## Concepts

 swMATH ID: 151 Software Authors: Frauenfelder, Philipp; Lage, Christian Description: The authors show how mathematical concepts can be used to identify and characterize the modules which can then be used to implement a mathematical method in an object oriented programming language. They propose an alternative way to approach the design challenge, which is called “concept oriented design”. The new design methodology is applied to Petrov-Galerkin methods leading to a class library for both boundary element methods and finite-element methods. As an example the authors implement of the $$hp$$-finite element method using the library with special attention to the handling of inconsistent meshes. Homepage: http://www.concepts.math.ethz.ch/ Programming Languages: C++ Keywords: object oriented design; concept oriented design; hp-FEM; adaptivity; Petrov-Galerkin methods; boundary element methods; finite-element methods Related Software: Gmsh; deal.ii; HP90; NewtonLib; AAA; RODAS; par2Dhp; 3Dhp90; Nektar++; XTOR; CHEASE; Boost C++ Libraries; PGFPlots; OpenBLAS; FEAPpv; Boost; MTL4; SuiteSparse; Open CASCADE; HyENA Cited in: 23 Publications
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### Cited by 39 Authors

 12 Schmidt, Kersten 4 Semin, Adrien 2 Engström, Christian 2 Frauenfelder, Philipp 2 Heier, Christian 2 Hiptmair, Ralf 2 Schroder, Andreas 1 Altmann, Robert 1 Arridge, Simon R. 1 Baitsch, Matthias 1 Banz, Lothar 1 Betcke, Timo 1 Bog, Tino 1 Byfut, Andreas 1 Delourme, Bérangère 1 Diaz, Julien 1 Drescher, Lukas 1 Elhaddad, Mohamed 1 Fliss, Sonia 1 Frischmann, Felix 1 Froidevaux, Marine 1 Hartmann, Dietrich 1 Heumann, Holger 1 Kauf, Peter 1 Klindworth, Dirk 1 Kollmannsberger, Stefan 1 Lage, Christian 1 Langer, Heinz 1 Ljulj, Matko 1 Phillips, Joel R. 1 Rank, Ernst 1 Schwab, Christoph 1 Schweiger, Martin 1 Smigaj, Wojciech 1 Tambača, Josip 1 Todor, Radu Alexandru 1 Tordeux, Sébastien 1 Tretter, Christiane 1 Zander, Nils
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### Cited in 15 Serials

 4 Computer Methods in Applied Mechanics and Engineering 3 Computers & Mathematics with Applications 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Numerische Mathematik 1 Applicable Analysis 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 ACM Transactions on Mathematical Software 1 BIT 1 Journal of Computational and Applied Mathematics 1 SIAM Journal on Numerical Analysis 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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### Cited in 13 Fields

 20 Numerical analysis (65-XX) 13 Partial differential equations (35-XX) 8 Optics, electromagnetic theory (78-XX) 3 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX)