Modeling & Simulation 225 Computer Methods in Applied Mechanics and Engineering 181 Journal of Scientific Computing 169 Journal of Computational and Applied Mathematics 146 SIAM Journal on Scientific Computing 129 Computers & Mathematics with Applications 127 Journal of Mathematical Imaging and Vision 124 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 121 SIAM Journal on Imaging Sciences 100 Applied and Computational Harmonic Analysis 84 Journal of Statistical Physics 81 SIAM Journal on Numerical Analysis 78 Computational Geosciences 75 Applied Mathematics and Computation 73 Archive for Rational Mechanics and Analysis 73 Journal of Mathematical Analysis and Applications 69 Journal of Mathematical Biology 68 Inverse Problems 65 Inverse Problems and Imaging 64 SIAM Journal on Applied Mathematics 64 SIAM Journal on Mathematical Analysis 63 Journal of Differential Equations 63 Numerische Mathematik 62 Mathematics of Computation 61 Applied Numerical Mathematics 59 Journal of Fluid Mechanics 59 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 57 Journal of Nonlinear Science 54 Bulletin of Mathematical Biology 52 Advances in Computational Mathematics 52 Mathematical Problems in Engineering 49 Physica D 43 Journal of Theoretical Biology 41 Computational Mechanics 38 International Journal for Numerical Methods in Engineering 36 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 35 Applied Mathematical Modelling 34 Numerical Algorithms 32 Applicable Analysis 31 Journal of Mathematical Physics 31 Mathematical Methods in the Applied Sciences 31 Discrete and Continuous Dynamical Systems. Series B 30 Journal of Optimization Theory and Applications 30 Computational Optimization and Applications 30 Calculus of Variations and Partial Differential Equations 29 SIAM/ASA Journal on Uncertainty Quantification 28 Computers and Fluids 28 Foundations of Computational Mathematics 27 BIT 27 Nonlinear Analysis. Real World Applications 26 Communications in Mathematical Physics 26 SIAM Journal on Optimization 26 Comptes Rendus. Mathématique. Académie des Sciences, Paris 25 Kinetic and Related Models 24 Mathematical Programming. Series A. Series B 24 Discrete and Continuous Dynamical Systems 24 Abstract and Applied Analysis 23 Journal of the Mechanics and Physics of Solids 23 Journal de Mathématiques Pures et Appliquées. Neuvième Série 23 Networks and Heterogeneous Media 22 European Journal of Applied Mathematics 22 International Journal of Computer Vision 21 Multidimensional Systems and Signal Processing 21 Discrete and Continuous Dynamical Systems. Series S 20 Mathematical Biosciences 20 ZAMP. Zeitschrift für angewandte Mathematik und Physik 20 Computational and Applied Mathematics 20 Chaos 20 International Journal of Wavelets, Multiresolution and Information Processing 19 Wave Motion 19 SIAM Journal on Control and Optimization 18 Computer Physics Communications 18 Nonlinearity 18 International Journal of Computer Mathematics 18 Pattern Recognition 18 Continuum Mechanics and Thermodynamics 18 Computational & Mathematical Methods in Medicine 17 Quarterly of Applied Mathematics 17 Applied Mathematics Letters 17 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 17 SIAM Journal on Applied Dynamical Systems 16 Information Sciences 16 Communications in Partial Differential Equations 16 SIAM Review 16 Journal of Inverse and Ill-Posed Problems 16 Mathematical Biosciences and Engineering 16 Research in the Mathematical Sciences 15 Optimization 15 Numerical Methods for Partial Differential Equations 15 Physics of Fluids 15 ETNA. Electronic Transactions on Numerical Analysis 14 Numerical Functional Analysis and Optimization 14 The Annals of Applied Probability 14 Numerical Linear Algebra with Applications 14 NoDEA. Nonlinear Differential Equations and Applications 14 The Journal of Fourier Analysis and Applications 14 GEM - International Journal on Geomathematics 13 Mathematical and Computer Modelling 13 Proceedings of the National Academy of Sciences of the United States of America ...and 394 more Journals
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#### Cited in 59 Fields

 2,775 Numerical analysis (65-XX) 2,279 Partial differential equations (35-XX) 1,171 Fluid mechanics (76-XX) 827 Information and communication theory, circuits (94-XX) 764 Mechanics of deformable solids (74-XX) 728 Biology and other natural sciences (92-XX) 660 Probability theory and stochastic processes (60-XX) 607 Statistical mechanics, structure of matter (82-XX) 576 Computer science (68-XX) 506 Operations research, mathematical programming (90-XX) 475 Calculus of variations and optimal control; optimization (49-XX) 301 Statistics (62-XX) 278 Optics, electromagnetic theory (78-XX) 251 Operator theory (47-XX) 208 Ordinary differential equations (34-XX) 203 Dynamical systems and ergodic theory (37-XX) 180 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 151 Harmonic analysis on Euclidean spaces (42-XX) 146 Systems theory; control (93-XX) 129 Geophysics (86-XX) 121 Integral equations (45-XX) 116 Quantum theory (81-XX) 110 Classical thermodynamics, heat transfer (80-XX) 79 Approximations and expansions (41-XX) 76 Linear and multilinear algebra; matrix theory (15-XX) 74 Mechanics of particles and systems (70-XX) 68 Functional analysis (46-XX) 62 Real functions (26-XX) 44 Differential geometry (53-XX) 43 Global analysis, analysis on manifolds (58-XX) 38 Combinatorics (05-XX) 27 Integral transforms, operational calculus (44-XX) 24 General and overarching topics; collections (00-XX) 19 Special functions (33-XX) 18 Measure and integration (28-XX) 15 Potential theory (31-XX) 12 Convex and discrete geometry (52-XX) 11 Topological groups, Lie groups (22-XX) 11 Functions of a complex variable (30-XX) 10 Difference and functional equations (39-XX) 9 General topology (54-XX) 9 Algebraic topology (55-XX) 9 Astronomy and astrophysics (85-XX) 8 History and biography (01-XX) 8 Manifolds and cell complexes (57-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 Mathematics education (97-XX) 2 Geometry (51-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-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) 1 Relativity and gravitational theory (83-XX)