Edit Profile (opens in new tab) Langer, Ulrich Compute Distance To: Compute Author ID: langer.ulrich Published as: Langer, Ulrich; Langer, U.; Langer, Ulrich. External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef Documents Indexed: 137 Publications since 1977, including 6 Books 19 Contributions as Editor · 1 Further Contribution Reviewing Activity: 195 Reviews Co-Authors: 87 Co-Authors with 130 Joint Publications 2,131 Co-Co-Authors all top 5 Co-Authors 24 single-authored 16 Haase, Gundolf 11 Steinbach, Olaf 9 Korneev, Vadim Glebovich 8 Schöberl, Joachim 8 Yang, Huidong 7 Hofer, Christoph D. 7 Jung, Michael 7 Meyer, Arnd 7 Repin, Sergeĭ Igorevich 7 Toulopoulos, Ioannis 7 Wick, Thomas 6 Kolmbauer, Michael 6 Pechstein, Clemens 6 Reitzinger, Stefan 5 Endtmayer, Bernhard 5 Hofreither, Clemens 5 Neumüller, Martin 5 Pusch, David 4 Hiptmair, Ralf 4 Hoppe, Ronald H. W. 4 Mantzaflaris, Angelos 4 Moore, Stephen Edward 4 Queck, Werner 4 Schafelner, Andreas 4 Wolfmayr, Monika 4 Zulehner, Walter 3 Copeland, Dylan Matthew 3 Joly, Patrick 3 Lerch, Reinhard 3 Matculevich, Svetlana 3 Schinnerl, M. 3 Tröltzsch, Fredi 3 Xanthis, Leonidas Spyridon 2 Gangl, Peter 2 Jodlbauer, Daniel 2 Jüttler, Bert 2 Kaltenbacher, Manfred 2 Khoromskiĭ, Boris Nikolaevich 2 Pauly, Dirk 1 Amrhein, Wolfgang 1 Apel, Thomas 1 Bachinger, F. 1 Bahlmann, Dieter 1 Basting, Steffen 1 Beuchler, Sven 1 Birken, Philipp 1 Canic, Sunica 1 Carstensen, Carsten 1 Colciago, Claudia Maria 1 Dauge, Monique 1 Deparis, Simone 1 Discacciati, Marco 1 Douglas, Craig C. 1 Eibner, Tino 1 Forti, Davide 1 Frei, Stefan 1 Globisch, Gerhard 1 Glowinski, Roland 1 Graham, Ivan G. 1 Gruber, Peter Günther 1 Günther, Michael 1 Hoffman, Johan 1 Holm, Bärbel 1 Keyes, David Elliot 1 Kickinger, Ferdinand 1 Kienesberger, Johanna 1 Kollmann, Markus 1 Kraus, Johannes K. 1 Kuznetsov, Yurii Alekseevich 1 Laurain, Antoine 1 Lindner, Ewald Hans 1 Matsokin, Aleksandr 1 Meftahi, Houcine 1 Melenk, Jens Markus 1 Monge, Azahar 1 Monk, Peter B. 1 Mühlhuber, Wolfram 1 Neitzel, Ira 1 Nepomnyashchikh, Sergeĭ Vladimirovich 1 Of, Günther 1 Paule, Peter 1 Quaini, Annalisa 1 Richter, Thomas 1 Samrowski, Tatiana S. 1 Schanz, Martin 1 Schicho, Josef 1 Schneckenleitner, Rainer 1 Shokrpour Roudbari, Mahnaz 1 Şimşek, Görkem 1 Sini, Mourad 1 Sturm, Kevin 1 Takacs, Stefan 1 Thiele, J. P. 1 Tomar, Satyendra K. 1 Valdman, Jan 1 Van Brummelen, Harald 1 van der Zee, Kristoffer George 1 van Rienen, Ursula 1 Wendland, Wolfgang L. 1 Widlund, Olof B. ...and 4 more Co-Authors all top 5 Serials 8 SIAM Journal on Scientific Computing 8 Computational Methods in Applied Mathematics 5 Computers & Mathematics with Applications 5 Oberwolfach Reports 5 Radon Series on Computational and Applied Mathematics 4 Computer Methods in Applied Mechanics and Engineering 4 Numerische Mathematik 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 3 Computing 3 U.S.S.R. Computational Mathematics and Mathematical Physics 3 ETNA. Electronic Transactions on Numerical Analysis 3 Journal of Numerical Mathematics 2 Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya 2 Wissenschaftliche Zeitschrift der Technischen Hochschule Karl-Marx-Stadt 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Numerical Analysis 2 Surveys on Mathematics for Industry 2 International Journal of Computer Mathematics 2 Computing and Visualization in Science 2 Lecture Notes in Computational Science and Engineering 1 BIT 1 Differential Equations 1 International Journal for Numerical Methods in Engineering 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Parallel Computing 1 Applied Numerical Mathematics 1 European Journal of Applied Mathematics 1 Numerical Linear Algebra with Applications 1 East-West Journal of Numerical Mathematics 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Hungarian Electronic Journal of Sciences. Applied and Numerical Mathematics Section 1 Journal of Applied Mathematics and Computing 1 HERMIS-\(\mu\pi\). Hellenic European Research on Mathematics and Informatics Science 1 Lecture Notes in Computer Science 1 Metody Vychisleniĭ 1 Teubner-Texte zur Mathematik 1 Software - Environments - Tools 1 Mathematics in Industry 1 Lecture Notes in Applied and Computational Mechanics 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Beiträge zur Numerischen Mathematik 1 Texts & Monographs in Symbolic Computation all top 5 Fields 142 Numerical analysis (65-XX) 90 Partial differential equations (35-XX) 25 Optics, electromagnetic theory (78-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 20 General and overarching topics; collections (00-XX) 20 Mechanics of deformable solids (74-XX) 13 Fluid mechanics (76-XX) 9 Potential theory (31-XX) 3 Functional analysis (46-XX) 3 Computer science (68-XX) 2 Operator theory (47-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 104 Publications have been cited 664 times in 454 Documents Cited by ▼ Year ▼ Numerical analysis of nonlinear multiharmonic eddy current problems. Zbl 1122.78016Bachinger, F.; Langer, U.; Schöberl, J. 38 2005 Multipatch discontinuous Galerkin isogeometric analysis. Zbl 1334.65194Langer, Ulrich; Mantzaflaris, Angelos; Moore, Stephen E.; Toulopoulos, Ioannis 