SIAM Journal on Scientific Computing Short Title: SIAM J. Sci. Comput. Publisher: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA ISSN: 1064-8275; 1095-7197/e Online: http://epubs.siam.org/loi/sjoce3 Predecessor: SIAM Journal on Scientific and Statistical Computing Comments: Journal; Indexed cover-to-cover Documents Indexed: 5,369 Publications (since 1993) References Indexed: 2,408 Publications with 101,629 References. all top 5 Latest Issues 47, No. 1 (2025) 46, No. 6 (2024) 46, No. 5 (2024) 46, No. 4 (2024) 46, No. 3 (2024) 46, No. 2 (2024) 46, No. 1 (2024) 45, No. 6 (2023) 45, No. 5 (2023) 45, No. 4 (2023) 45, No. 3 (2023) 45, No. 2 (2023) 45, No. 1 (2023) 44, No. 6 (2022) 44, No. 5 (2022) 44, No. 4 (2022) 44, No. 3 (2022) 44, No. 2 (2022) 44, No. 1 (2022) 43, No. 6 (2021) 43, No. 5 (2021) 43, No. 4 (2021) 43, No. 3 (2021) 43, No. 2 (2021) 43, No. 1 (2021) 42, No. 6 (2020) 42, No. 5 (2020) 42, No. 4 (2020) 42, No. 3 (2020) 42, No. 2 (2020) 42, No. 1 (2020) 41, No. 6 (2019) 41, No. 5 (2019) 41, No. 4 (2019) 41, No. 3 (2019) 41, No. 2 (2019) 41, No. 1 (2019) 40, No. 6 (2018) 40, No. 5 (2018) 40, No. 4 (2018) 40, No. 3 (2018) 40, No. 2 (2018) 40, No. 1 (2018) 39, No. 6 (2017) 39, No. 5 (2017) 39, No. 4 (2017) 39, No. 3 (2017) 39, No. 2 (2017) 39, No. 1 (2017) 38, No. 6 (2016) 38, No. 5 (2016) 38, No. 4 (2016) 38, No. 3 (2016) 38, No. 2 (2016) 38, No. 1 (2016) 37, No. 6 (2015) 37, No. 5 (2015) 37, No. 4 (2015) 37, No. 3 (2015) 37, No. 2 (2015) 37, No. 1 (2015) 36, No. 6 (2014) 36, No. 5 (2014) 36, No. 4 (2014) 36, No. 3 (2014) 36, No. 2 (2014) 36, No. 1 (2014) 35, No. 6 (2013) 35, No. 5 (2013) 35, No. 4 (2013) 35, No. 3 (2013) 35, No. 2 (2013) 35, No. 1 (2013) 34, No. 6 (2012) 34, No. 5 (2012) 34, No. 4 (2012) 34, No. 3 (2012) 34, No. 2 (2012) 34, No. 1 (2012) 33, No. 6 (2011) 33, No. 5 (2011) 33, No. 4 (2011) 33, No. 3 (2011) 33, No. 2 (2011) 33, No. 1 (2011) 32, No. 6 (2010) 32, No. 5 (2010) 32, No. 4 (2010) 32, No. 3 (2010) 32, No. 2 (2010) 32, No. 1 (2010) 31, No. 6 (2009/2010) 31, No. 5 (2009) 31, No. 4 (2009) 31, No. 3 (2009) 31, No. 2 (2008/2009) 31, No. 1 (2008) 30, No. 6 (2008) 30, No. 5 (2008) 30, No. 4 (2008) ...and 100 more Volumes all top 5 Authors 42 Karniadakis, George Em 42 Manteuffel, Thomas A. 36 Vassilevski, Panayot Spirov 35 Gander, Martin Jakob 35 Saad, Yousef 34 McCormick, Steve Fahrney 31 Ng, Michael Kwok-Po 27 Cai, Xiao-Chuan 26 Higham, Nicholas John 26 Shu, Chi-Wang 24 Ghattas, Omar N. 24 Shen, Jie 23 MacLachlan, Scott P. 21 Ainsworth, Mark 21 Oosterlee, Cornelis Willebrordus 21 Yavneh, Irad 20 Benzi, Michele 20 Chan, Tony Fan-Cheong 20 Elman, Howard C. 20 Trefethen, Lloyd Nicholas 20 Xiu, Dongbin 19 Benner, Peter 19 Falgout, Robert D. 19 Farrell, Patrick E. 18 De Sterck, Hans 18 Narayan, Akil C. 18 Rüde, Ulrich 18 Russo, Giovanni 18 Ying, Lexing 17 Adler, James H. 17 Keyes, David Elliot 17 Klawonn, Axel 17 Tůma, Miroslav 16 Biros, George 16 Greengard, Leslie F. 16 Hu, Xiaozhe 16 Kelley, Carl T. 16 Kilmer, Misha Elena 16 Rokhlin, Vladimir 16 Silvester, David J. 16 Simoncini, Valeria 16 Vandewalle, Stefan G. 16 Wathen, Andrew John 16 Willcox, Karen E. 16 Wohlmuth, Barbara I. 15 Aykanat, Cevdet 15 Demmel, James Weldon 15 Gugercin, Serkan 15 Jin, Shi 15 Kolev, Tzanio V. 15 Stathopoulos, Andreas 14 Bao, Weizhu 14 Chan, Raymond Hon-Fu 14 Golub, Gene Howard 14 Olson, Luke N. 14 Sandu, Adrian 14 Southworth, Ben S. 14 Tuminaro, Ray S. 14 Zhou, Tao 13 Bui-Thanh, Tan 13 Cai, Zhenning 13 Chow, Edmond 13 de Sturler, Eric 13 Duff, Iain S. 13 Meerbergen, Karl 13 Pavarino, Luca Franco 13 Peherstorfer, Benjamin 13 Reusken, Arnold 13 Schroder, Jacob B. 12 Abgrall, Rémi 12 Ascher, Uri M. 12 Brandt, Achi E. 12 Burman, Erik 12 Chung, Julianne M. 12 Haber, Eldad 12 Hansen, Per Christian 12 He, Xiaoming 12 Huang, Weizhang 12 Ito, Kazufumi 12 LeVeque, Randall J. 12 Marzouk, Youssef M. 12 Notay, Yvan 12 Oseledets, Ivan Valer’evich 12 Quarteroni, Alfio M. 12 Scott, Jennifer 12 Shadid, John N. 12 Szyld, Daniel B. 12 Treister, Eran 12 Wen, Zaiwen 12 Xi, Yuanzhe 11 Giraud, Luc 11 Grigori, Laura 11 Kirby, Robert C. 11 Knepley, Matthew G. 11 Kressner, Daniel 11 Lin, Ping 11 Mary, Theo A. 11 Peskin, Charles S. 11 Petzold, Linda Ruth 11 Puppo, Gabriella ...and 7,051 more Authors all top 5 Fields 4,881 Numerical analysis (65-XX) 1,846 Partial differential equations (35-XX) 895 Fluid mechanics (76-XX) 404 