Communications in Computational Physics Short Title: Commun. Comput. Phys. Publisher: Global Science Press, Hong Kong; Cambridge University Press, Cambridge ISSN: 1815-2406; 1991-7120/e Online: http://www.global-sci.com/cicp/periodical_list.htmlhttp://www.global-sci.com/issue/contents/index.htmlhttps://www.cambridge.org/core/journals/communications-in-computational-physics/all-issues Documents Indexed: 1,036 Publications (since 2006) References Indexed: 1 Publication with 8 References. all top 5 Latest Issues 21, No. 4 (2017) 21, No. 1 (2017) 20, No. 5 (2016) 20, No. 4 (2016) 20, No. 3 (2016) 20, No. 2 (2016) 20, No. 1 (2016) 19, No. 5 (2016) 19, No. 4 (2016) 19, No. 3 (2016) 19, No. 2 (2016) 19, No. 1 (2016) 18, No. 5 (2015) 18, No. 4 (2015) 18, No. 3 (2015) 18, No. 2 (2015) 18, No. 1 (2015) 17, No. 5 (2015) 17, No. 4 (2015) 17, No. 3 (2015) 17, No. 2 (2015) 17, No. 1 (2015) 16, No. 5 (2014) 16, No. 4 (2014) 16, No. 3 (2014) 16, No. 2 (2014) 16, No. 1 (2014) 15, No. 5 (2014) 15, No. 4 (2014) 15, No. 3 (2014) 15, No. 2 (2014) 15, No. 1 (2014) 14, No. 5 (2013) 14, No. 4 (2013) 14, No. 3 (2013) 14, No. 2 (2013) 14, No. 1 (2013) 13, No. 5 (2013) 13, No. 4 (2013) 13, No. 3 (2013) 13, No. 2 (2013) 13, No. 1 (2013) 12, No. 5 (2012) 12, No. 4 (2012) 12, No. 3 (2012) 12, No. 2 (2012) 12, No. 1 (2012) 11, No. 5 (2012) 11, No. 4 (2012) 11, No. 3 (2012) 11, No. 2 (2012) 11, No. 1 (2012) 10, No. 5 (2011) 10, No. 4 (2011) 10, No. 3 (2011) 10, No. 2 (2011) 10, No. 1 (2011) 9, No. 5 (2011) 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 (2010) 7, No. 5 (2010) 7, No. 4 (2010) 7, No. 3 (2010) 7, No. 2 (2010) 7, No. 1 (2010) 6, No. 5 (2009) 6, No. 4 (2009) 6, No. 3 (2009) 6, No. 2 (2009) 6, No. 1 (2009) 5, No. 5 (2009) 5, No. 2-4 (2009) 5, No. 1 (2009) 4, No. 5 (2008) 4, No. 4 (2008) 4, No. 3 (2008) 4, No. 2 (2008) 4, No. 1 (2008) 3, No. 5 (2008) 3, No. 4 (2008) 3, No. 3 (2008) 3, No. 2 (2008) 3, No. 1 (2008) 2, No. 6 (2007) 2, No. 5 (2007) 2, No. 4 (2007) 2, No. 3 (2007) 2, No. 2 (2007) 2, No. 1 (2007) 1, No. 6 (2006) 1, No. 5 (2006) 1, No. 4 (2006) 1, No. 3 (2006) all top 5 Authors 16 Shu, Chi-Wang 12 Cai, Wei 12 Sjogreen, Bjorn 11 Zhang, Pingwen 10 Sheu, Tony Wen-Hann 10 Tang, Tao 9 Li, Ruo 9 Succi, Sauro 9 Xu, Kun 8 Guo, Zhaoli 8 Khoo, Boo Cheong 8 Shen, Jie 7 Han, Houde 7 Mishra, Siddhartha 7 Shi, Baochang 7 Xiu, Dongbin 7 Xu, Yan 6 Bao, Weizhu 6 Diaz, Julien 6 Du, Qiang 6 Hesthaven, Jan S. 6 Hong, Jialin 6 Huang, Huaxiong 6 Huang, Yunqing 6 Li, Zhilin 6 Liang, Dong 6 Petersson, N. Anders 6 Wang, Desheng 6 Yuan, Guangwei 5 Chai, Zhenhua 5 Cheng, Xiaoliang 5 Cherubini, Christian 5 Dumbser, Michael 5 E, Weinan 5 Filippi, Simonetta 5 Gunzburger, Max D. 5 Hu, Guanghui 5 Liu, Tiegang 5 Ng, Michael Kwok-Po 5 Qiu, Jianxian 5 Tan, Zhijun 5 Toro, Eleuterio F. 5 Ubertini, Stefano 5 Xu, Zhenli 5 Yang, Jaw-Yen 5 Yee, Helen C. 5 Zheng, Chunxiong 4 Abgrall, Rémi 4 Barucq, Hélène 4 Brull, Stephane 4 Chen, Shiyi 4 Degond, Pierre 4 Deng, Xiaogang 4 Efendiev, Yalchin R. 4 Huang, Jingfang 4 Jin, Shi 4 Joly, Patrick 4 Kurganov, Alexander 4 Leung, Shingyu 4 Li, Xiaofan 4 Lim, Kian-Meng 4 Liu, Hailiang 4 Lu, Benzhuo 4 Lu, Tiao 4 Ming, Pingbing 4 Nordström, Jan 4 Palpacelli, Silvia 4 Qiao, Zhonghua 4 Shao, Sihong 4 Shashkov, Mikhail J. 4 Shih, Yintzer 4 Tang, Huazhong 4 Torrilhon, Manuel 4 Wang, Qi 4 Wang, Yushun 4 Yao, Jun 4 Ying, Wenjun 4 Zhang, Hanxin 4 Zhou, Tao 4 Zhu, Jun 3 Ansumali, Santosh 3 Antoine, Xavier 3 Auteri, Franco 3 Banks, Jeffrey W. 3 Bao, Gang 3 Beale, J. Thomas 3 Bella, Gino 3 Besse, Christophe 3 Cai, Xiao-Chuan 3 Chen, Jingrun 3 Chen, Ke 3 Chen, Long-Qing 3 Chen, Wenbin 3 Chen, Xiaopeng 3 Cheng, Juan 3 Chertock, Alina E. 3 Chiappini, Daniele 3 Cohen, Gary C. 3 Cui, Junzhi 3 Don, Wai Sun ...and 1,833 more Authors all top 5 Fields 652 Numerical analysis (65-XX) 503 Fluid mechanics (76-XX) 229 Partial differential equations (35-XX) 100 Mechanics of deformable solids (74-XX) 100 Statistical mechanics, structure of matter (82-XX) 85 Optics, electromagnetic theory (78-XX) 51 Biology and other natural sciences (92-XX) 41 Geophysics (86-XX) 39 Quantum theory (81-XX) 34 Probability theory and stochastic processes (60-XX) 30 Classical thermodynamics, heat transfer (80-XX) 28 Computer science (68-XX) 19 Dynamical systems and ergodic theory (37-XX) 19 Information and communication theory, circuits (94-XX) 15 Statistics (62-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 9 Integral equations (45-XX) 8 General and overarching topics; collections (00-XX) 8 Operations research, mathematical programming (90-XX) 7 Ordinary differential equations (34-XX) 7 Operator theory (47-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Relativity and gravitational theory (83-XX) 5 Approximations and expansions (41-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Mechanics of particles and systems (70-XX) 