34 2015 Boundary element tearing and interconnecting methods. Zbl 1037.65123Langer, U.; Steinbach, O. 30 2003 A robust preconditioned minres solver for distributed time-periodic eddy current optimal control problems. Zbl 1258.49059Kolmbauer, Michael; Langer, Ulrich 25 2012 Shape optimization of an electric motor subject to nonlinear magnetostatics. Zbl 1330.49042Gangl, P.; Langer, U.; Laurain, A.; Meftahi, H.; Sturm, K. 23 2015 Space-time isogeometric analysis of parabolic evolution problems. Zbl 1436.76027Langer, Ulrich; Moore, Stephen E.; Neumüller, Martin 20 2016 From the boundary element domain decomposition methods to local Trefftz finite element methods on polyhedral meshes. Zbl 1183.65158Copeland, Dylan; Langer, Ulrich; Pusch, David 17 2009 The approximate Dirichlet domain decomposition method. I: An algebraic approach. Zbl 0741.65091Haase, G.; Langer, U.; Meyer, A. 17 1991 Analysis of multipatch discontinuous Galerkin IgA approximations to elliptic boundary value problems. Zbl 1388.65152Langer, Ulrich; Toulopoulos, Ioannis 16 2015 Fast parallel solvers for symmetric boundary element domain decomposition equations. Zbl 0907.65119Carstensen, C.; Kuhn, M.; Langer, U. 16 1998 Matrix generation in isogeometric analysis by low rank tensor approximation. Zbl 1360.65282Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, B. N.; Langer, Ulrich 16 2015 Low rank tensor methods in Galerkin-based isogeometric analysis. Zbl 1439.65185Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, Boris N.; Langer, Ulrich 14 2017 Parallel iterative solution of symmetric coupled FE/BE-equations via domain decomposition. Zbl 0798.65110Langer, U. 13 1994 Multiharmonic finite element analysis of a time-periodic parabolic optimal control problem. Zbl 1284.65078Langer, U.; Wolfmayr, M. 13 2013 A robust finite element solver for a multiharmonic parabolic optimal control problem. Zbl 1319.49043Kollmann, M.; Kolmbauer, M.; Langer, U.; Wolfmayr, M.; Zulehner, W. 13 2013 The approximate Dirichlet domain decomposition method. II: Applications to 2nd-order elliptic B.V.P.s. Zbl 0741.65092Haase, G.; Langer, U.; Meyer, A. 12 1991 The regularity of solutions of problems from plastic-flow theory. Zbl 0574.73047Korneev, V. G.; Langer, U. 11 1984 Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methods. Zbl 1035.65144Langer, U.; Pusch, D.; Reitzinger, S. 11 2003 Inexact data-sparse boundary element tearing and interconnecting methods. Zbl 1133.65105Langer, U.; Of, G.; Steinbach, O.; Zulehner, W. 11 2007 Dual-primal isogeometric tearing and interconnecting solvers for multipatch dG-Iga equations. Zbl 1439.65140Hofer, Christoph; Langer, Ulrich 11 2017 Multigrid preconditioners and their applications. Zbl 0699.65076Jung, Michael; Langer, Ulrich; Meyer, Arnd; Queck, Werner; Schneider, Manfred 10 1989 Hierarchical extension operators and local multigrid methods in domain decomposition preconditioners. Zbl 0849.65089Haase, G.; Langer, U.; Meyer, A.; Nepomnyaschikh, S. V. 10 1994 Discontinuous Galerkin isogeometric analysis of elliptic PDEs on surfaces. Zbl 1339.65219Langer, Ulrich; Moore, Stephen E. 9 2016 Approximate solution of plastic flow theory problems. Zbl 0555.73039Korneev, Vadim G.; Langer, Ulrich 9 1984 On the convergence factor of Uzawa’s algorithm. Zbl 0601.76021Langer, U.; Queck, W. 9 1986 Analysis of a non-standard finite element method based on boundary integral operators. Zbl 1205.65315Hofreither, Clemens; Langer, Ulrich; Pechstein, Clemens 9 2010 Two-side a posteriori error estimates for the dual-weighted residual method. Zbl 1440.65200Endtmayer, B.; Langer, U.; Wick, T. 9 2020 Applications of multilevel methods to practical problems. Zbl 0743.65031Jung, Michael; Langer, Ulrich 8 1991 On fast domain decomposition solving procedures for \(hp\)-discretizations of 3-D elliptic problems. Zbl 1038.65133Korneev, V. G.; Langer, U.; Xanthis, L. S. 8 2003 Parallel multigrid 3D Maxwell solvers. Zbl 0969.65128Haase, G.; Kuhn, M.; Langer, U. 7 2001 The non-overlapping domain decomposition multiplicative Schwarz method. Zbl 0758.65024Haase, Gundolf; Langer, Ulrich 7 1992 Dirichlet-Dirichlet domain decomposition methods for elliptic problems. \(h\) and \(hp\) finite element discretizations. Zbl 1323.65121Korneev, Vadim Glebovich; Langer, Ulrich 7 2015 Discontinuous Galerkin isogeometric analysis of elliptic diffusion problems on segmentations with gaps. Zbl 1352.65509Hofer, Christoph; Langer, Ulrich; Toulopoulos, Ioannis 7 2016 Functional a posteriori error estimates for time-periodic parabolic optimal control problems. Zbl 1377.49029Langer, Ulrich; Repin, Sergey; Wolfmayr, Monika 7 2016 Coupled finite and boundary element tearing and interconnecting solvers for nonlinear potential problems. Zbl 1110.78009Langer, U.; Pechstein, C. 7 2006 Preconditioned Uzawa-type iterative methods for solving mixed finite element equations. Theory - applications - software. Zbl 0619.65052Langer, Ulrich; Queck, Werner 6 1987 Scientific computing tools for 3D magnetic field problems. Zbl 0983.78026Kuhn, Michael; Langer, Ulrich; Schöberl, Joachim 6 2000 Parallelization and preconditioning of the CG-method by means of domain