Computer science (68-XX) 356 Calculus of variations and optimal control; 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collections (00-XX) 11 Convex and discrete geometry (52-XX) 8 Difference and functional equations (39-XX) 8 Relativity and gravitational theory (83-XX) 7 Number theory (11-XX) 7 Measure and integration (28-XX) 6 Field theory and polynomials (12-XX) 6 Manifolds and cell complexes (57-XX) 3 Algebraic geometry (14-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Mathematics education (97-XX) 2 Commutative algebra (13-XX) 2 Nonassociative rings and algebras (17-XX) 2 Sequences, series, summability (40-XX) 2 Geometry (51-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 4,843 Publications have been cited 104,136 times in 53,282 Documents Cited by ▼ Year ▼ The Wiener–Askey polynomial chaos for stochastic differential equations. Zbl 1014.65004 Xiu, Dongbin; Karniadakis, George Em 1,053 2002 Nonlinear model reduction via discrete empirical interpolation. Zbl 1217.65169 Chaturantabut, Saifon; Sorensen, Danny C. 634 2010 A limited memory algorithm for bound constrained optimization. Zbl 0836.65080 Byrd, Richard H.; Lu, Peihuang; Nocedal, Jorge; Zhu, Ciyou 623 1995 Atomic decomposition by basis pursuit. Zbl 0919.94002 Chen, Scott Shaobing; Donoho, David L.; Saunders, Michael A. 610 1999 A fast and high quality multilevel scheme for partitioning irregular graphs. Zbl 0915.68129 Karypis, George; Kumar, Vipin 609 1999 High-order collocation methods for differential equations with random inputs. Zbl 1091.65006 Xiu, Dongbin; Hesthaven, Jan S. 510 2005 Tensor-train decomposition. Zbl 1232.15018 Oseledets, I. V. 484 2011 The MATLAB ODE suite. Zbl 0868.65040 Shampine, Lawrence F.; Reichelt, Mark W. 474 1997 A flexible inner-outer preconditioned GMRES algorithm. Zbl 0780.65022 Saad, Youcef 470 1993 Fourth-order time-stepping for stiff PDEs. Zbl 1077.65105 Kassam, Aly-Khan; Trefethen, Lloyd N. 430 2005 A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. Zbl 1133.65308 Audusse, Emmanuel; Bouchut, François; Bristeau, Marie-Odile; Klein, Rupert; Perthame, Benoît 421 2004 A novel two-grid method for semilinear elliptic equations. Zbl 0795.65077 Xu, Jinchao 405 1994 Weighted ENO schemes for Hamilton-Jacobi equations. Zbl 0957.35014 Jiang, Guang-Shan; Peng, Danping 359 2000 Efficient spectral-Galerkin method. I: Direct solvers of second- and fourth-order equations using Legendre polynomials. Zbl 0811.65097 Shen, Jie 344 1994 The use of the \(L\)-curve in the regularization of discrete ill-posed problems. Zbl 0789.65030 Hansen, Per Christian; O’Leary, Dianne Prost 322 1993 Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations. Zbl 0947.82008 Jin, Shi 280 1999 A note on preconditioning for indefinite linear systems. Zbl 0959.65063 Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. 271 2000 Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. Zbl 0952.76060 Lax, Peter D.; Liu, Xu-Dong 262 1998 Modeling fractures and barriers as interfaces for flow in porous media. Zbl 1083.76058 Martin, Vincent; Jaffré, Jérôme; Roberts, Jean E. 257 2005 High-order total variation-based image restoration. Zbl 0968.68175 Chan, Tony; Marquina, Antonio; Mulet, Pep 256 2000 Choosing the forcing terms in an inexact Newton method. Zbl 0845.65021 Eisenstat, Stanley C.; Walker, Homer F. 253 1996 Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. Zbl 1079.65028 Bai, Zhong-Zhi; Golub, Gene H.; Lu, Lin-Zhang; Yin, Jun-Feng 246 2005 A novel pricing method for European options based on Fourier-cosine series expansions. Zbl 1186.91214 Fang, F.; Oosterlee, C. W. 244 2008 Exponential integrators for large systems of differential equations. Zbl 0912.65058 Hochbruck, Marlis; Lubich, Christian 241 1998 Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. Zbl 0998.65091 Kurganov, Alexander; Noelle, Sebastian; Petrova, Guergana 240 2001 Alternating direction algorithms for \(\ell_1\)-problems in compressive sensing. Zbl 1256.65060 Yang, Junfeng; Zhang, Yin 235 2011 Immersed interface methods for Stokes flow with elastic boundaries or surface tension. Zbl 0879.76061 LeVeque, Randall J.; Li, Zhilin 234 1997 Runge-Kutta discontinuous Galerkin method using WENO limiters. Zbl 1077.65109 Qiu, Jianxian; Shu, Chi-Wang 230 2005 The use of finite difference/element approaches for solving the time-fractional subdiffusion equation. Zbl 