5 Systems theory; control (93-XX) 4 Convex and discrete geometry (52-XX) 4 Astronomy and astrophysics (85-XX) 3 Combinatorics (05-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Special functions (33-XX) 2 History and biography (01-XX) 2 Abstract harmonic analysis (43-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 794 Publications have been cited 6,643 times in 5,206 Documents Cited by ▼ Year ▼ Existence and uniqueness of the weak solution of the space-time fractional diffusion equation and a spectral method approximation. Zbl 1364.35424Li, Xianjuan; Xu, Chuanju 147 2010 Heterogeneous multiscale methods: a review. Zbl 1164.65496E, Weinan; Engquist, Bjorn; Li, Xiantao; Ren, Weiqing; Vanden-Eijnden, Eric 139 2007 Phase-field models for multi-component fluid flows. Zbl 1373.76030Kim, Junseok 110 2012 Fast numerical methods for stochastic computations: a review. Zbl 1364.65019Xiu, Dongbin 103 2009 Local discontinuous Galerkin methods for high-order time-dependent partial differential equations. Zbl 1364.65205Xu, Yan; Shu, Chi-Wang 103 2010 Efficient collocational approach for parametric uncertainty analysis. Zbl 1164.65302Xiu, Dongbin 95 2007 A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Zbl 1364.65178Antoine, Xavier; Arnold, Anton; Besse, Christophe; Ehrhardt, Matthias; Schadle, Achim 95 2008 A finite-volume method for nonlinear nonlocal equations with a gradient flow structure. Zbl 1388.65077Carrillo, José A.; Chertock, Alina; Huang, Yanghong 76 2015 Third order WENO scheme on three dimensional tetrahedral meshes. Zbl 1364.65177Zhang, Yong-Tao; Shu, Chi-Wang 68 2009 Some recent advances on spectral methods for unbounded domains. Zbl 1364.65265Shen, Jie; Wang, Li-Lian 63 2009 Numerical methods for fluid-structure interaction – a review. Zbl 1373.76001Hou, Gene; Wang, Jin; Layton, Anita 62 2012 On universal Osher-type schemes for general nonlinear hyperbolic conservation laws. Zbl 1373.76125Dumbser, Michael; Toro, Eleuterio F. 61 2011 A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. Zbl 1115.65096Xing, Yulong; Shu, Chi-Wang 57 2006 All speed scheme for the low Mach number limit of the isentropic Euler equations. Zbl 1364.76129Degond, Pierre; Tang, Min 56 2011 A stochastic collocation approach to Bayesian inference in inverse problems. Zbl 1364.62064Marzouk, Youssef; Xiu, Dongbin 56 2009 Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations. Zbl 1373.76121Chandrashekar, Praveen 54 2013 The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200Liu, Hailiang; Yan, Jue 53 2010 Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications. Zbl 1186.92005Lu, B. Z.; Zhou, Y. C.; Holst, M. J.; McCammon, J. A. 53 2008 On the reduction of numerical dissipation in central-upwind schemes. Zbl 1164.65455Kurganov, Alexander; Lin, Chitien 45 2007 A new family of high order unstructured MOOD and ADER finite volume schemes for multidimensional systems of hyperbolic conservation laws. Zbl 1373.76137Loubère, Raphaël; Dumbser, Michael; Diot, Steven 45 2014 A high-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids. Zbl 1164.76360Sun, Yuzhi; Wang, Z. J.; Liu, Yen 44 2007 Galerkin method for wave equations with uncertain coefficients. Zbl 1195.65009Gottlieb, David; Xiu, Dongbin 44 2008 An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations. Zbl 1373.76284Haack, Jeffrey; Jin, Shi; Liu, Jian-guo 44 2012 Upwind and high-resolution methods for compressible flow: From donor cell to residual-distribution schemes. Zbl 1114.76049van Leer, B. 42 2006 WENO schemes for mixed-element unstructured meshes. Zbl 1364.76121Titarev, V. A.; Tsoutsanis, P.; Drikakis, D. 39 2010 An efficient, energy stable scheme for the Cahn-Hilliard-Brinkman system. Zbl 1373.76161Collins, Craig; Shen, Jie; Wise, Steven M. 39 2013 Mathematical principles of anisotropic mesh adaptation. Zbl 1122.65124Huang, Weizhang 38 2006 Enforcing the discrete maximum principle for linear finite element solutions of second-order elliptic problems. Zbl 1199.65381Liska, Richard; Shashkov, Mikhail 37 2008 An adaptive time-stepping strategy for the Cahn-Hilliard equation. Zbl 1388.65072Zhang, Zhengru; Qiao, Zhonghua 37 2012 A unified gas-kinetic scheme for continuum and rarefied flows. II: Multi-dimensional cases. Zbl 1373.76216Huang, Juan-Chen; Xu, Kun; Yu, Pubing 37 2012 Efficient energy stable schemes with spectral discretization in space for anisotropic Cahn-Hilliard systems. Zbl 1388.65117Chen, Feng; Shen, Jie 36 2013 Finite volume evolution Galerkin methods for the shallow water equations with dry beds. Zbl 1364.76109Bollermann, Andreas; Noelle, Sebastian; Lukáčová-Medvid’ová, Maria 34 2011 Staggered Lagrangian discretization based on cell-centered Riemann solver and associated hydrodynamics scheme. Zbl 1373.76138Maire, Pierre-Henri; Loubère, Raphaël; Váchal, Pavel 34 2011 Fourth order difference