decomposition. (Parallelisierung und Vorkonditionierung des CG-Verfahrens durch Gebietszerlegung.) Zbl 0797.65033Haase, Gundolf; Langer, Ulrich; Meyer, Arnd 6 1993 A tutorial on elliptic PDE solvers and their parallelization. Zbl 1029.65121Douglas, Craig C.; Haase, Gundolf; Langer, Ulrich 6 2003 Coupled boundary and finite element tearing and interconnecting methods. Zbl 1066.65136Langer, Ulrich; Steinbach, Olaf 6 2005 Coupled finite and boundary element domain decomposition methods. Zbl 1298.65189Langer, Ulrich; Steinbach, Olaf 6 2007 Adaptive domain decomposition methods for finite and boundary element equations. Zbl 0884.65109Haase, G.; Heise, B.; Kuhn, M.; Langer, U. 5 1997 Comparison of geometrical and algebraic multigrid preconditioners for data-sparse boundary element matrices. Zbl 1142.65346Langer, U.; Pusch, D. 5 2006 Multigrid methods: from geometrical to algebraic versions. Zbl 1054.65122Haase, Gundolf; Langer, Ulrich; Reitzinger, Stefan 5 2002 Data-sparse algebraic multigrid methods for large scale boundary element equations. Zbl 1073.65135Langer, U.; Pusch, D. 5 2005 A non-standard finite element method based on boundary integral operators. Zbl 1310.65146Hofreither, Clemens; Langer, Ulrich; Pechstein, Clemens 5 2012 Space-time finite element methods for parabolic evolution problems with variable coefficients. Zbl 1433.65217Langer, Ulrich; Neumüller, Martin; Schafelner, Andreas 5 2019 Matrix-free multigrid solvers for phase-field fracture problems. Zbl 07337916Jodlbauer, D.; Langer, U.; Wick, T. 5 2020 Parallel and robust preconditioning for Space-Time isogeometric analysis of parabolic evolution problems. Zbl 1420.65022Hofer, Christoph; Langer, Ulrich; Neumüller, Martin; Schneckenleitner, Rainer 4 2019 Two-level hierarchically preconditioned conjugate gradient methods for solving linear elasticity finite element equations. Zbl 0701.65024Jung, M.; Langer, U.; Semmler, U. 4 1989 Algebraic multigrid methods based on element preconditioning. Zbl 1027.65169Haase, G.; Langer, U.; Reitzinger, S.; Schoberl, J. 4 2001 Partitioned solution algorithms for fluid-structure interaction problems with hyperelastic models. Zbl 1297.74039Langer, Ulrich; Yang, Huidong 4 2015 Fluid-structure interaction. Modeling, adaptive discretizations and solvers. Zbl 1390.74004 4 2017 Functional a posteriori error estimates for parabolic time-periodic boundary value problems. Zbl 1330.65150Langer, Ulrich; Repin, Sergey; Wolfmayr, Monika 4 2015 A new approach to the Dirichlet domain decomposition method. Zbl 0714.65088Haase, Gundolf; Langer, Ulrich; Meyer, Arnd 4 1990 Efficient solvers for some classes of time-periodic eddy current optimal control problems. Zbl 1291.78065Kolmbauer, Michael; Langer, Ulrich 4 2013 Isogeometric analysis on non-matching segmentation: discontinuous Galerkin techniques and efficient solvers. Zbl 1427.65404Hofer, Christoph; Langer, Ulrich; Toulopoulos, Ioannis 4 2019 Primal and dual interface concentrated iterative substructuring methods. Zbl 1180.65144Beuchler, Sven; Eibner, Tino; Langer, Ulrich 3 2008 On the use of multigrid preconditioners in the domain decomposition method. Zbl 0742.65084Haase, G.; Langer, Ulrich 3 1991 Topology optimization of electric machines based on topological sensitivity analysis. Zbl 1360.49036Gangl, Peter; Langer, Ulrich 3 2012 Time-multipatch discontinuous Galerkin space-time isogeometric analysis of parabolic evolution problems. Zbl 1394.35212Hofer, Christoph; Langer, Ulrich; Neumüller, Martin; Toulopoulos, Ioannis 3 2018 Domain decomposition solvers for nonlinear multiharmonic finite element equations. Zbl 1204.65121Copeland, D. M.; Langer, U. 3 2010 Multigoal-oriented error estimates for non-linear problems. Zbl 1435.65200Endtmayer, Bernhard; Langer, Ulrich; Wick, Thomas 3 2019 An efficient method for the numerical simulation of magneto-mechanical sensors and actuators. Zbl 1167.74047Schinnerl, M.; Kaltenbacher, M.; Langer, U.; Lerch, R.; Schöberl, J. 2 2007 Domain decomposition methods in science and engineering XVII. Selected papers based on the presentations at the 17th international conference on domain decomposition methods, St. Wolfgang/Strobl, Austria, July 3–7, 2006. Zbl 1130.65004 2 2008 Coupled FETI/BETI solvers for nonlinear potential problems in (un)bounded domains. Zbl 1132.78013Langer, Ulrich; Pechstein, Clemens 2 2007 The efficient parallel solution of PDEs. Zbl 0874.65094Haase, G.; Langer, U. 2 1996 Eigenvalue problems in surface acoustic wave filter simulations. Zbl 1308.76252Zaglmayr, S.; Schöberl, J.; Langer, Ulrich 2 2006 Multigrid methods for the fast numerical simulation of coupled magnetomechanical systems. Zbl 0964.78019Schinnerl, M.; Schöberl, J.; Kaltenbacher, M.; Langer, U.; Lerch, R. 2 2000 Adaptive space-time isogeometric analysis for parabolic evolution problems. Zbl 1453.65330Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey 2 2019 Dual-primal isogeometric tearing and interconnecting methods. Zbl 1418.65130Hofer, Christoph; Langer, Ulrich 2 2019 Fast solvers and a posteriori error estimates in elastoplasticity. Zbl 06082197Gruber, Peter G.; Kienesberger, Johanna; Langer, Ulrich; Schöberl, Joachim; Valdman, Jan 2 2012 Inexact