1292.65096 Zeng, Fanhai; Li, Changpin; Liu, Fawang; Turner, Ian 230 2013 Numerical solution of the Riemann problem for two-dimensional gas dynamics. Zbl 0785.76050 Schulz-Rinne, Carsten W.; Collins, James P.; Glaz, Harland M. 229 1993 Iterative methods for total variation denoising. Zbl 0847.65083 Vogel, C. R.; Oman, M. E. 229 1996 Probing the Pareto frontier for basis pursuit solutions. Zbl 1193.49033 van den Berg, Ewout; Friedlander, Michael P. 229 2008 A restricted additive Schwarz preconditioner for general sparse linear systems. Zbl 0944.65031 Cai, Xiao-Chuan; Sarkis, Marcus 220 1999 A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods. Zbl 1275.65065 Gassner, Gregor J. 219 2013 A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118 Chan, Tony F.; Golub, Gene H.; Mulet, Pep 218 1999 Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method. Zbl 0992.65028 Knyazev, Andrew V. 217 2001 Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. Zbl 1061.82025 Bao, Weizhu; Du, Qiang 216 2004 p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees. Zbl 1230.65106 Burstedde, Carsten; Wilcox, Lucas C.; Ghattas, Omar 215 2011 A fourth-order compact ADI scheme for two-dimensional nonlinear space fractional Schrödinger equation. Zbl 1328.65187 Zhao, Xuan; Sun, Zhi-Zhong; Hao, Zhao-Peng 214 2014 A cell-centered Lagrangian scheme for two-dimensional compressible flow problems. Zbl 1251.76028 Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Ovadia, Jean 213 2007 A phase-field model and its numerical approximation for two-phase incompressible flows with different densities and viscosities. Zbl 1410.76464 Shen, Jie; Yang, Xiaofeng 211 2010 On the choice of wavespeeds for the HLLC Riemann solver. Zbl 0992.65088 Batten, P.; Clarke, N.; Lambert, C.; Causon, D. M. 208 1997 Analysis of the parareal time-parallel time-integration method. Zbl 1141.65064 Gander, Martin J.; Vandewalle, Stefan 208 2007 Compact central WENO schemes for multidimensional conservation laws. Zbl 0967.65089 Levy, Doron; Puppo, Gabriella; Russo, Giovanni 207 2000 Stable computations with Gaussian radial basis functions. Zbl 1227.65018 Fornberg, Bengt; Larsson, Elisabeth; Flyer, Natasha 202 2011 Two fully discrete schemes for fractional diffusion and diffusion-wave equations with nonsmooth data. Zbl 1381.65082 Jin, Bangti; Lazarov, Raytcho; Zhou, Zhi 202 2016 FPINNs: fractional physics-informed neural networks. Zbl 1420.35459 Pang, Guofei; Lu, Lu; Karniadakis, George Em 201 2019 A simple method for compressible multifluid flows. Zbl 0957.76057 Saurel, Richard; Abgrall, Rémi 195 1999 An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. Zbl 0958.76070 Sussman, Mark; Fatemi, Emad 191 1999 A preconditioner for substructuring based on constrained energy minimization. Zbl 1038.65039 Dohrmann, Clark R. 187 2003 Efficient algorithms for computing a strong rank-revealing QR factorization. Zbl 0858.65044 Gu, Ming; Eisenstat, Stanley C. 182 1996 Iterative Bregman projections for regularized transportation problems. Zbl 1319.49073 Benamou, Jean-David; Carlier, Guillaume; Cuturi, Marco; Nenna, Luca; Peyré, Gabriel 182 2015 Multi-element generalized polynomial chaos for arbitrary probability measures. Zbl 1128.65009 Wan, Xiaoliang; Karniadakis, George Em 179 2006 Optimized Schwarz methods without overlap for the Helmholtz equation. Zbl 1021.65061 Gander, Martin J.; Magoulès, Frédéric; Nataf, Frédéric 175 2002 Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation. Zbl 1217.26011 Chen, Chang-Ming; Liu, F.; Anh, V.; Turner, I. 172 2010 Comparison of several difference schemes on 1D and 2D test problems for the Euler equations. Zbl 1096.65089 Liska, Richard; Wendroff, Burton 171 2003 Computing the action of the matrix exponential, with an application to exponential integrators. Zbl 1234.65028 Al-Mohy, Awad H.; Higham, Nicholas J. 171 2011 Parallel preconditioning with sparse approximate inverses. Zbl 0872.65031 Grote, Marcus J.; Huckle, Thomas 168 1997 A fast finite difference method for two-dimensional space-fractional diffusion equations. Zbl 1256.35194 Wang, Hong; Basu, Treena S. 168 2012 A cyclic low-rank Smith method for large sparse Lyapunov equations. Zbl 0958.65052 Penzl, Thilo 167 2000 A new iterative method for solving large-scale Lyapunov matrix equations. Zbl 1146.65038 Simoncini, V. 167 2007 Fractional spectral collocation