approximations for space Riemann-Liouville derivatives based on weighted and shifted Lubich difference operators. Zbl 1388.65130Chen, Minghua; Deng, Weihua 34 2014 Numerical bifurcation methods and their application to fluid dynamics: analysis beyond simulation. Zbl 1373.76026Dijkstra, Henk A.; Wubs, Fred W.; Cliffe, Andrew K.; Doedel, Eusebius; Dragomirescu, Ioana F.; Eckhardt, Bruno; Gelfgat, Alexander Yu.; Hazel, Andrew L.; Lucarini, Valerio; Salinger, Andy G.; Phipps, Erik T.; Sanchez-Umbria, Juan; Schuttelaars, Henk; Tuckerman, Laurette S.; Thiele, Uwe 31 2014 A compressed sensing approach for partial differential equations with random input data. Zbl 1388.65018Mathelin, L.; Gallivan, K. A. 30 2012 Semi-implicit interior penalty discontinuous Galerkin methods for viscous compressible flows. Zbl 1364.76085Dolejsi, Vit 29 2008 On the volume conservation of the immersed boundary method. Zbl 1373.74098Griffith, Boyce E. 29 2012 On the order of accuracy and numerical performance of two classes of finite volume WENO schemes. Zbl 1364.65176Zhang, Rui; Zhang, Mengping; Shu, Chi-Wang 28 2011 Exponentially-convergent strategies for defeating the Runge phenomenon for the approximation of non-periodic functions. I: Single-interval schemes. Zbl 1364.65025Boyd, John P.; Ong, Jun Rong 28 2009 Application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system. Zbl 1364.65203Xia, Yinhua; Xu, Yan; Shu, Chi-Wang 28 2009 Arbitrary-Lagrangian-Eulerian one-step WENO finite volume schemes on unstructured triangular meshes. Zbl 1388.65075Boscheri, Walter; Dumbser, Michael 28 2013 A computational study of a data assimilation algorithm for the two-dimensional Navier-Stokes equations. Zbl 1373.76027Gesho, Masakazu; Olson, Eric; Titi, Edriss S. 28 2016 Lumped parameter outflow models for 1-D blood flow simulations: effect on pulse waves and parameter estimation. Zbl 1364.76248Alastruey, J.; Parker, K. H.; Peiro, J.; Sherwin, S. J. 27 2008 Efficient deterministic modelling of three-dimensional rarefied gas flows. Zbl 1373.82084Titarev, V. A. 27 2012 Generalized multiscale finite element methods. Nonlinear elliptic equations. Zbl 1388.65146Efendiev, Yalchin; Galvis, Juan; Li, Guanglian; Presho, Michael 27 2014 A numerical study on the weak Galerkin method for the Helmholtz equation. Zbl 1388.65156Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan 27 2014 Stochastic collocation on unstructured multivariate meshes. Zbl 1388.65127Narayan, Akil; Zhou, Tao 27 2015 A third order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equations. Zbl 1364.76111Cheng, Juan; Shu, Chi-Wang 25 2008 A bilinear immersed finite volume element method for the diffusion equation with discontinuous coefficient. Zbl 1364.65225He, X.-M.; Lin, T.; Lin, Y. 25 2009 Truncation errors, exact and heuristic stability analysis of two-relaxation-times lattice Boltzmann schemes for anisotropic advection-diffusion equation. Zbl 1373.76241Ginzburg, Irina 25 2012 A numerical method for solving elasticity equations with interfaces. Zbl 1373.74091Hou, Songming; Li, Zhilin; Wang, Liqun; Wang, Wei 25 2012 Exact boundary conditions for periodic waveguides containing a local perturbation. Zbl 1125.78008Joly, P.; Li, J.-R.; Fliss, S. 24 2006 Numerical simulation of time-harmonic waves in inhomogeneous media using compact high order schemes. Zbl 1364.78034Britt, Steven; Tsynkov, Semyon; Turkel, Eli 24 2011 A stable finite difference method for the elastic wave equation on complex geometries with free surfaces. Zbl 1364.74016Appelo, Daniel; Petersson, N. Anders 24 2009 Conservative semi-Lagrangian finite difference WENO formulations with applications to the Vlasov equation. Zbl 1388.65066Qiu, Jing-Mei; Shu, Chi-Wang 24 2011 Mass and volume conservation in phase field models for binary fluids. Zbl 1373.76317Shen, Jie; Yang, Xiaofeng; Wang, Qi 24 2013 A unified gas-kinetic scheme for continuum and rarefied flows. III: Microflow simulations. Zbl 1373.76217Huang, Juan-Chen; Xu, Kun; Yu, Pubing 24 2013 Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrödinger equations. Zbl 1388.65086Liang, Xiao; Khaliq, A. Q. M.; Xing, Yulong 24 2015 Non-oscillatory hierarchical reconstruction for central and finite volume schemes. Zbl 1164.65456Liu, Yingjie; Shu, Chiwang; Tadmor, Eitan; Zhang, Mengping 23 2007 Numerical entropy and adaptivity for finite volume schemes. Zbl 1373.76140Puppo, Gabriella; Semplice, Matteo 23 2011 An all-regime Lagrange-projection like scheme for the gas dynamics equations on unstructured meshes. Zbl 1373.76120Chalons, Christophe; Girardin, Mathieu; Kokh, Samuel 23 2016 Mathematical models and numerical methods for high frequency waves. Zbl 1164.78300Runborg, Olof 22 2007 Recent developments in numerical techniques for transport-based medical imaging methods. Zbl 1364.94100Ren, Kui 22 2010 Preconditioned iterative methods for