MaiProgs

Publications

In the following you find a nonexhaustive list of papers, PhD theses and diploma and master theses whose numerical experiments where performed using MaiProgs or an extension of it.

Papers

• Stephan, E. P.; Maischak, M.; Leydecker, F. An $hp$-adaptive finite element/boundary element coupling method for electromagnetic problems. Comput. Mech. 39 (2007), no. 5, 673--680. 
• Maischak, Matthias; Stephan, Ernst P. Adaptive $hp$-versions of boundary element methods for elastic contact problems. Comput. Mech. 39 (2007), no. 5, 597--607.
• Maischak, Matthias Multiplicative Schwarz algorithms for the $p$-version Galerkin boundary element method in 3D. Appl. Numer. Math. 56 (2006), no. 10-11, 1370--1382. 
• Stephan, Ernst P.; Maischak, Matthias; Leydecker, Florian Some Schwarz methods for integral equations on surfaces---$h$ and $p$ versions. Comput. Vis. Sci. 8 (2005), no. 3-4, 211--216.
• Maischak, Matthias; Stephan, Ernst P. Adaptive $hp$-versions of BEM for Signorini problems. Appl. Numer. Math. 54 (2005), no. 3-4, 425--449. 
• Gatica, Gabriel N.; Maischak, Matthias A posteriori error estimates for the mixed finite element method with Lagrange multipliers. Numer. Methods Partial Differential Equations 21 (2005), no. 3, 421--450.
• Maischak, Matthias; Stephan, Ernst P. A FEM-BEM coupling method for a nonlinear transmission problem modelling Coulomb friction contact. Comput. Methods Appl. Mech. Engrg. 194 (2005), no. 2-5, 453--466.
• Stephan, E. P.; Maischak, M. A posteriori error estimates for fem-bem couplings of three-dimensional electromagnetic problems. Comput. Methods Appl. Mech. Engrg. 194 (2005), no. 2-5, 441--452.
• Maischak, M.; Stephan, E. P. A least squares coupling method with finite elements and boundary elements for transmission problems. Comput. Math. Appl. 48 (2004), no. 7-8, 995--1016.
• Carstensen, Carsten; Maischak, M.; Praetorius, D.; Stephan, E. P. Residual-based a posteriori error estimate for hypersingular equation on surfaces. Numer. Math. 97 (2004), no. 3, 397--425.
• Maischak, Matthias; Stephan, Ernst P.; Tran, Thanh A multiplicative Schwarz algorithm for the Galerkin boundary element approximation of the weakly singular integral operator in three dimensions. Int. J. Pure Appl. Math. 12 (2004), no. 1, 1--21
• Barrientos, Mauricio A.; Gatica, Gabriel N.; Maischak, Matthias A posteriori error estimates for linear exterior problems via mixed-FEM and DtN mappings. M2AN Math. Model. Numer. Anal. 36 (2002), no. 2, 241--272.
• Carstensen, C.; Maischak, M.; Stephan, E. P. A posteriori error estimate and $h$-adaptive algorithm on surfaces for Symm's integral equation. Numer. Math. 90 (2001), no. 2, 197--213.
• Maischak, Matthias; Stephan, Ernst P.; Tran, Thanh Multiplicative Schwarz algorithms for the Galerkin boundary element method. SIAM J. Numer. Anal. 38 (2000), no. 4, 1243--1268
• Heuer, Norbert; Maischak, Matthias; Stephan, Ernst P. Preconditioned minimum residual iteration for the $h$-$p$ version of the coupled FEM/BEM with quasi-uniform meshes. Iterative solution methods for the elasticity equations in mechanics and biomechanics, IMMB'98, Part 1 (Nijmegen). Numer. Linear Algebra Appl. 6 (1999), no. 6, 435--456.
• Heuer, Norbert; Maischak, Matthias; Stephan, Ernst P. Exponential convergence of the $hp$-version for the boundary element method on open surfaces. Numer. Math. 83 (1999), no. 4, 641--666.
• Maischak, M.; Stephan, E. P. Schwarz methods for graded meshes in $2$D-BEM: numerical results. Analysis, numerics and applications of differential and integral equations (Stuttgart, 1996), 132--136, Pitman Res. Notes Math. Ser., 379, Longman, Harlow, 1998.
• Maischak, M.; Stephan, E. P. The $hp$-version of the BEM with geometric meshes in $3\rm D$. Boundary element topics (Stuttgart, 1995), 351--362, Springer, Berlin, 1997.
• Maischak, M.; Mund, P.; Stephan, E. P. Adaptive multilevel BEM for acoustic scattering. Symposium on Advances in Computational Mechanics, Vol. 2 (Austin, TX, 1997). Comput. Methods Appl. Mech. Engrg. 150 (1997), no. 1-4, 351--367.
• Maischak, M.; Stephan, E. P. The $hp$-version of the boundary element method in $\bold R\sp 3$: the basic approximation results. Math. Methods Appl. Sci. 20 (1997), no. 5, 461--476.
• Maischak, Matthias; Stephan, Ernst P.; Tran, Thanh Domain decomposition methods for boundary integral equations of the first kind: numerical results. Appl. Anal. 63 (1996), no. 1-2, 111--132.
• Holm, H.; Maischak, M.; Stephan, E. P. The $hp$-version of the boundary element method for Helmholtz screen problems. Computing 57 (1996), no. 2, 105--134.
• Maischak, Matthias The gravitational anomalies in de Sitter space. Lett. Math. Phys. 25 (1992), no. 4, 307--316.

PhD theses

• Matthias Maischak: hp-Methoden für Randintegralgleichungen bei 3D-Problemen, Theorie und Implementierung (1995)
• Matthias Teltscher: A posteriori Fehlerschätzer für elektromagnetische Kopplungsprobleme in drei Dimensionen (2002)
• Stephan Oestmann: Fehlerkontrollierte adaptive FEM-BEM Kopplungsmethoden und Anwendungen (2005)
• Alexey Chernov: Nonconforming boundary elements and finite elements for interface and contact problems with friction - hp-version for mortar, penalty and Nitsche's methods (2006)
• Florian Leydecker: hp-version of the boundary element method for electromagnetic problems - error analysis, adaptivity, preconditioners (2006)
• Sergey Geyn: FEM-BEM procedures for elastoplastic, thermo-viscoplastic contact problems (2007)

Diploma and Master theses

• L. Doniga-Crivat: Kopplung von Randelementen und finiten Elementen für viskoplastische Probleme (2005)
• E. Ostermann: Diskretisierung zeitabhängiger Kontaktprobleme in der Viskoelastiziät (2005)
• E. Röhrich: Helmholz Multiskalen/Multigrid (2006)
• M. Andres: Finite Elemente und Dirichlet-zu-Neumann Abbildung mit Anwendungen in der Mechanik (2006)
• M. Ludwig: BEM für elastodynamische Problem (2007)
• V. Likhodzievski: Gebietszerlegung mit nichtpassenden Gittern, Erweiterte Lagrange-Methode (2007)