method. Zbl 1294.65097 Zayernouri, Mohsen; Karniadakis, George Em 167 2014 An immersed interface method for incompressible Navier–Stokes equations. Zbl 1163.65322 Lee, Long; LeVeque, Randall J. 166 2003 Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy. Zbl 1334.65162 Zeng, Fanhai; Li, Changpin; Liu, Fawang; Turner, Ian 165 2015 Breaking the curse of dimensionality, or how to use SVD in many dimensions. Zbl 1200.65028 Oseledets, I. V.; Tyrtyshnikov, E. E. 164 2009 Entropy stable spectral collocation schemes for the Navier-Stokes equations: discontinuous interfaces. Zbl 1457.65140 Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H. 162 2014 A new finite element gradient recovery method: Superconvergence property. Zbl 1078.65110 Zhang, Zhimin; Naga, Ahmed 159 2005 Three-dimensional front tracking. Zbl 0912.65075 Glimm, James; Grove, John W.; Li, Xiao Lin; Shyue, Keh-ming; Zeng, Yanni 155 1998 Fast Fourier transforms for nonequispaced data. Zbl 0791.65108 Dutt, A.; Rokhlin, V. 154 1993 The compact discontinuous Galerkin (CDG) method for elliptic problems. Zbl 1167.65436 Peraire, J.; Persson, P.-O. 154 2008 An adaptive time-stepping strategy for the molecular beam epitaxy models. Zbl 1234.35274 Qiao, Zhonghua; Zhang, Zhengru; Tang, Tao 154 2011 Minimization of \(\ell_{1-2}\) for compressed sensing. Zbl 1316.90037 Yin, Penghang; Lou, Yifei; He, Qi; Xin, Jack 154 2015 Wavelet and Fourier methods for solving the sideways heat equation. Zbl 0959.65107 Eldén, Lars; Berntsson, Fredrik; Reginska, Teresa 153 2000 Nonoscillatory central schemes for multidimensional hyperbolic conservation laws. Zbl 0914.65095 Jiang, Guang-Shan; Tadmor, Eitan 153 1998 Parallel time integration with multigrid. Zbl 1310.65115 Falgout, R. D.; Friedhoff, S.; Kolev, Tz. V.; Maclachlan, S. P.; Schroder, J. B. 151 2014 Understanding and mitigating gradient flow pathologies in physics-informed neural networks. Zbl 1530.68232 Wang, Sifan; Teng, Yujun; Perdikaris, Paris 150 2021 Novel numerical methods for solving the time-space fractional diffusion equation in two dimensions. Zbl 1229.35315 Yang, Qianqian; Turner, Ian; Liu, Fawang; Ilić, Milos 149 2011 An efficient implicit FEM scheme for fractional-in-space reaction-diffusion equations. Zbl 1253.65146 Burrage, Kevin; Hale, Nicholas; Kay, David 149 2012 Physical systems with random uncertainties: Chaos representations with arbitrary probability measure. Zbl 1075.60084 Soize, Christian; Ghanem, Roger 147 2004 Correction of high-order BDF convolution quadrature for fractional evolution equations. Zbl 1379.65078 Jin, Bangti; Li, Buyang; Zhou, Zhi 147 2017 A novel multigrid based preconditioner for heterogeneous Helmholtz problems. Zbl 1095.65109 Erlangga, Y. A.; Oosterlee, C. W.; Vuik, C. 147 2006 A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. Zbl 1250.65011 Martin, James; Wilcox, Lucas C.; Burstedde, Carsten; Ghattas, Omar 145 2012 A computational framework for infinite-dimensional Bayesian inverse problems. I: The linearized case, with application to global seismic inversion. Zbl 1287.35087 Bui-Thanh, Tan; Ghattas, Omar; Martin, James; Stadler, Georg 144 2013 A fast algorithm for deblurring models with Neumann boundary conditions. Zbl 0951.65038 Ng, Michael K.; Chan, Raymond H.; Tang, Wun-Cheung 143 1999 The perfectly matched layer in curvilinear coordinates. Zbl 0940.78011 Collino, Francis; Monk, Peter 142 1998 Discretization on unstructured grids for inhomogeneous, anisotropic media. I: Derivation of the methods. Zbl 0951.65080 Aavatsmark, I.; Barkve, T.; Bøe, O.; Mannseth, T. 139 1998 Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. Zbl 1116.65039 Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 138 2006 A novel high order space-time spectral method for the time fractional Fokker-Planck equation. Zbl 1320.82052 Zheng, Minling; Liu, Fawang; Turner, Ian; Anh, Vo 136 2015 A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. Zbl 0781.65022 Freund, Roland W. 135 1993 A stable algorithm for flat radial basis functions on a sphere. Zbl 1159.65307 Fornberg, Bengt; Piret, Cécile 135 2007 Quadratic convergence for valuing American options using a penalty method. Zbl 1020.91017 Forsyth, P. A.; Vetzal, K. R. 135 2002 Algorithms for numerical analysis in high dimensions. Zbl 1085.65045 Beylkin, Gregory; Mohlenkamp, Martin J. 135 2005 Model reduction for large-scale systems