two-dimensional space-fractional diffusion equations. Zbl 1388.65057Jin, Xiao-Qing; Lin, Fu-Rong; Zhao, Zhi 22 2015 A new weak Galerkin finite element scheme for the Brinkman model. Zbl 1373.76108Zhai, Qilong; Zhang, Ran; Mu, Lin 22 2016 An efficient spectral method for acoustic scattering from rough surfaces. Zbl 1164.65303Xiu, Dongbin; Shen, Jie 21 2007 A robust WENO type finite volume solver for steady Euler equations on unstructured grids. Zbl 1364.65226Hu, Guanghui; Li, Ruo; Tang, Tao 21 2011 Efficient implicit non-linear LU-SGS approach for compressible flow computation using high-order spectral difference method. Zbl 1364.76139Sun, Yuzhi; Wang, Z. J.; Liu, Yen 21 2009 Molecular hydrodynamics of the moving contact line in two-phase immiscible flows. Zbl 1115.76079Qian, Tiezheng; Wang, Xiao-Ping; Sheng, Ping 20 2006 Two-dimensional multi-domain hybrid spectral-WENO methods for conservation laws. Zbl 1114.76050Costa, B.; Don, W. S.; Gottlieb, D.; Sendersky, R. 20 2006 A parallel, reconstructed discontinuous Galerkin method for the compressible flows on arbitrary grids. Zbl 1364.76090Luo, Hong; Luo, Luqing; Ali, Amjad; Nourgaliev, Robert; Cai, Chunpei 20 2011 Multiscale modeling and simulations of flows in naturally fractured karst reservoirs. Zbl 1364.76225Popov, Peter; Efendiev, Yalchin; Qin, Guan 20 2009 Particulate flow simulation via a boundary condition-enforced immersed boundary-lattice Boltzmann scheme. Zbl 1364.76193Wu, J.; Shu, C. 20 2010 Convergence analysis for stochastic collocation methods to scalar hyperbolic equations with a random wave speed. Zbl 1364.65215Tang, Tao; Zhou, Tao 20 2010 Numerical simulation of moving contact lines with surfactant by immersed boundary method. Zbl 1364.76125Lai, Ming-Chih; Tseng, Yu-Hau; Huang, Huaxiong 20 2010 Spectral-element and adjoint methods in seismology. Zbl 1183.74320Tromp, Jeroen; Komatitsch, Dimitri; Liu, Qinya 20 2008 Simulations of compressible two-medium flow by Runge-Kutta discontinuous Galerkin methods with the ghost fluid method. Zbl 1195.76262Qiu, Jianxian; Liu, Tiegang; Khoo, Boo Cheong 20 2008 Adaptive finite element modeling techniques for the Poisson-Boltzmann equation. Zbl 1373.82077Holst, M.; McCammon, J. A.; Yu, Z.; Zhou, Y. C.; Zhu, Y. 20 2012 Flow in collapsible tubes with discontinuous mechanical properties: mathematical model and exact solutions. Zbl 1373.76362Toro, Eleuterio F.; Siviglia, Annunziato 20 2013 On arbitrary-Lagrangian-Eulerian one-step WENO schemes for stiff hyperbolic balance laws. Zbl 1373.76126Dumbser, Michael; Uuriintsetseg, Ariunaa; Zanotti, Olindo 20 2013 PVFMM: A parallel kernel independent FMM for particle and volume potentials. Zbl 1388.65169Malhotra, Dhairya; Biros, George 20 2015 Phase-field models for biofilms. II: 2-D numerical simulations of biofilm-flow interaction. Zbl 1365.92024Zhang, Tianyu; Cogan, Nick; Wang, Qi 19 2008 Velocity-based moving mesh methods for nonlinear partial differential equations. Zbl 1388.65094Baines, M. J.; Hubbard, M. E.; Jimack, P. K. 19 2011 A reconstructed discontinuous Galerkin method for the Euler equations on arbitrary grids. Zbl 1388.65124Luo, Hong; Luo, Luqing; Nourgaliev, Robert 19 2012 A moving mesh method for the Euler flow calculations using a directional monitor function. Zbl 1115.76362Tang, H.-Z. 18 2006 Accuracy of the adaptive GRP scheme and the simulation of 2-D Riemann problems for compressible Euler equations. Zbl 1373.76130Han, Ee; Li, Jiequan; Tang, Huazhong 18 2011 Computing the ground and first excited states of the fractional Schrödinger equation in an infinite potential well. Zbl 1388.65051Duo, Siwei; Zhang, Yanzhi 18 2015 Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation. Zbl 1164.76422Liu, Chun; Shen, Jie; Yang, Xiaofeng 16 2007 A Cartesian embedded boundary method for hyperbolic conservation laws. Zbl 1164.76354Sjögreen, Björn; Petersson, N. Anders 16 2007 Phase field model of thermo-induced Marangoni effects in the mixtures and its numerical simulations with mixed finite element method. Zbl 1364.76097Sun, Pengtao; Liu, Chun; Xu, Jinchao 16 2009 A general moving mesh framework in 3D and its application for simulating the mixture of multi-phase flows. Zbl 1195.76252Di, Yana; Li, Ruo; Tang, Tao 16 2008 A review of residual distribution schemes for hyperbolic and parabolic problems: the July 2010 state of the art. Zbl 1373.76114Abgrall, Remi 16 2012 Numerical regularized moment method for high Mach number flow. Zbl 1373.76296Cai, Zhenning; Li, Ruo; Wang, Yanli 16 2012 On diffuse interface modeling and simulation of surfactants in two-phase fluid flow. Zbl 1373.76334Engblom, Stefan; Do-Quang, Minh; Amberg, Gustav; Tornberg, Anna-Karin 16 2013 IMEX large time step finite volume methods for low Froude number shallow water flows. Zbl 1373.76117Bispen, Georgij; Arun, K. R.; Lukáčová-Medvid’ová, Mária; Noelle, Sebastian 