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 22 articles , 1 standard article )

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  1. Egger, H.; Schmidt, K.; Shashkov, V.: Multistep and Runge-Kutta convolution quadrature methods for coupled dynamical systems (2021)
  2. Altmann, Robert; Froidevaux, Marine: PDE eigenvalue iterations with applications in two-dimensional photonic crystals (2020)
  3. Semin, Adrien; Delourme, Bérangère; Schmidt, Kersten: On the homogenization of the Helmholtz problem with thin perforated walls of finite length (2018)
  4. Semin, Adrien; Schmidt, Kersten: On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model (2018)
  5. Byfut, Andreas; Schröder, Andreas: Unsymmetric multi-level hanging nodes and anisotropic polynomial degrees in (H^1)-conforming higher-order finite element methods (2017)
  6. Drescher, Lukas; Heumann, Holger; Schmidt, Kersten: A high order method for the approximation of integrals over implicitly defined hypersurfaces (2017)
  7. Engström, Christian; Langer, Heinz; Tretter, Christiane: Rational eigenvalue problems and applications to photonic crystals (2017)
  8. Schmidt, Kersten; Hiptmair, Ralf: Asymptotic expansion techniques for singularly perturbed boundary integral equations (2017)
  9. Semin, Adrien; Schmidt, Kersten: Absorbing boundary conditions for acoustic models at low viscosity in a waveguide (2016)
  10. Zander, Nils; Bog, Tino; Elhaddad, Mohamed; Frischmann, Felix; Kollmannsberger, Stefan; Rank, Ernst: The multi-level (hp)-method for three-dimensional problems: dynamically changing high-order mesh refinement with arbitrary hanging nodes (2016)
  11. Banz, Lothar; Schröder, Andreas: Biorthogonal basis functions in (hp)-adaptive FEM for elliptic obstacle problems (2015)
  12. Fliss, Sonia; Klindworth, Dirk; Schmidt, Kersten: Robin-to-Robin transparent boundary conditions for the computation of guided modes in photonic crystal wave-guides (2015)
  13. Schmidt, Kersten; Diaz, Julien; Heier, Christian: Non-conforming Galerkin finite element methods for local absorbing boundary conditions of higher order (2015)
  14. Schmidt, Kersten; Heier, Christian: An analysis of Feng’s and other symmetric local absorbing boundary conditions (2015)
  15. Schmidt, Kersten; Hiptmair, Ralf: Asymptotic boundary element methods for thin conducting sheets (2015)
  16. Śmigaj, Wojciech; Betcke, Timo; Arridge, Simon; Phillips, Joel; Schweiger, Martin: Solving boundary integral problems with BEM++ (2015)
  17. Engström, Christian: Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations (2014)
  18. Schmidt, Kersten; Tordeux, Sébastien: Asymptotic modelling of conductive thin sheets (2010)
  19. Baitsch, Matthias; Hartmann, Dietrich: Piecewise polynomial shape functions for (hp)-finite element methods (2009)
  20. Schmidt, K.; Kauf, P.: Computation of the band structure of two-dimensional photonic crystals with (hp) finite elements (2009)

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