with high-dimensional parametric input space. Zbl 1196.37127 Bui-Thanh, T.; Willcox, K.; Ghattas, O. 133 2008 An augmented Lagrangian-based approach to the Oseen problem. Zbl 1126.76028 Benzi, Michele; Olshanskii, Maxim A. 131 2006 On the numerical integration of ordinary differential equations by symmetric composition methods. Zbl 0821.65048 McLachlan, Robert I. 130 1995 The method of regularized stokeslets. Zbl 1064.76080 Cortez, Ricardo 129 2001 Unconditionally convergent \(L1\)-Galerkin FEMs for nonlinear time-fractional Schrödinger equations. Zbl 1379.65079 Li, Dongfang; Wang, Jilu; Zhang, Jiwei 129 2017 Stable evaluation of Gaussian radial basis function interpolants. Zbl 1252.65028 Fasshauer, Gregory E.; McCourt, Michael J. 127 2012 Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Zbl 1077.65042 Zhang, Zhenyue; Zha, Hongyuan 126 2004 Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix. Zbl 0890.65149 Dietrich, C. R.; Newsam, G. N. 124 1997 Stage-parallel fully implicit Runge-Kutta implementations with optimal multilevel preconditioners at the scaling limit. Zbl 1537.65088 Munch, Peter; Dravins, Ivo; Kronbichler, Martin; Neytcheva, Maya 4 2024 Leveraging multitime Hamilton-Jacobi PDEs for certain scientific machine learning problems. Zbl 1537.35157 Chen, Paula; Meng, Tingwei; Zou, Zongren; Darbon, Jérôme; Karniadakis, George Em 4 2024 Computation of two-dimensional Stokes flows via lightning and AAA rational approximation. Zbl 1535.76029 Xue, Yidan; Waters, Sarah L.; Trefethen, Lloyd N. 4 2024 New artificial tangential motions for parametric finite element approximation of surface evolution. Zbl 1536.53177 Duan, Beiping; Li, Buyang 4 2024 A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system. Zbl 1545.65371 Liu, Chen; Riviere, Beatrice; Shen, Jie; Zhang, Xiangxiong 3 2024 Algebraic multigrid methods for metric-perturbed coupled problems. Zbl 1537.65185 Budiša, Ana; Hu, Xiaozhe; Kuchta, Miroslav; Mardal, Kent-Andre; Zikatanov, Ludmil 3 2024 A conservative low rank tensor method for the Vlasov dynamics. Zbl 1533.65195 Guo, Wei; Qiu, Jing-Mei 3 2024 AONN: an adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problems. Zbl 1534.49022 Yin, Pengfei; Xiao, Guangqiang; Tang, Kejun; Yang, Chao 3 2024 A unified design of energy stable schemes with variable steps for fractional gradient flows and nonlinear integro-differential equations. Zbl 1532.35462 Qi, Ren-jun; Zhao, Xuan 3 2024 On generalized preconditioners for time-parallel parabolic optimal control. Zbl 1543.49019 Bouillon, Arne; Samaey, Giovanni; Meerbergen, Karl 3 2024 Data-driven construction of hierarchical matrices with nested bases. Zbl 07837042 Cai, Difeng; Huang, Hua; Chow, Edmond; Xi, Yuanzhe 2 2024 Energy stable and conservative dynamical low-rank approximation for the Su-Olson problem. Zbl 1537.65116 Baumann, Lena; Einkemmer, Lukas; Klingenberg, Christian; Kusch, Jonas 2 2024 Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics. Zbl 1537.65005 Ribera Borrell, Enric; Quer, Jannes; Richter, Lorenz; Schütte, Christof 2 2024 A restricted SVD type CUR decomposition for matrix triplets. Zbl 1537.65044 Gidisu, Perfect Y.; Hochstenbach, Michiel E. 2 2024 Linear-complexity black-box randomized compression of rank-structured matrices. Zbl 1545.65117 Levitt, James; Martinsson, Per-Gunnar 2 2024 A posteriori local subcell correction of high-order discontinuous Galerkin scheme for conservation laws on two-dimensional unstructured grids. Zbl 1535.65159 Vilar, François; Abgrall, Rémi 2 2024 AAA rational approximation on a continuum. Zbl 1534.65032 Driscoll, Tobin A.; Nakatsukasa, Yuji; Trefethen, Lloyd N. 2 2024 Sparse recovery of elliptic solvers from matrix-vector products. Zbl 1535.65298 Schäfer, Florian; Owhadi, Houman 2 2024 High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation. Zbl 1535.65216 Bai, Genming; Hu, Jiashun; Li, Buyang 2 2024 A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations. Zbl 1531.65138 Ding, Shengrong; Wu, Kailiang 2 2024 Stable rank-adaptive dynamically orthogonal Runge-Kutta schemes. Zbl 07805923 Charous, Aaron; Lermusiaux, Pierre F. J. 2 2024 A second-order, linear, \(L^\infty\)-convergent, and energy stable scheme for the phase field crystal equation. Zbl 1532.65099 Li, Xiao; Qiao, Zhonghua 2 2024 Bayesian deep learning framework for uncertainty quantification in stochastic partial