16 2014 Discontinuous-Galerkin discretization of a new class of Green-Naghdi equations. Zbl 1373.76082Duran, Arnaud; Marche, Fabien 16 2015 Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter. Zbl 1373.76113Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian 16 2016 An \(r\)-adaptive finite element method for the solution of the two-dimensional phase-field equations. Zbl 1114.80308Beckett, G.; Mackenzie, J. A.; Robertson, M. L. 15 2006 Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport. Zbl 1364.65211Shao, Sihong; Lu, Tiao; Cai, Wei 15 2011 Optimal superconvergence of energy conserving local discontinuous Galerkin methods for wave equations. Zbl 1388.65097Cao, Waixiang; Li, Dongfang; Zhang, Zhimin 9 2017 High order accurate direct arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for non-conservative hyperbolic systems with stiff source terms. Zbl 1388.65076Boscheri, Walter; Loubère, Raphaël 7 2017 Artificial boundary conditions for nonlocal heat equations on unbounded domain. Zbl 1373.45011Zhang, Wei; Yang, Jiang; Zhang, Jiwei; Du, Qiang 6 2017 Construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems. Zbl 1388.65183Wang, Peng; Hong, Jialin; Xu, Dongsheng 6 2017 A compact scheme for coupled stochastic nonlinear Schrödinger equations. Zbl 1373.60108Chen, Chuchu; Hong, Jialin; Ji, Lihai; Kong, Linghua 5 2017 Numerical study of partially conservative moment equations in kinetic theory. Zbl 1373.82079Koellermeier, Julian; Torrilhon, Manuel 5 2017 Pressure-correction projection FEM for time-dependent natural convection problem. Zbl 1373.76106Wu, Jilian; Feng, Xinlong; Liu, Fei 5 2017 A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws. Zbl 1373.49030Yang, Feng Wei; Venkataraman, Chandrasekhar; Styles, Vanessa; Madzvamuse, Anotida 4 2017 A simple explanation of superconvergence for discontinuous Galerkin solutions to \(u_t+u_x=0\). Zbl 1388.65105Roe, Philip 4 2017 Schemes with well-controlled dissipation. hyperbolic systems in nonconservative form. Zbl 1373.76155Beljadid, Abdelaziz; Lefloch, Philippe G.; Mishra, Siddhartha; Parés, Carlos 4 2017 Nonconforming finite element method applied to the driven cavity problem. Zbl 1373.76095Lim, Roktaek; Sheen, Dongwoo 4 2017 Monotone finite volume scheme for three dimensional diffusion equation on tetrahedral meshes. Zbl 1388.65081Lai, Xiang; Sheng, Zhiqiang; Yuan, Guangwei 3 2017 Second-order two-scale computational method for nonlinear dynamic thermo-mechanical problems of composites with cylindrical periodicity. Zbl 1373.74088Dong, Hao; Cui, Junzhi; Nie, Yufeng; Yang, Zihao 2 2017 Computing optimal interfacial structure of modulated phases. Zbl 1373.82032Xu, Jie; Wang, Chu; Shi, An-Chang; Zhang, Pingwen 1 2017 A mathematical analysis of scale similarity. Zbl 1373.76051Wang, Z. J.; Li, Yanan 1 2017 A computational study of a data assimilation algorithm for the two-dimensional Navier-Stokes equations. Zbl 1373.76027Gesho, Masakazu; Olson, Eric; Titi, Edriss S. 28 2016 An all-regime Lagrange-projection like scheme for the gas dynamics equations on unstructured meshes. Zbl 1373.76120Chalons, Christophe; Girardin, Mathieu; Kokh, Samuel 23 2016 A new weak Galerkin finite element scheme for the Brinkman model. Zbl 1373.76108Zhai, Qilong; Zhang, Ran; Mu, Lin 22 2016 Runge-Kutta discontinuous Galerkin method with a simple and compact Hermite WENO limiter. Zbl 1373.76113Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian 16 2016 Entropy stable scheme on two-dimensional unstructured grids for Euler equations. Zbl 1373.76143Ray, Deep; Chandrashekar, Praveen; Fjordholm, Ulrik S.; Mishra, Siddhartha 14 2016 Two-grid method for miscible displacement problem by mixed finite element methods and mixed finite element method of characteristics. Zbl 1373.76079Chen, Yanping; Hu, Hanzhang 13 2016 A comparative study of rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations. Zbl 1373.76096Liu, Xiaodong; Xia, Yidong; Luo, Hong; Xuan, Lijun 12 2016 Divergence-free WENO reconstruction-based finite volume scheme for solving ideal MHD equations on triangular meshes. Zbl 1373.76149Xu, Zhiliang; Balsara, Dinshaw S.; Du, Huijing 11 2016 Solving Maxwell’s equation in meta-materials by a CG-DG method. Zbl 1388.65111Xie, Ziqing; Wang, Jiangxing; Wang, Bo; Chen, Chuanmiao 11 2016 On fully decoupled, convergent schemes for diffuse interface models for two-phase flow with general mass densities. Zbl 1373.76089Grün, Günther; Guillén-González, Francisco; Metzger, Stefan 11 2016 A posteriori error estimates for conservative local discontinuous Galerkin methods for the generalized Korteweg-de Vries equation. Zbl 1388.65100Karakashian, Ohannes; Xing, Yulong 10 2016 On the disclination lines of nematic liquid crystals. Zbl 1373.76012Hu, Yucheng; Qu, Yang; Zhang, Pingwen 9 2016 The mass-preserving S-DDM scheme for two-dimensional parabolic