## ALBERTA

 swMATH ID: 1061 Software Authors: Alfred Schmidt, Kunibert G. Siebert, Claus-Justus Heine, Daniel Köster, Oliver Kriessl Description: ALBERTA is an Adaptive multiLevel finite element toolbox using Bisectioning refinement and Error control by Residual Techniques for scientific Applications. ALBERTA, a sequential adaptive finite-element toolbox, is being used widely in the fields of scientific and engineering computation, especially in the numerical simulation of electromagnetics. But the nature of sequentiality has become the bottle-neck while solving large scale problems. So we develop a parallel adaptive finite-element package based on ALBERTA, using ParMETIS and PETSc. The package is able to deal with any problem that ALBERT solved. Furthermore, it is suitable for distributed memory parallel computers including PC clusters Homepage: http://www.alberta-fem.de/ Keywords: finite-element method; adaption; parallel algorithm; ALBERTA; package; numerical experiments Related Software: UMFPACK; ALBERT; DUNE; deal.ii; FEniCS; PETSc; SyFi; PLTMG; UG; Gmsh; AFEM@matlab; ISTL; Triangle; Matlab; Trilinos; ParaView; MUMPS; LDL; El-Topo; PROST Referenced in: 179 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
A parallel adaptive finite-element package based on ALBERTA. Zbl 1154.65091
Liu, Qingkai; Mo, Zeyao; Zhang, Linbo
2008
all top 5

### Referenced by 212 Authors

 28 Nürnberg, Robert 23 Garcke, Harald 17 Nochetto, Ricardo Horacio 16 Barrett, John William 13 Morin, Pedro 13 Siebert, Kunibert G. 12 Elliott, Charles M. 9 Demlow, Alan 7 Cascón, José Manuel 7 Kreuzer, Christian 7 Veeser, Andreas 6 Kahle, Christian 6 Styles, Vanessa 5 Lakkis, Omar 5 Lam, Kei Fong 5 Madzvamuse, Anotida 5 Venkataraman, Chandrasekhar 4 Berrone, Stefano 4 Chen, Zhiming 4 Dziuk, Gerhard 4 Garau, Eduardo M. 4 Hinze, Michael 4 Makridakis, Charalambos G. 4 Sander, Oliver 4 Verani, Marco 3 Barreira, Raquel 3 Dedner, Andreas S. 3 Du, Qiang 3 Klöfkorn, Robert 3 Ohlberger, Mario 3 Pryer, Tristan 3 Schmidt, Alfred 3 Stevenson, Rob P. 3 Xiao, Yuanming 3 Xu, Jinchao 3 Zhang, Chensong 3 Zhang, Linbo 3 Zuppa, Carlos 2 Abdulle, Assyr 2 Bänsch, Eberhard 2 Bastian, Peter 2 Bermejo, Rodolfo 2 Blank, Luise 2 Blatt, Markus 2 Bonito, Andrea 2 Carpio, Jaime 2 Chen, Long 2 Deckelnick, Klaus 2 Diening, Lars 2 Doǧan, Günay 2 Engwer, Christian 2 Escobar, José María 2 Gaspoz, Fernando D. 2 Gräser, Carsten 2 Hintermüller, Michael 2 Kanschat, Guido 2 Kashima, Yohei 2 Keil, Tobias 2 Kimura, Masato 2 Köster, Daniel 2 Linke, Alexander 2 Marro, Massimo 2 Mekchay, Khamron 2 Montenegro, Rafael 2 Montero, Gustavo 2 Ranner, Thomas 2 Rodríguez, Eduardo 2 Sacconi, Andrea 2 Schmuck, Markus 2 Sitka, Emanuel 2 Stinner, Bjorn 2 Tian, Li 2 Tucker, Edward J. W. 2 von Petersdorff, Tobias 2 Wittum, Gabriel 2 Zhang, Jian 1 Agnese, Marco 1 Aguilera, Néstor E. 1 Aland, Sebastian 1 Alauzet, Frédéric 1 Ambati, Vijaya R. 1 Asensio, Maria Isabel 1 Bai, Yun 1 Baňas, Ľubomír 1 Baran, Ágnes 1 Bartlett, Roscoe A. 1 Bause, Markus 1 Belenki, Liudmila 1 Bell, Alexander 1 Bespalov, Alexei 1 Bi, Chunjia 1 Blum, Heribert 1 Bokhove, Onno 1 Brix, Kolja 1 Burman, Erik 1 Buša, Ján jun. 1 Butz, Martin V. 1 Chaplain, Mark A. J. 1 Chen, Dongquan 1 Chen, Falai ...and 112 more Authors
all top 5

### Referenced in 59 Serials

 15 Numerische Mathematik 11 IMA Journal of Numerical Analysis 11 SIAM Journal on Scientific Computing 10 Mathematics of Computation 9 Computer Methods in Applied Mechanics and Engineering 9 Journal of Computational Physics 8 SIAM Journal on Numerical Analysis 6 Applied Numerical Mathematics 6 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Computing 4 International Journal of Numerical Analysis and Modeling 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Computers & Mathematics with Applications 3 Journal of Scientific Computing 3 European Journal of Applied Mathematics 3 Interfaces and Free Boundaries 3 Lecture Notes in Computational Science and Engineering 3 Numerical Mathematics: Theory, Methods and Applications 2 Computers and Fluids 2 Inverse Problems 2 Journal of Mathematical Biology 2 Calcolo 2 Journal of Computational and Applied Mathematics 2 Numerical Methods for Partial Differential Equations 2 Numerical Algorithms 2 Advances in Computational Mathematics 2 Computing and Visualization in Science 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Foundations of Computational Mathematics 1 International Journal of Modern Physics B 1 Journal of Engineering Mathematics 1 Journal of Mathematical Physics 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 Kybernetika 1 Computational Mechanics 1 Applied Mathematical Modelling 1 International Journal of Computer Mathematics 1 SIAM Journal on Mathematical Analysis 1 SIAM Journal on Optimization 1 Journal of Nonlinear Science 1 Computational Optimization and Applications 1 Optimization Methods & Software 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Computational Geosciences 1 Optimization and Engineering 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Milan Journal of Mathematics 1 Communications in Mathematical Sciences 1 Communications in Computational Physics 1 Mathematical Modelling of Natural Phenomena 1 SIAM Journal on Imaging Sciences 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Theoretical Biology 1 SIAM/ASA Journal on Uncertainty Quantification 1 De Gruyter Studium 1 SMAI Journal of Computational Mathematics
all top 5

### Referenced in 25 Fields

 147 Numerical analysis (65-XX) 91 Partial differential equations (35-XX) 35 Fluid mechanics (76-XX) 19 Mechanics of deformable solids (74-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 16 Biology and other natural sciences (92-XX) 9 Optics, electromagnetic theory (78-XX) 9 Statistical mechanics, structure of matter (82-XX) 7 Differential geometry (53-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Computer science (68-XX) 5 Operations research, mathematical programming (90-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)