differential equations. Zbl 07805930 Jung, Jeahan; Shin, Hyomin; Choi, Minseok 2 2024 Efficient tensor-product spectral-element operators with the summation-by-parts property on curved triangles and tetrahedra. Zbl 1544.65186 Montoya, Tristan; Zingg, David W. 2 2024 Solving linear systems of the form \((A+\gamma UU^T)\,x=b\) by preconditioned iterative methods. Zbl 1543.65034 Benzi, Michele; Faccio, Chiara 1 2024 Hybrid projection methods for solution decomposition in large-scale Bayesian inverse problems. Zbl 1537.65038 Chung, Julianne; Jiang, Jiahua; Miller, Scot M.; Saibaba, Arvind K. 1 2024 Efficient algorithms for Bayesian inverse problems with Whittle-Matérn priors. Zbl 1541.65143 Antil, Harbir; Saibaba, Arvind K. 1 2024 Krylov subspace residual and restarting for certain second order differential equations. Zbl 1537.65047 Botchev, Mike A.; Knizhnerman, Leonid; Schweitzer, Marcel 1 2024 Iterated Gauss-Seidel GMRES. Zbl 1541.65020 Thomas, Stephen; Carson, Erin; Rozložník, Miroslav; Carr, Arielle; Świrydowicz, Katarzyna 1 2024 Multivariate Hermite interpolation on Riemannian manifolds. Zbl 1537.65009 Zimmermann, Ralf; Bergmann, Ronny 1 2024 Direct/iterative hybrid solver for scattering by inhomogeneous media. Zbl 07837062 Bruno, Oscar P.; Pandey, Ambuj 1 2024 Local characteristic decomposition-free high-order finite difference WENO schemes for hyperbolic systems endowed with a coordinate system of Riemann invariants. Zbl 1547.65120 Xu, Ziyao; Shu, Chi-Wang 1 2024 An entropy stable essentially oscillation-free discontinuous Galerkin method for hyperbolic conservation laws. Zbl 1541.65104 Liu, Yong; Lu, Jianfang; Shu, Chi-Wang 1 2024 A divergence preserving cut finite element method for Darcy flow. Zbl 1540.65484 Frachon, Thomas; Hansbo, Peter; Nilsson, Erik; Zahedi, Sara 1 2024 Rank-minimizing and structured model inference. Zbl 07860855 Goyal, Pawan; Peherstorfer, Benjamin; Benner, Peter 1 2024 Hermitian preconditioning for a class of non-Hermitian linear systems. Zbl 1545.65146 Spillane, Nicole 1 2024 A parallel rank-adaptive integrator for dynamical low-rank approximation. Zbl 07843961 Ceruti, Gianluca; Kusch, Jonas; Lubich, Christian 1 2024 A framework for implementing general virtual element spaces. Zbl 1541.65095 Dedner, Andreas; Hodson, Alice 1 2024 Additive Schwarz methods for semilinear elliptic problems with convex energy functionals: convergence rate independent of nonlinearity. Zbl 1542.65184 Park, Jongho 1 2024 Multilevel Monte Carlo with numerical smoothing for robust and efficient computation of probabilities and densities. Zbl 1541.65002 Bayer, Christian; Ben Hammouda, Chiheb; Tempone, Raúl 1 2024 Multigrid solvers for the de Rham complex with optimal complexity in polynomial degree. Zbl 1545.65467 Brubeck, Pablo D.; Farrell, Patrick E. 1 2024 A multiscale hybrid method. Zbl 1540.65473 Barrenechea, Gabriel R.; Gomes, Antonio Tadeu A.; Paredes, Diego 1 2024 A new locally divergence-free path-conservative central-upwind scheme for ideal and shallow water magnetohydrodynamics. Zbl 1547.65124 Chertock, Alina; Kurganov, Alexander; Redle, Michael; Wu, Kailiang 1 2024 Learning robust marking policies for adaptive mesh refinement. Zbl 1532.65119 Gillette, Andrew; Keith, Brendan; Petrides, Socratis 1 2024 Sketching with spherical designs for noisy data fitting on spheres. Zbl 1533.68318 Lin, Shao-Bo; Wang, Di; Zhou, Ding-Xuan 1 2024 Nonlinearly constrained pressure residual (NCPR) algorithms for fractured reservoir simulation. Zbl 1536.76088 Yang, Haijian; Li, Rui; Yang, Chao 1 2024 Accelerating exponential integrators to efficiently solve semilinear advection-diffusion-reaction equations. Zbl 1535.65128 Caliari, Marco; Cassini, Fabio; Einkemmer, Lukas; Ostermann, Alexander 1 2024 Rapid evaluation of Newtonian potentials on planar domains. Zbl 1534.65271 Shen, Zewen; Serkh, Kirill 1 2024 A new ParaDiag time-parallel time integration method. Zbl 1534.65278 Gander, Martin J.; Palitta, Davide 1 2024 A recursively recurrent neural network (R2N2) architecture for learning iterative algorithms. Zbl 1534.65073 Doncevic, Danimir T.; Mitsos, Alexander; Guo, Yue; Li, Qianxiao; Dietrich, Felix; Dahmen, Manuel; Kevrekidis, Ioannis G. 1 2024 An efficient block rational Krylov solver for Sylvester equations with adaptive pole selection. Zbl 1534.65063 Casulli, A.; Robol, L. 1 2024 On optimal zero-padding of kernel truncation method. Zbl 1533.65261 Liu, Xin; Tang, Qinglin; Zhang, Shaobo; Zhang, Yong 1 2024 A multilevel method for many-electron Schrödinger equations based on the atomic cluster expansion. Zbl 1537.81219 Zhou, Dexuan; Chen, Huajie; Ho, Cheuk Hin; Ortner, Christoph 1 2024 BDDC preconditioners for virtual element approximations of the three-dimensional Stokes equations. Zbl 1533.65244 Bevilacqua, Tommaso; Dassi, Franco; Zampini, Stefano; Scacchi, Simone 1 2024 Behavior of the discontinuous Galerkin method for compressible flows at low Mach number on triangles and tetrahedrons. Zbl 1533.65171 Jung, Jonathan; Perrier, Vincent 1 2024 Data-driven kernel designs for optimized greedy schemes: a machine learning perspective. Zbl 1533.65044 Wenzel, Tizian; Marchetti, Francesco; Perracchione, Emma 1 2024 A fast iterative PDE-based algorithm for feedback controls of nonsmooth mean-field control problems. Zbl 1546.49078 Reisinger, Christoph; Stockinger, Wolfgang; Zhang, Yufei 1 2024 A sketch-and-select Arnoldi process. Zbl 1546.65022 Güttel, Stefan; Simunec, Igor 1 2024 Inverse source problem of the biharmonic equation from multifrequency phaseless data. Zbl 1546.65099 Chang, Yan; Guo, Yukun; Zhao, Yue 1 2024 A new provably stable weighted state redistribution algorithm. Zbl 1544.65153 Berger, Marsha; Giuliani, Andrew 1 2024 Least-squares neural network (LSNN) method for linear advection-reaction equation: discontinuity interface. Zbl 1545.65477 Cai, Zhiqiang; Choi, Junpyo; Liu, Min 1 2024 A meshless solver for blood flow simulations in elastic vessels using a physics-informed neural network. Zbl 07899178 Zhang, Han; Chan, Raymond H.; Tai, Xue-Cheng 1 2024 A high-order fast direct solver for surface PDEs. Zbl 1546.65083 Fortunato, Daniel 1 2024 LFA-tuned matrix-free multigrid method for the elastic Helmholtz equation. Zbl 07931236 Yovel, Rachel; Treister, Eran 1 2024 A robust two-level overlapping preconditioner for Darcy flow in high-contrast media. Zbl 07931273 Ye, Changqing; Fu, Shubin; Chung, Eric T.; Huang, Jizu 1 2024 Cut finite element discretizations of cell-by-cell EMI electrophysiology models. Zbl 07894728 Berre, Nanna; Rognes, Marie E.; Massing, André 1 2024 Computing \(H^2\)-conforming finite element approximations without having to implement \(C^1\)-elements. Zbl 1548.65266 Ainsworth, Mark; Parker, Charles 1 2024 Constrained local approximate ideal restriction for advection-diffusion problems. Zbl 07931241 Ali, Ahsan; Brannick, James J.; Kahl, Karsten; Krzysik, Oliver A.; Schroder, Jacob B.; Southworth, Ben S. 1 2024 Super-localized orthogonal decomposition for high-frequency Helmholtz problems. Zbl 1543.65187 Freese, Philip; Hauck, Moritz; Peterseim, Daniel 1 2024 Slow invariant manifolds of singularly perturbed systems via physics-informed machine learning. Zbl 1543.65204 Patsatzis, Dimitrios; Fabiani, Gianluca; Russo, Lucia; Siettos, Constantinos 1 2024 Multivariate rational approximation of functions with curves of singularities. Zbl 07944244 Boullé, Nicolas; Herremans, Astrid; Huybrechs, Daan 1 2024 Computing singular and near-singular integrals over curved boundary elements: the strongly singular case. Zbl 07955202 Montanelli, Hadrien; Collino, Francis; Haddar, Houssem 1 2024 Failure-informed adaptive sampling for PINNs. Zbl 07729492 Gao, Zhiwei; Yan, Liang; Zhou, Tao 23 2023 Relaxation exponential Rosenbrock-type methods for oscillatory Hamiltonian systems. Zbl 1537.65194 Li, Dongfang; Li, Xiaoxi 12 2023 On the stability of robust dynamical low-rank approximations for hyperbolic problems. Zbl 07673274 Kusch, Jonas; Einkemmer, Lukas; Ceruti, Gianluca 11 2023 Symplectic model reduction of Hamiltonian systems on nonlinear manifolds and approximation with weakly symplectic autoencoder. Zbl 1537.65193 Buchfink, Patrick; Glas, Silke; Haasdonk, Bernard 11 2023 Manifold approximations via transported subspaces: model reduction for transport-dominated problems. Zbl 1514.78017 Rim, Donsub; Peherstorfer, Benjamin; Mandli, Kyle T. 10 2023 Randomized algorithms for rounding in the tensor-train format. Zbl 07673280 Al Daas, Hussam; Ballard, Grey; Cazeaux, Paul; Hallman, Eric; Międlar, Agnieszka; Pasha, Mirjeta; Reid, Tim W.; Saibaba, Arvind K. 9 2023 A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs. Zbl 1516.65087 Haasdonk, Bernard; Kleikamp, Hendrik; Ohlberger, Mario; Schindler, Felix; Wenzel, Tizian 