equations. Zbl 1388.65073Zhou, Zhongguo; Liang, Dong 9 2016 A 3D multi-phase hydrodynamic model for cytokinesis of eukaryotic cells. Zbl 1373.92036Zhao, Jia; Wang, Qi 9 2016 A simple method for computing singular or nearly singular integrals on closed surfaces. Zbl 1388.65167Beale, J. Thomas; Ying, Wenjun; Wilson, Jason R. 9 2016 Asymptotic-preserving scheme for the M1-Maxwell system in the quasi-neutral regime. Zbl 1373.76169Guisset, S.; Brull, S.; Dubroca, B.; D’humières, E.; Karpov, S.; Potapenko, I. 8 2016 Parameter-free time adaptivity based on energy evolution for the Cahn-Hilliard equation. Zbl 1388.65060Luo, Fuesheng; Tang, Tao; Xie, Hehu 8 2016 An energy-preserving wavelet collocation method for general multi-symplectic formulations of Hamiltonian PDEs. Zbl 1388.65120Gong, Yuezheng; Wang, Yushun 7 2016 High order numerical methods for the dynamic SGS model of turbulent flows with shocks. Zbl 1373.76061Kotov, D. V.; Yee, H. C.; Wray, A. A.; Hadjadj, A.; Sjögreen, B. 7 2016 A multigrid method for ground state solution of Bose-Einstein condensates. Zbl 1373.82042Xie, Hehu; Xie, Manting 7 2016 Finite volume lattice Boltzmann method for nearly incompressible flows on arbitrary unstructured meshes. Zbl 1373.76256Li, Weidong; Luo, Li-Shi 7 2016 Two-size moment multi-fluid model: A robust and high-fidelity description of polydisperse moderately dense evaporating sprays. Zbl 1373.76322Laurent, Frédérique; Sibra, Alaric; Doisneau, François 6 2016 An efficient immersed boundary-lattice Boltzmann method for the simulation of thermal flow problems. Zbl 1373.76244Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong 6 2016 A numerical methodology for enforcing maximum principles and the non-negative constraint for transient diffusion equations. Zbl 1388.65087Nakshatrala, K. B.; Nagarajan, H.; Shabouei, M. 6 2016 An adaptive perfectly matched layer method for multiple cavity scattering problems. Zbl 1388.65160Wu, Xinming; Zheng, Weiying 6 2016 A second-order finite difference method for two-dimensional fractional percolation equations. Zbl 1388.65053Guo, Boling; Xu, Qiang; Zhu, Ailing 6 2016 Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT. Zbl 1388.65115Bao, Weizhu; Tang, Qinglin; Zhang, Yong 6 2016 DASHMM: dynamic adaptive system for hierarchical multipole methods. Zbl 1373.70002Debuhr, J.; Zhang, B.; Tsueda, A.; Tilstra-Smith, V.; Sterling, T. 5 2016 Geometric numerical integration for peakon \(b\)-family equations. Zbl 1388.65116Cai, Wenjun; Sun, Yajuan; Wang, Yushun 5 2016 RECFMM: recursive parallelization of the adaptive fast multipole method for Coulomb and screened Coulomb interactions. Zbl 1373.78001Zhang, Bo; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai 5 2016 Particle methods for viscous flows: analogies and differences between the SPH and DVH methods. Zbl 1373.76233Colagrossi, Andrea; Rossi, Emanuele; Marrone, Salvatore; Le Touzé, David 5 2016 High order fixed-point sweeping WENO methods for steady state of hyperbolic conservation laws and its convergence study. Zbl 1388.65068Wu, Liang; Zhang, Yong-Tao; Zhang, Shuhai; Shu, Chi-Wang 5 2016 Scale transitions in magnetisation dynamics. Zbl 1373.78033Poluektov, Mikhail; Eriksson, Olle; Kreiss, Gunilla 4 2016 An adaptive grid method for singularly perturbed time-dependent convection-diffusion problems. Zbl 1388.65049Chen, Yanping; Liu, Li-Bin 4 2016 A fast solver for an H1 regularized PDE-constrained optimization problem. Zbl 1373.49028Barker, Andrew T.; Rees, Tyrone; Stoll, Martin 4 2016 Practical techniques in ghost fluid method for compressible multi-medium flows. Zbl 1373.76223Xu, Liang; Feng, Chengliang; Liu, Tiegang 4 2016 A comparison of higher-order weak numerical schemes for stopped stochastic differential equations. Zbl 1388.65013Bernal, Francisco; Acebrón, Juan A. 4 2016 Reinitialization of the level-set function in 3d simulation of moving contact lines. Zbl 1373.76201Xu, Shixin; Ren, Weiqing 3 2016 An element decomposition method for the Helmholtz equation. Zbl 1388.65159Wang, Gang; Cui, Xiangyang; Li, Guangyao 3 2016 A discrete-ordinate discontinuous-streamline diffusion method for the radiative transfer equation. Zbl 1388.65158Wang, Cheng; Sheng, Qiwei; Han, Weimin 3 2016 A new coupled complex boundary method for bioluminescence tomography. Zbl 1373.74095Gong, Rongfang; Cheng, Xiaoliang; Han, Weimin 3 2016 Simulating biofilm deformation and detachment with the immersed boundary method. Zbl 1373.76014Sudarsan, Rangarajan; Ghosh, Sudeshna; Stockie, John M.; Eberl, Hermann J. 3 2016 A two-stage image segmentation model for multi-channel images. Zbl 1373.94246Li, Zhi; Zeng, Tieyong 3 2016 Single component multiphase lattice Boltzmann method for Taylor/Bretherton bubble train flow simulations. Zbl 1373.76318Dzikowski, Michał; Łaniewski-Wołłk, Łukasz; Rokicki, Jacek 3 2016 Pseudo-arclength continuation algorithms for binary Rydberg-dressed Bose-Einstein condensates. Zbl 1388.65039Sriburadet, Sirilak; Wang, Y.-S.; Chien, C.-S.; Shih, Y. 3 2016 Direct calculation of permeability by high-accurate finite difference and numerical integration methods. Zbl 1373.76198Wang, Yi; Sun, Shuyu 3 2016 Fast solution of three-dimensional modified Helmholtz equations by the method of fundamental solutions. Zbl 1388.65180Lin, Ji; Chen, C. S.; Liu, Chein-Shan 3 2016 Application of the LS-STAG immersed boundary/cut-cell method to viscoelastic flow computations. Zbl 1373.76118Botella, Olivier; Cheny, Yoann; Nikfarjam, Farhad; Stoica, Marcela 2 2016 Estimation of impacts of removing arbitrarily constrained domain details to the analysis of incompressible fluid flows. Zbl 1373.76036Zhang, Kai; Li, Ming; Li, Jingzhi 2 2016 Hybrid and multiplicative overlapping Schwarz algorithms with standard coarse spaces for mixed linear elasticity and Stokes problems. Zbl 1373.74104Cai, Mingchao; Pavarino, Luca F. 2 2016 Quadrature weights on tensor-product nodes for accurate integration of hypersingular functions over some simple 3-D geometric shapes. Zbl 1388.65026Zinser, Brian; Cai, Wei; Chen, Duan 2 2016 A conservative parallel iteration scheme for nonlinear diffusion equations on unstructured meshes. Zbl 1388.65083Yu, Yunlong; Yao, Yanzhong; Yuan, Guangwei; Chen, Xingding 2 2016 Towards translational invariance of total energy with finite element methods for Kohn-Sham equation. Zbl 1388.65141Bao, Gang; Hu, Guanghui; Liu, Di 2 2016 A front tracking method for the simulation of compressible multimedium flows. Zbl 1373.76180Lu, Haitian; Zhao, Ning; Wang, Donghong 2 2016 Relaxation schemes for the \(M_1\) model with space-dependent flux: application to radiotherapy dose calculation. Zbl 1388.65089Pichard, Teddy; Aregba-Driollet, Denise; Brull, Stéphane; Dubroca, Bruno; Frank, Martin 2 2016 Patch-recovery filters for curvature in discontinuous Galerkin-based level-set methods. Zbl 1388.65102Kummer, Florian; Warburton, Tim 2 2016 Development of a combined compact difference scheme to simulate soliton collision in a shallow water equation. Zbl 1373.76204Yu, Ching-Hao; Sheu, Tony Wen-Hann 2 2016 A semi-Lagrangian approach for dilute non-collisional fluid-particle flows. Zbl 1388.65074Bernard-Champmartin, Aude; Braeunig, Jean-Philippe; Fochesato, Christophe; Goudon, Thierry 2 2016 On invariant-preserving finite difference schemes for the Camassa-Holm equation and the two-component Camassa-Holm system. Zbl 1388.65059Liu, Hailiang; Pendleton, Terrance 2 2016 A dimensional splitting of ETD schemes for reaction-diffusion systems. Zbl 1388.65045Asante-Asamani, E. O.; Wade, Bruce A. 2 2016 Analysis of a two-level algorithm for HDG methods for diffusion problems. Zbl 1388.65153Li, Binjie; Xie, Xiaoping; Zhang, Shiquan 2 2016 Do current lattice Boltzmann methods for diffusion and advection-diffusion equations respect maximum principle and the non-negative constraint? Zbl 1373.76250Karimi, S.; Nakshatrala, K. B. 2 2016 Extended hydrodynamic models and multigrid solver of a silicon diode simulation. Zbl 1373.82009Hu, Zhicheng; Li, Ruo; Qiao, Zhonghua 2 2016 Numerical analysis of inverse elasticity problem with Signorini’s condition. Zbl 1373.74092Zheng, Cong; Cheng, Xiaoliang; Liang, Kewei 1 2016 Godunov-type numerical methods for a model of granular flow on open tables with walls. Zbl 1373.76115Adimurthi; Aggarwal, Aekta; Gowda, G. D. Veerappa 1 2016 Mechanics-based solution verification for porous media models. Zbl 1373.76315Shabouei, M.; Nakshatrala, K. B. 1 2016 On the dynamics of the weak Fréedericksz transition for nematic liquid crystals. Zbl 1373.76010Aursand, Peder; Napoli, Gaetano; Ridder, Johanna 1 2016 ADI-FDTD method for two-dimensional transient electromagnetic problems. Zbl 1373.78437Li, Wanshan; Zhang, Yile; Wong, Yau Shu; Liang, Dong 1 2016 Monotone finite difference schemes for anisotropic diffusion problems via nonnegative directional splittings. Zbl 1388.65137Ngo, Cuong; Huang, Weizhang 1 2016 Stability of soft quasicrystals in a coupled-mode Swift-Hohenberg model for three-component systems. Zbl 1373.82094Jiang, Kai; Tong, Jiajun; Zhang, Pingwen 1 2016 Efficient implementation of smoothed particle hydrodynamics (SPH) with plane sweep algorithm. Zbl 1373.76270Wang, Dong; Zhou, Yisong; Shao, Sihong 1 2016 Investigating the selectivity of KcsA channel by an image charge solvation method (ICSM) in molecular dynamics simulations. Zbl 1373.94035Baker, Katherine; Chen, Duan; Cai, Wei 1 2016 A numerical study of complex reconstruction in inverse elastic scattering. Zbl 1373.74055Hu, Guanghui; Li, Jingzhi; Liu, Hongyu; Wang, Qi 1 2016 A novel technique for constructing difference schemes for systems of singularly perturbed equations. Zbl 1388.65133Hsieh, Po-Wen; Shih, Yin-Tzer; Yang, Suh-Yuh; You, Cheng-Shu 