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”. \parThe 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.

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Byfut, Andreas; Schröder, Andreas: Unsymmetric multi-level hanging nodes and anisotropic polynomial degrees in $H^1$-conforming higher-order finite element methods (2017)
  2. Engström, Christian; Langer, Heinz; Tretter, Christiane: Rational eigenvalue problems and applications to photonic crystals (2017)
  3. Schmidt, Kersten; Hiptmair, Ralf: Asymptotic expansion techniques for singularly perturbed boundary integral equations (2017)
  4. Fliss, Sonia; Klindworth, Dirk; Schmidt, Kersten: Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides (2015)
  5. Śmigaj, Wojciech; Betcke, Timo; Arridge, Simon; Phillips, Joel; Schweiger, Martin: Solving boundary integral problems with BEM++ (2015)
  6. Engström, Christian: Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations (2014)
  7. Schmidt, Kersten; Tordeux, Sébastien: Asymptotic modelling of conductive thin sheets (2010)
  8. Baitsch, Matthias; Hartmann, Dietrich: Piecewise polynomial shape functions for $hp$-finite element methods (2009)
  9. Schmidt, K.; Kauf, P.: Computation of the band structure of two-dimensional photonic crystals with $hp$ finite elements (2009)
  10. Frauenfelder, Philipp; Schwab, Christoph; Todor, Radu Alexandru: Finite elements for elliptic problems with stochastic coefficients (2005)
  11. Frauenfelder, Philipp; Lage, Christian: Concepts -- an object-oriented software package for partial differential equations (2002)