9 2023 SOBMOR: structured optimization-based model order reduction. Zbl 1514.93031 Schwerdtner, Paul; Voigt, Matthias 8 2023 Convergence analysis of BDDC preconditioners for composite DG discretizations of the cardiac cell-by-cell model. Zbl 1527.65138 Huynh, Ngoc Mai Monica; Chegini, Fatemeh; Pavarino, Luca Franco; Weiser, Martin; Scacchi, Simone 7 2023 High order compact schemes for flux type BCs. Zbl 1516.65115 Li, Zhilin; Pan, Kejia 7 2023 Low-order preconditioning for the high-order finite element de Rham complex. Zbl 1525.65127 Pazner, Will; Kolev, Tzanio; Dohrmann, Clark R. 7 2023 Horseshoe priors for edge-preserving linear Bayesian inversion. Zbl 07695777 Uribe, Felipe; Dong, Yiqiu; Hansen, Per Christian 6 2023 Globally convergent multilevel training of deep residual networks. Zbl 1515.65166 Kopaničáková, Alena; Krause, Rolf 6 2023 Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment. Zbl 1517.65117 Smetana, Kathrin; Taddei, Tommaso 6 2023 Port-Hamiltonian dynamic mode decomposition. Zbl 1523.37086 Morandin, Riccardo; Nicodemus, Jonas; Unger, Benjamin 5 2023 Friedrichs learning: weak solutions of partial differential equations via deep learning. Zbl 07704383 Chen, Fan; Huang, Jianguo; Wang, Chunmei; Yang, Haizhao 5 2023 The p-AAA algorithm for data-driven modeling of parametric dynamical systems. Zbl 1528.93001 Rodriguez, Andrea Carracedo; Balicki, Linus; Gugercin, Serkan 5 2023 An offline-online decomposition method for efficient linear Bayesian goal-oriented optimal experimental design: application to optimal sensor placement. Zbl 1541.62197 Wu, Keyi; Chen, Peng; Ghattas, Omar 5 2023 Long-term analysis of stochastic Hamiltonian systems under time discretizations. Zbl 1512.65014 D’Ambrosio, Raffaele; Di Giovacchino, Stefano 5 2023 Geometrically higher order unfitted space-time methods for PDEs on moving domains. Zbl 1512.65210 Heimann, Fabian; Lehrenfeld, Christoph; Preuß, Janosch 5 2023 A strongly mass conservative method for the coupled Brinkman-Darcy flow and transport. Zbl 1529.65094 Zhao, Lina; Sun, Shuyu 5 2023 A unified analysis framework for iterative parallel-in-time algorithms. Zbl 1523.65109 Gander, Martin J.; Lunet, Thibaut; Ruprecht, Daniel; Speck, Robert 4 2023 Model reduction for nonlinear systems by balanced truncation of state and gradient covariance. Zbl 1520.65080 Otto, Samuel E.; Padovan, Alberto; Rowley, Clarence W. 4 2023 HODLR2D: a new class of hierarchical matrices. Zbl 1525.65138 Kandappan, V. A.; Gujjula, Vaishnavi; Ambikasaran, Sivaram 4 2023 Compatible energy dissipation of the variable-step \(L1\) scheme for the space-time fractional Cahn-Hilliard equation. Zbl 07749377 Xue, Zhongqin; Zhao, Xuan 4 2023 Streaming tensor train approximation. Zbl 1523.65042 Kressner, Daniel; Vandereycken, Bart; Voorhaar, Rik 4 2023 Multigrid-augmented deep learning preconditioners for the Helmholtz equation. Zbl 07704368 Azulay, Yael; Treister, Eran 4 2023 MGM: a meshfree geometric multilevel method for systems arising from elliptic equations on point cloud surfaces. Zbl 1512.65249 Wright, Grady B.; Jones, Andrew; Shankar, Varun 4 2023 ...and 1516 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 49,365 Authors 167 Shu, Chi-Wang 165 Karniadakis, George Em 154 Benner, Peter 144 Dehghan Takht Fooladi, Mehdi 144 Huang, Ting-Zhu 132 Reichel, Lothar 125 Shen, Jie 118 Dumbser, Michael 115 Yang, Xiaofeng 114 Huang, Yunqing 113 Zhang, Zhimin 112 Feng, Xinlong 110 He, Yinnian 108 Gander, Martin Jakob 108 Wang, Hong 103 Chung, Tsz Shun Eric 101 Qiu, Jianxian 98 Chen, Yanping 97 Ng, Michael Kwok-Po 96 Nordström, Jan 94 Wei, Yimin 90 Jiang, Yaolin 89 Rozza, Gianluigi 88 Hesthaven, Jan S. 88 Serra-Capizzano, Stefano 86 Kurganov, Alexander 86 Quarteroni, Alfio M. 77 Oosterlee, Cornelis Willebrordus 76 Ma, Changfeng 73 Abgrall, Rémi 73 Ju, Lili 73 Zhang, Guofeng 72 Liu, Fawang 72 Ying, Lexing 70 Kressner, Daniel 70 Zhu, Jun 69 Du, Qiang 69 Lin, Guang 69 Yuan, Guangwei 68 Gunzburger, Max Donald 68 Rui, Hongxing 68 Sun, Shuyu 68 Wohlmuth, Barbara I. 67 Jin, Shi 67 Xu, Kun 66 He, Xiaoming 66 Li, Ruo 66 Vuik, Cornelis 66 Wick, Thomas 66 Zheng, Xiangcheng 65 Harbrecht, Helmut 65 Wall, Wolfgang A. 63 Schwab, Christoph 61 Zhang, Chengjian 61 Zhang, Jiwei 60 Jbilou, Khalide 60 Seaïd, Mohammed 60 Wang, Yushun 59 Bao, Weizhu 59 Kirby, Robert M. 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