dual-primal isogeometric tearing and interconnecting methods. Zbl 1450.65166Hofer, Christoph; Langer, Ulrich; Takacs, Stefan 2 2018 Multipatch space-time isogeometric analysis of parabolic diffusion problems. Zbl 1465.65099Langer, U.; Neumüller, M.; Toulopoulos, I. 2 2018 Numerical simulation of fluid-structure interaction problems with hyperelastic models: a monolithic approach. Zbl 07316175Langer, Ulrich; Yang, Huidong 2 2018 Space-time finite element discretization of parabolic optimal control problems with energy regularization. Zbl 1467.65094Langer, Ulrich; Steinbach, Olaf; Tröltzsch, Fredi; Yang, Huidong 2 2021 Unstructured space-time finite element methods for optimal control of parabolic equations. Zbl 1460.49002Langer, Ulrich; Steinbach, Olaf; Tröltzsch, Fredi; Yang, Huidong 2 2021 Method of finite elements for engineers. An introduction to the numerical foundations and computer simulation. 2nd revised and extended ed. (Methode der finiten Elemente für Ingenieure. Eine Einführung in die numerischen Grundlagen und Computersimulation.) Zbl 1264.65001Jung, Michael; Langer, Ulrich 1 2013 Untersuchungen zum Kummerschen Verfahren zur numerischen Behandlung nichtlinearer Eigenwertaufgaben. Zbl 0363.65049Langer, Ulrich 1 1977 Domain decomposition solvers for frequency-domain finite element equations. Zbl 1217.65186Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich 1 2011 Iterative solution of some schemes of the finite element method for elliptic equations of order 2n,n\(\geq 1\). Zbl 0561.65081Langer, U. 1 1983 On an iterative solution of some schemes of the finite element method for elliptic equations of order 2n, n\(\geq 1\). Zbl 0538.65074Langer, U. 1 1983 Effektive Auflösungsverfahren für elliptische Randwertaufgaben in speziellen und beliebigen Gebieten. Zbl 0549.65077Langer, Ulrich 1 1984 Schnelle Verfahren zur Lösung des ersten biharmonischen Randwertproblems. II. (Fast and memory-efficient methods for solving the first biharmonic boundary value problem in special and general regions. II). Zbl 0587.65067Langer, U. 1 1986 Vorkonditionierte Iterationsverfahren vom UZAWA-Typ zur Lösung eines gemischten FEM-Schemas für das erste biharmonische Randwertproblem. I. Zbl 0565.65064Langer, U. 1 1985 Domain decomposition vs. adaptivity. Zbl 0813.65132Haase, Gundolf; Langer, Ulrich 1 1994 Numerical and symbolic scientific computing. Progress and prospects. Zbl 1234.65014 1 2012 Multigoal-oriented optimal control problems with nonlinear PDE constraints. Zbl 1445.49012Endtmayer, Bernhard; Langer, Ulrich.; Neitzel, I.; Wick, Thomas; Wollner, W. 1 2020 Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems. Zbl 1443.65185Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey 1 2019 Fast boundary element methods in engineering and industrial applications. Zbl 1235.65005 1 2012 Space-time methods. Applications to partial differential equations. Zbl 1425.65008 1 2019 A robust preconditioned MinRes solver for time periodic eddy current problems. Zbl 1284.35421Kolmbauer, Michael; Langer, Ulrich 1 2013 A fast iteration method for solving the first value problem for the biharmonic equation. Zbl 0647.65069Langer, U. 1 1988 Symbolic and numerical scientific computation. Second international conference, SNSC 2001, Hagenberg, Austria, September 12–14, 2001. Revised papers. Zbl 1019.00016 1 2003 Symbolic methods for the element preconditioning technique. Zbl 1019.68145Langer, Ulrich; Reitzinger, Stefan; Schicho, Josef 1 2003 Fast adaptive domain decomposition algorithms for \(hp\)-discretizations of 2-\(D\) and 3-\(D\) elliptic equations: recent advances. Zbl 1069.65136Korneev, V.; Langer, U.; Xanthis, L. 1 2003 Boundary element simulation of linear water waves in a model basin. Zbl 1280.76022Hofreither, Clemens; Langer, Ulrich; Tomar, Satyendra 1 2010 Advanced finite element methods with applications. Selected papers from the 30th Chemnitz finite element symposium, St. Wolfgang/Strobl, Austria, September 25–27, 2017. Zbl 1422.65009 1 2019 Boundary and finite element domain decomposition methods. Zbl 1157.65505Langer, U. 1 2008 A frequency-robust solver for the time-harmonic eddy current problem. Zbl 1247.78040Kolmbauer, Michael; Langer, Ulrich 1 2012 Space-time finite element discretization of parabolic optimal control problems with energy regularization. Zbl 1467.65094Langer, Ulrich; Steinbach, Olaf; Tröltzsch, Fredi; Yang, Huidong 2 2021 Unstructured space-time finite element methods for optimal control of parabolic equations. Zbl 1460.49002Langer, Ulrich; Steinbach, Olaf; Tröltzsch, Fredi; Yang, Huidong 2 2021 Efficient direct space-time finite element solvers for parabolic initial-boundary value problems In anisotropic Sobolev spaces. Zbl 07379634Langer, Ulrich; Zank, Marco 1 2021 Reliability and efficiency of DWR-type a posteriori error estimates with smart sensitivity weight recovering. Zbl 1476.65297Endtmayer, Bernhard; Langer, Ulrich; Wick, Thomas 1 2021 Two-side a posteriori error estimates for the dual-weighted residual method. Zbl 1440.65200Endtmayer, B.; Langer, U.; Wick, T. 9 2020 Matrix-free multigrid solvers for phase-field fracture problems. Zbl 07337916Jodlbauer, D.; Langer, U.; Wick, T. 