1 2016 A full space-time convergence order analysis of operator splittings for linear dissipative evolution equations. Zbl 1388.65099Hansen, Eskil; Henningsson, Erik 1 2016 Near-field imaging point-like scatterers and extended elastic solid in a fluid. Zbl 1373.74057Yin, Tao; Hu, Guanghui; Xu, Liwei 1 2016 Novel symplectic discrete singular convolution method for Hamiltonian PDEs. Zbl 1388.65181Cai, Wenjun; Zhang, Huai; Wang, Yushun 1 2016 Construction and analysis of an adapted spectral finite element method to convective acoustic equations. Zbl 1373.76209Hüppe, Andreas; Cohen, Gary; Imperiale, Sébastien; Kaltenbacher, Manfred 1 2016 A time-space adaptive method for the Schrödinger equation. Zbl 1388.65101Kormann, Katharina 1 2016 A robust immersed boundary-lattice Boltzmann method for simulation of fluid-structure interaction problems. Zbl 1373.76277Wu, Jie; Wu, Jing; Zhan, Jiapu; Zhao, Ning; Wang, Tongguang 1 2016 The kinematic effects of the defects in liquid crystal dynamics. Zbl 1373.76011Chen, Rui; Bao, Weizhu; Zhang, Hui 1 2016 Efficient semi-Lagrangian Vlasov-Maxwell simulations of high order harmonic generation from relativistic laser-plasma interactions. Zbl 1373.82010Lehmann, Götz 1 2016 Towards a unified macroscopic description of exciton diffusion in organic semiconductors. Zbl 1373.82100Chen, Jingrun; Lin, Jason D. A.; Nguyen, Thuc-Quyen 1 2016 A finite-volume method for nonlinear nonlocal equations with a gradient flow structure. Zbl 1388.65077Carrillo, José A.; Chertock, Alina; Huang, Yanghong 76 2015 Stochastic collocation on unstructured multivariate meshes. Zbl 1388.65127Narayan, Akil; Zhou, Tao 27 2015 ...and 694 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,266 Authors 65 Shu, Chi-Wang 60 Dumbser, Michael 38 Huang, Yunqing 37 Xu, Kun 36 Kurganov, Alexander 33 Carrillo de la Plata, José Antonio 32 Qiu, Jianxian 32 Yang, Xiaofeng 30 Chung, Tsz Shun Eric 29 Liu, Hailiang 27 Shen, Jie 27 Tang, Huazhong 25 Loubère, Raphaël 25 Xu, Yan 25 Zhu, Jun 23 Antoine, Xavier 23 Li, Ruo 22 Sun, Shuyu 22 Yuan, Guangwei 21 Gassner, Gregor J. 21 Liu, Tiegang 21 Tang, Tao 21 Toro, Eleuterio F. 20 Boscheri, Walter 20 Chertock, Alina E. 20 Dehghan Takht Fooladi, Mehdi 20 Qiu, Jingmei 20 Wang, Cheng 19 Balsara, Dinshaw S. 19 He, Xiaoming 19 Li, Jichun 19 Xing, Yulong 19 Xiu, Dongbin 19 Zhang, Jiwei 18 Chen, Yanping 18 Efendiev, Yalchin R. 18 Kim, Junseok 18 Nordström, Jan 18 Titarev, Vladimir A. 18 Wang, Qi 17 Hu, Guanghui 17 Huang, Weizhang 17 Jin, Shi 17 Luo, Hong 17 Winters, Andrew R. 17 Zhao, Jia 17 Zhou, Tao 16 Hong, Jialin 16 Karniadakis, George Em 16 Lai, Mingchih 15 Abgrall, Rémi 15 Fox, Rodney O. 15 Guo, Zhaoli 15 Kreiss, Gunilla 15 Li, Qin 15 Li, Zhilin 15 Liang, Dong 15 Lowengrub, John Samuel 15 Wang, Hong 15 Wise, Steven M. 14 Cai, Wei 14 Cai, Zhenning 14 Kou, Jisheng 14 Lorin, Emmanuel 14 Miranville, Alain M. 14 Sjogreen, Bjorn 14 Titi, Edriss Saleh 14 Wang, Lilian 14 Wang, Liqun 13 Degond, Pierre 13 Du, Qiang 13 Guo, Wei 13 Khoo, Boo Cheong 13 Narayan, Akil C. 13 Torrilhon, Manuel 13 Vasilyeva, Maria V. 13 Wang, Yushun 13 Yao, Jun 13 Zhai, Qilong 13 Zheng, Chunxiong 12 Castro, Manuel J. 12 Chen, Ke 12 Cheng, Jian 12 Hesthaven, Jan S. 12 Mattsson, Ken 12 Morgan, Nathaniel R. 12 Qiao, Zhonghua 12 Sun, Weiwei 12 Xia, Yinhua 12 Yi, Nianyu 12 Zabaras, Nicholas J. 12 Zhang, Pingwen 11 Banks, Jeffrey W. 11 Boyd, John Philip 11 Dimarco, Giacomo 11 Gong, Yuezheng 11 He, Yinnian 11 Iollo, Angelo 11 Jiang, Song 11 Leung, Wingtat ...and 7,166 more Authors all top 5 Cited in 317 Journals 1,238 Journal of Computational Physics 399 Journal of Scientific Computing 356 Computers and Fluids 224 Journal of Computational and Applied Mathematics 199 Computer Methods in Applied Mechanics and Engineering 184 Computers & Mathematics with Applications 165 SIAM Journal on Scientific Computing 144 Applied Numerical Mathematics 126 Applied Mathematics and Computation 72 Journal of Fluid Mechanics 68 SIAM Journal on Numerical Analysis 55 Numerische Mathematik 55 Advances in Applied Mathematics and Mechanics 51 International Journal for Numerical Methods in Engineering 51 Multiscale Modeling & Simulation 50 Engineering Analysis with Boundary Elements 46 Advances in Computational Mathematics 45 Mathematics of Computation 44 Numerical Methods for Partial Differential Equations 44 Numerical Algorithms 40 Mathematics and Computers in Simulation 40 Applied Mathematical Modelling 38 Computational Geosciences 38 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 34 Computational Mechanics 33 BIT 30 East Asian Journal on Applied Mathematics 27 SIAM/ASA Journal on Uncertainty Quantification 26 International Journal for Numerical Methods in Fluids 26 Mathematical Methods in the Applied Sciences 25 Discrete and Continuous Dynamical Systems. 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