5 2020 Multigoal-oriented optimal control problems with nonlinear PDE constraints. Zbl 1445.49012Endtmayer, Bernhard; Langer, Ulrich.; Neitzel, I.; Wick, Thomas; Wollner, W. 1 2020 Adaptive space-time finite element methods for non-autonomous parabolic problems with distributional sources. Zbl 07284944Langer, Ulrich; Schafelner, Andreas 1 2020 Space-time finite element methods for parabolic evolution problems with variable coefficients. Zbl 1433.65217Langer, Ulrich; Neumüller, Martin; Schafelner, Andreas 5 2019 Parallel and robust preconditioning for Space-Time isogeometric analysis of parabolic evolution problems. Zbl 1420.65022Hofer, Christoph; Langer, Ulrich; Neumüller, Martin; Schneckenleitner, Rainer 4 2019 Isogeometric analysis on non-matching segmentation: discontinuous Galerkin techniques and efficient solvers. Zbl 1427.65404Hofer, Christoph; Langer, Ulrich; Toulopoulos, Ioannis 4 2019 Multigoal-oriented error estimates for non-linear problems. Zbl 1435.65200Endtmayer, Bernhard; Langer, Ulrich; Wick, Thomas 3 2019 Adaptive space-time isogeometric analysis for parabolic evolution problems. Zbl 1453.65330Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey 2 2019 Dual-primal isogeometric tearing and interconnecting methods. Zbl 1418.65130Hofer, Christoph; Langer, Ulrich 2 2019 Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems. Zbl 1443.65185Langer, Ulrich; Matculevich, Svetlana; Repin, Sergey 1 2019 Space-time methods. Applications to partial differential equations. Zbl 1425.65008 1 2019 Advanced finite element methods with applications. Selected papers from the 30th Chemnitz finite element symposium, St. Wolfgang/Strobl, Austria, September 25–27, 2017. Zbl 1422.65009 1 2019 Time-multipatch discontinuous Galerkin space-time isogeometric analysis of parabolic evolution problems. Zbl 1394.35212Hofer, Christoph; Langer, Ulrich; Neumüller, Martin; Toulopoulos, Ioannis 3 2018 Inexact dual-primal isogeometric tearing and interconnecting methods. Zbl 1450.65166Hofer, Christoph; Langer, Ulrich; Takacs, Stefan 2 2018 Multipatch space-time isogeometric analysis of parabolic diffusion problems. Zbl 1465.65099Langer, U.; Neumüller, M.; Toulopoulos, I. 2 2018 Numerical simulation of fluid-structure interaction problems with hyperelastic models: a monolithic approach. Zbl 07316175Langer, Ulrich; Yang, Huidong 2 2018 Low rank tensor methods in Galerkin-based isogeometric analysis. Zbl 1439.65185Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, Boris N.; Langer, Ulrich 14 2017 Dual-primal isogeometric tearing and interconnecting solvers for multipatch dG-Iga equations. Zbl 1439.65140Hofer, Christoph; Langer, Ulrich 11 2017 Fluid-structure interaction. Modeling, adaptive discretizations and solvers. Zbl 1390.74004 4 2017 Space-time isogeometric analysis of parabolic evolution problems. Zbl 1436.76027Langer, Ulrich; Moore, Stephen E.; Neumüller, Martin 20 2016 Discontinuous Galerkin isogeometric analysis of elliptic PDEs on surfaces. Zbl 1339.65219Langer, Ulrich; Moore, Stephen E. 9 2016 Discontinuous Galerkin isogeometric analysis of elliptic diffusion problems on segmentations with gaps. Zbl 1352.65509Hofer, Christoph; Langer, Ulrich; Toulopoulos, Ioannis 7 2016 Functional a posteriori error estimates for time-periodic parabolic optimal control problems. Zbl 1377.49029Langer, Ulrich; Repin, Sergey; Wolfmayr, Monika 7 2016 Multipatch discontinuous Galerkin isogeometric analysis. Zbl 1334.65194Langer, Ulrich; Mantzaflaris, Angelos; Moore, Stephen E.; Toulopoulos, Ioannis 34 2015 Shape optimization of an electric motor subject to nonlinear magnetostatics. Zbl 1330.49042Gangl, P.; Langer, U.; Laurain, A.; Meftahi, H.; Sturm, K. 23 2015 Analysis of multipatch discontinuous Galerkin IgA approximations to elliptic boundary value problems. Zbl 1388.65152Langer, Ulrich; Toulopoulos, Ioannis 16 2015 Matrix generation in isogeometric analysis by low rank tensor approximation. Zbl 1360.65282Mantzaflaris, Angelos; Jüttler, Bert; Khoromskij, B. N.; Langer, Ulrich 16 2015 Dirichlet-Dirichlet domain decomposition methods for elliptic problems. \(h\) and \(hp\) finite element discretizations. Zbl 1323.65121Korneev, Vadim Glebovich; Langer, Ulrich 7 2015 Partitioned solution algorithms for fluid-structure interaction problems with hyperelastic models. Zbl 1297.74039Langer, Ulrich; Yang, Huidong 4 2015 Functional a posteriori error estimates for parabolic time-periodic boundary value problems. Zbl 1330.65150Langer, Ulrich; Repin, Sergey; Wolfmayr, Monika 4 2015 Multiharmonic finite element analysis of a time-periodic parabolic optimal control problem. Zbl 1284.65078Langer, U.; Wolfmayr, M. 13 2013 A robust finite element solver for a multiharmonic parabolic optimal control problem. Zbl 1319.49043Kollmann, M.; Kolmbauer, M.; Langer, U.; Wolfmayr, M.; Zulehner, W. 13 2013 Efficient solvers for some classes of time-periodic eddy current optimal control problems. Zbl 1291.78065Kolmbauer, Michael; Langer, Ulrich 4 2013 Method of finite elements for engineers. An introduction to the numerical foundations and computer simulation. 2nd revised and extended ed. (Methode der finiten Elemente für Ingenieure. Eine Einführung in die numerischen Grundlagen und Computersimulation.) Zbl 1264.65001Jung, Michael; Langer, Ulrich 1 2013 A robust preconditioned MinRes solver for time periodic eddy current problems. Zbl 1284.35421Kolmbauer, Michael; Langer, Ulrich 1 2013 Direct and inverse problems in wave propagation and applications. Selected papers of the workshop on wave propagation and scattering, inverse problems and applications in energy and the environment, Linz, Austria, November 21–25, 2011. Zbl 1272.78001 1 2013 A robust preconditioned minres solver for distributed time-periodic eddy current optimal control problems. Zbl 1258.49059Kolmbauer, Michael; Langer, Ulrich 25 2012 A non-standard finite element method based on boundary integral operators. Zbl 1310.65146Hofreither, Clemens; Langer, Ulrich; Pechstein, Clemens 5 2012 Topology optimization of electric machines based on topological sensitivity analysis. Zbl 1360.49036Gangl, Peter; Langer, Ulrich 3 2012 Fast solvers and a posteriori error estimates in elastoplasticity. Zbl 06082197Gruber, Peter G.; Kienesberger, Johanna; Langer, Ulrich; Schöberl, Joachim; Valdman, Jan 2 2012 Numerical and symbolic scientific computing. Progress and prospects. Zbl 1234.65014 1 2012 Fast boundary element methods in engineering and industrial applications. Zbl 1235.65005 1 2012 A frequency-robust solver for the time-harmonic eddy current problem. Zbl 1247.78040Kolmbauer, Michael; Langer, Ulrich 1 2012 Domain decomposition solvers for frequency-domain finite element equations. Zbl 1217.65186Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich 1 2011 Analysis of a non-standard finite element method based on boundary integral operators. Zbl 1205.65315Hofreither, Clemens; Langer, Ulrich; Pechstein, Clemens 9 2010 Domain decomposition solvers for nonlinear multiharmonic finite element equations. Zbl 1204.65121Copeland, D. M.; Langer, U. 3 2010 Boundary element simulation of linear water waves in a model basin. Zbl 1280.76022Hofreither, Clemens; Langer, Ulrich; Tomar, Satyendra 1 2010 From the boundary element domain decomposition methods to local Trefftz finite element methods on polyhedral meshes. Zbl 1183.65158Copeland, Dylan; Langer, Ulrich; Pusch, David 17 2009 Primal and dual interface concentrated iterative substructuring methods. Zbl 1180.65144Beuchler, Sven; Eibner, Tino; Langer, Ulrich 3 2008 Domain decomposition methods in science and engineering XVII. Selected papers based on the presentations at the 17th international conference on domain decomposition methods, St. Wolfgang/Strobl, Austria, July 3–7, 2006. Zbl 1130.65004 2 2008 Boundary and finite element domain decomposition methods. Zbl 1157.65505Langer, U. 1 2008 Inexact data-sparse boundary element tearing and interconnecting methods. Zbl 1133.65105Langer, U.; Of, G.; Steinbach, O.; Zulehner, W. 11 2007 Coupled finite and boundary element domain decomposition methods. Zbl 1298.65189Langer, Ulrich; Steinbach, Olaf 6 2007 An efficient method for the numerical simulation of magneto-mechanical sensors and actuators. Zbl 1167.74047Schinnerl, M.; Kaltenbacher, M.; Langer, U.; Lerch, R.; Schöberl, J. 2 2007 Coupled FETI/BETI solvers for nonlinear potential problems in (un)bounded domains. Zbl 1132.78013Langer, Ulrich; Pechstein, Clemens 2 2007 Coupled finite and boundary element tearing and interconnecting solvers for nonlinear potential problems. Zbl 1110.78009Langer, U.; Pechstein, C. 7 2006 Comparison of geometrical and algebraic multigrid preconditioners for data-sparse boundary element matrices. Zbl 1142.65346Langer, U.; Pusch, D. 5 2006 Eigenvalue problems in surface acoustic wave filter simulations. Zbl 1308.76252Zaglmayr, S.; Schöberl, J.; Langer, Ulrich 2 2006 Numerical analysis of nonlinear multiharmonic eddy current problems. Zbl 1122.78016Bachinger, F.; Langer, U.; Schöberl, J. 38 2005 Coupled boundary and finite element tearing and interconnecting methods. Zbl 1066.65136Langer, Ulrich; Steinbach, Olaf 6 2005 Data-sparse algebraic multigrid methods for large scale boundary element equations. Zbl 1073.65135Langer, U.; Pusch, D. 5 2005 Boundary element tearing and interconnecting methods. Zbl 1037.65123Langer, U.; Steinbach, O. 30 2003 Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methods. Zbl 1035.65144Langer, U.; Pusch, D.; Reitzinger, S. 11 2003 On fast domain decomposition solving procedures for \(hp\)-discretizations of 3-D elliptic problems. Zbl 1038.65133Korneev, V. G.; Langer, U.; Xanthis, L. S. 8 2003 A tutorial on elliptic PDE solvers and their parallelization. Zbl 1029.65121Douglas, Craig C.; Haase, Gundolf; Langer, Ulrich 6 2003 Symbolic and numerical scientific computation. Second international conference, SNSC 2001, Hagenberg, Austria, September 12–14, 2001. Revised papers. Zbl 1019.00016 1 2003 Symbolic methods for the element preconditioning technique. Zbl 1019.68145Langer, Ulrich; Reitzinger, Stefan; Schicho, Josef 1 2003 Fast adaptive domain decomposition algorithms for \(hp\)-discretizations of 2-\(D\) and 3-\(D\) elliptic equations: recent advances. Zbl 1069.65136Korneev, V.; Langer, U.; Xanthis, L. 1 2003 Multigrid methods: from geometrical to algebraic versions. Zbl 1054.65122Haase, Gundolf; Langer, Ulrich; Reitzinger, Stefan 5 2002 Parallel multigrid 3D Maxwell solvers. Zbl 0969.65128Haase, G.; Kuhn, M.; Langer, U. 7 2001 Algebraic multigrid methods based on element preconditioning. Zbl 1027.65169Haase, G.; Langer, U.; Reitzinger, S.; Schoberl, J. 4 2001 Scientific computing tools for 3D magnetic field problems. Zbl 0983.78026Kuhn, Michael; Langer, Ulrich; Schöberl, Joachim 6 2000 Multigrid methods for the fast numerical simulation of coupled magnetomechanical systems. Zbl 0964.78019Schinnerl, M.; Schöberl, J.; Kaltenbacher, M.; Langer, U.; Lerch, R. 2 2000 Fast parallel solvers for symmetric boundary element domain decomposition equations. Zbl 0907.65119Carstensen, C.; Kuhn, M.; Langer, U. 16 1998 Adaptive domain decomposition methods for finite and boundary element equations. Zbl 0884.65109Haase, G.; Heise, B.; Kuhn, M.; Langer, U. 5 1997 The efficient parallel solution of PDEs. Zbl 0874.65094Haase, G.; Langer, U. 2 1996 Parallel iterative solution of symmetric coupled FE/BE-equations via domain decomposition. Zbl 0798.65110Langer, U. 13 1994 Hierarchical extension operators and local multigrid methods in domain decomposition preconditioners. Zbl 0849.65089Haase, G.; Langer, U.; Meyer, A.; Nepomnyaschikh, S. V. 10 1994 Domain decomposition vs. adaptivity. Zbl 0813.65132Haase, Gundolf; Langer, Ulrich 1 1994 Parallelization and preconditioning of the CG-method by means of domain decomposition. (Parallelisierung und Vorkonditionierung des CG-Verfahrens durch Gebietszerlegung.) Zbl 0797.65033Haase, Gundolf; Langer, Ulrich; Meyer, Arnd 6 1993 The non-overlapping domain decomposition multiplicative Schwarz method. Zbl 0758.65024Haase, Gundolf; Langer, Ulrich 7 1992 The approximate Dirichlet domain decomposition method. I: An algebraic approach. Zbl 0741.65091Haase, G.; Langer, U.; Meyer, A. 17 1991 The approximate Dirichlet domain decomposition method. II: Applications to 2nd-order elliptic B.V.P.s. Zbl 0741.65092Haase, G.; Langer, U.; Meyer, A. 12 1991 Applications of multilevel methods to practical problems. Zbl 0743.65031Jung, Michael; Langer, Ulrich 8 1991 On the use of multigrid preconditioners in the domain decomposition method. Zbl 0742.65084Haase, G.; Langer, Ulrich 3 1991 A new approach to the Dirichlet domain decomposition method. Zbl 0714.65088Haase, Gundolf; Langer, Ulrich; Meyer, Arnd 4 1990 Multigrid preconditioners and their applications. Zbl 0699.65076Jung, Michael; Langer, Ulrich; Meyer, Arnd; Queck, Werner; Schneider, Manfred 10 1989 Two-level hierarchically preconditioned conjugate gradient methods for solving linear elasticity finite element equations. Zbl 0701.65024Jung, M.; Langer, U.; Semmler, U. 4 1989 A fast iteration method for solving the first value problem for the biharmonic equation. Zbl 0647.65069Langer, U. 1 1988 Preconditioned Uzawa-type iterative methods for solving mixed finite element equations. Theory - applications - software. Zbl 0619.65052Langer, Ulrich; Queck, Werner 6 1987 On the convergence factor of Uzawa’s algorithm. Zbl 0601.76021Langer, U.; Queck, W. 9 1986 Schnelle Verfahren zur Lösung des ersten biharmonischen Randwertproblems. II. (Fast and memory-efficient methods for solving the first biharmonic boundary value problem in special and general regions. II). Zbl 0587.65067Langer, U. 1 1986 Vorkonditionierte Iterationsverfahren vom UZAWA-Typ zur Lösung eines gemischten FEM-Schemas für das erste biharmonische Randwertproblem. I. Zbl 0565.65064Langer, U. 1 1985 The regularity of solutions of problems from plastic-flow theory. Zbl 0574.73047Korneev, V. G.; Langer, U. 11 1984 Approximate solution of plastic flow theory problems. Zbl 0555.73039Korneev, Vadim G.; Langer, Ulrich 9 1984 ...and 4 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 672 Authors 43 Langer, Ulrich 17 Steinbach, Olaf 13 Axelsson, Axel Owe Holger 13 Jüttler, Bert 12 Wick, Thomas 11 Hofer, Christoph D. 10 Toulopoulos, Ioannis 10 Weißer, Steffen 9 Haase, Gundolf 9 Pechstein, Clemens 9 Schöberl, Joachim 8 Mantzaflaris, Angelos 8 Tröltzsch, Fredi 7 Beuchler, Sven 7 Yang, Huidong 6 Of, Günther 6 Repin, Sergeĭ Igorevich 6 Siebenborn, Martin 6 Tani, Mattia 6 Wolfmayr, Monika 5 Kraus, Johannes K. 5 Laurain, Antoine 5 Liang, Zhaozheng 5 Reitzinger, Stefan 5 Sangalli, Giancarlo 5 Takacs, Stefan 5 Welker, Kathrin 5 Yousept, Irwin 5 Zou, Jun 4 Angelov, Todor Angelov 4 Claeys, Xavier 4 Hiptmair, Ralf 4 Hsiao, George C. 4 Jung, Michael 4 Korneev, Vadim Glebovich 4 Moore, Stephen Edward 4 Neumüller, Martin 4 Neytcheva, Maya G. 4 Nicaise, Serge 4 Ovall, Jeffrey S. 4 Pan, Maodong 4 Pan, Xingbin 4 Scheichl, Robert 4 Schöps, Sebastian 4 Sturm, Kevin 4 Zhang, Guofeng 4 Zheng, Weiying 3 Blaheta, Radim 3 Bouchala, Jiří 3 Chen, Falai 3 Dostál, Zdeněk 3 Elleithy, Wael M. 3 Endtmayer, Bernhard 3 Führer, Thomas 3 Gangl, Peter 3 Heuer, Norbert 3 Hughes, Thomas J. R. 3 Jiang, Xue 3 Kaltenbacher, Manfred 3 Khoromskiĭ, Boris Nikolaevich 3 Ledger, Paul David 3 Leithäuser, Christian 3 Lukáš, Dalibor 3 Manohar, Ram P. 3 Mellado, Mario E. 3 Montardini, Monica 3 Niyonzima, Innocent 3 Noii, Nima 3 Reynolds, Samuel E. 3 Sadowská, Marie 3 Schafelner, Andreas 3 Schneckenleitner, Rainer 3 Scholz, Felix 3 Schulz, Volker H. 3 Sinha, Rajen Kumar 3 Stephan, Ernst Peter 3 Stevenson, Rob P. 3 Valli, Alberto 3 Vodička, Roman 3 Wendland, Wolfgang L. 3 Wriggers, Peter 3 Zank, Marco 2 Acevedo, Ramiro 2 Aldakheel, Fadi 2 Anand, Akash 2 Antolin, Pablo 2 Arioli, Clarissa 2 Augustin, Christoph M. 2 Bartel, Andreas 2 Bastl, Bohumír 2 Bause, Markus 2 Benedusi, Pietro 2 Blauth, Sebastian 2 Braess, Dietrich 2 Bramble, James H. 2 Buchegger, Florian 2 Chan, Jesse 2 Cho, Durkbin 2 Clemens, Markus 2 Cockburn, Bernardo ...and 572 more Authors all top 5 Cited in 102 Serials 56 Computer Methods in Applied Mechanics and Engineering 33 Computers & Mathematics with Applications 22 SIAM Journal on Scientific Computing 15 Computing 15 Journal of Computational and Applied Mathematics 15 Numerische Mathematik 13 Journal of Computational Physics 13 International Journal for Numerical Methods in Engineering 12 Applied Numerical Mathematics 12 Computational Methods in Applied Mathematics 11 Numerical Linear Algebra with Applications 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 9 Computational Mechanics 8 Mathematics of Computation 7 Mathematics and Computers in Simulation 7 SIAM Journal on Numerical Analysis 7 Journal of Scientific Computing 6 Applicable Analysis 6 Applied Mathematics and Computation 6 COMPEL 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 Engineering Analysis with Boundary Elements 6 Computing and Visualization in Science 5 Mathematical Methods in the Applied Sciences 5 ETNA. Electronic Transactions on Numerical Analysis 5 Advances in Computational Mathematics 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 Numerical Algorithms 3 International Journal of Engineering Science 3 Journal of Optimization Theory and Applications 3 Computer Aided Geometric Design 3 Numerical Methods for Partial Differential Equations 3 SIAM Journal on Optimization 3 Mathematical Problems in Engineering 3 Archives of Computational Methods in Engineering 3 Journal of Numerical Mathematics 2 Journal of Mathematical Analysis and Applications 2 Applied Mathematics and Optimization 2 BIT 2 Applied Mathematics Letters 2 Computational Mathematics and Mathematical Physics 2 Applied Mathematical Modelling 2 International Journal of Computer Mathematics 2 Linear Algebra and its Applications 2 Vietnam Journal of Mathematics 2 Optimization Methods & Software 2 Journal of Mathematical Fluid Mechanics 2 Multiscale Modeling & Simulation 2 Communications in Computational Physics 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Mathematics in Industry 2 Communications in Mathematics and Statistics 1 Computers and Fluids 1 Communications on Pure and Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of the Franklin Institute 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Journal of the Mechanics and Physics of Solids 1 Nonlinearity 1 Periodica Mathematica Hungarica 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Journal of Differential Equations 1 Mathematische Nachrichten 1 Numerical Functional Analysis and Optimization 1 Advances in Applied Mathematics 1 Applied Mathematics and Mechanics. (English Edition) 1 Parallel Computing 1 Optimization 1 Computational Mathematics and Modeling 1 Japan Journal of Industrial and Applied Mathematics 1 Applications of Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Computational Optimization and Applications 1 Calculus of Variations and Partial Differential Equations 1 Communications in Numerical Methods in Engineering 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Journal of Inverse and Ill-Posed Problems 1 Discrete and Continuous Dynamical Systems 1 Doklady Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 European Journal of Mechanics. A. Solids 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Engineering Computations 1 Lobachevskii Journal of Mathematics 1 Differential Equations 1 Mathematical Modelling and Analysis 1 Journal of Applied Mathematics and Computing 1 Journal of Computational Acoustics 1 International Journal of Parallel, Emergent and Distributed Systems 1 Frontiers of Mathematics in China 1 Mathematical Control and Related Fields 1 Journal of Modern Methods in Numerical Mathematics 1 Evolution Equations and Control Theory 1 SIAM/ASA Journal on Uncertainty Quantification 1 Nonlinear Analysis. Theory, Methods & Applications ...and 2 more Serials all top 5 Cited in 31 Fields 354 Numerical analysis (65-XX) 178 Partial differential equations (35-XX) 100 Mechanics of deformable solids (74-XX) 72 Calculus of variations and optimal control; optimization (49-XX) 64 Optics, electromagnetic theory (78-XX) 48 Fluid mechanics (76-XX) 12 Computer science (68-XX) 8 Biology and other natural sciences (92-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Operations research, mathematical programming (90-XX) 6 Potential theory (31-XX) 5 Systems theory; control (93-XX) 4 Operator theory (47-XX) 4 Manifolds and cell complexes (57-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Ordinary differential equations (34-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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