Research Group of Prof. Dr. Daniel Peterseim

Mr. Peterseim is now at University of Augsburg. This page is no longer maintained.

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Teaching

Winter semester 2016/17

Summer semester 2016

See teaching activities of the whole group.

Completed Research Projects

Adaptive isogeometric modeling of propagating strong discontinuities in heterogeneous materials

DFG Priority Programme 1748.

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Multi-material lightweight designs and smart devices with characteristic microscopic material structures are the key features for the development of innovative products. In this context, an adaptive isogeometric framework for the modeling and simulation of crack propagation in heterogeneous materials is to be developed, implemented, and mathematically analyzed in this project. The mechanical modeling of interface failure will be based on increasing knot multiplicities driven by cohesive zone models for crack propagation along material interfaces. In addition, a phase-field model will account for propagating cracks in the bulk material including interaction phenomena such as crack branching and coalescence. The spline-based discretization used offers higher efficiency compared to Lagrangian polynomials, control of regularity, accurate approximation of strong gradients in the phase-field order parameter, as well as the possibility to discretize higher-order phase-field equations. Local mesh adaptivity required for the resolution of material interfaces and the phase-field variables will be provided by T-splines as well as hierarchical spline approximations. In addition to the physical modeling, open mathematical problems include a practicable characterization of T-meshes suitable for IGA in 3D and clear understanding of the role of increased regularity in the approximation.

See all projects of the group.

Publications

  1. On the stability of the Rayleigh-Ritz method for eigenvalues. D. Gallistl, P. Huber, and D. Peterseim. Accepted for publication in Numerische Mathematik. Available as INS Preprint No. 1527, 2017. BibTeX PDF
  2. Numerical stochastic homogenization by quasi-local effective diffusion tensors. D. Gallistl and D. Peterseim. INS Preprint No. 1701, 2017. BibTeX PDF arXiv
  3. Relaxing the CFL condition for the wave equation on adaptive meshes. D. Peterseim and M. Schedensack. J. Sci. Comput., 2017. Online First. BibTeX PDF DOI arXiv
  4. Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison. P. Hennig, M. Kästner, P. Morgenstern, and D. Peterseim. Comp. Meth. Appl. Mech. Eng., 316:424––448, 2017. BibTeX PDF DOI arXiv
  5. Generalized finite element methods for quadratic eigenvalue problems. A. Målqvist and D. Peterseim. ESAIM Math. Model. Numer. Anal., 51(1):147–163, 2017. BibTeX PDF DOI arXiv
  6. Eliminating the pollution effect in Helmholtz problems by local subscale correction. D. Peterseim. Math. Comp., 86:1005–1036, 2017. BibTeX PDF DOI arXiv
  7. Towards adaptive discontinuous petrov-galerkin methods. P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, and J. Storn. PAMM, 16(1):741–742, 2016. BibTeX DOI
  8. Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations. D. Brown, D. Gallistl, and D. Peterseim. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, Lecture Notes in Computational Science and Engineering. 2016. BibTeX PDF arXiv
  9. Complexity of hierarchical refinement for a class of admissible mesh configurations. A. Buffa, C. Giannelli, P. Morgenstern, and D. Peterseim. Computer Aided Geometric Design, 47:83–92, 2016. BibTeX PDF DOI
  10. Computation of local and quasi-local effective diffusion tensors in elliptic homogenization. D. Gallistl and D. Peterseim. INS Preprint No. 1619, 2016. BibTeX PDF arXiv
  11. Multiscale petrov-galerkin fem for acoustic scattering. D. Gallistl, D. Peterseim, and C. Carstensen. PAMM, 16(1):745–746, 2016. BibTeX DOI
  12. Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with disorder potentials. P. Henning and D. Peterseim. INS Preprint No. 1621, 2016. BibTeX PDF
  13. An analysis of a class of variational multiscale methods based on subspace decomposition. R. Kornhuber, D. Peterseim, and H. Yserentant. Submitted for publication, November 2016. BibTeX
  14. Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d. G. Li, D. Peterseim, and M. Schedensack. ArXiv e-prints, 2016. Also available as INS Preprint No. 1612. BibTeX PDF arXiv
  15. Computational Multiscale Methods for Partial Differential Equations. D. Peterseim. Habilitation thesis, Humboldt-Universität zu Berlin, 2016. BibTeX PDF
  16. Robust numerical upscaling of elliptic multiscale problems at high contrast. D. Peterseim and R. Scheichl. Computational Methods in Applied Mathematics, 16:579–603, 2016. BibTeX PDF DOI arXiv
  17. Variational multiscale stabilization and the exponential decay of fine-scale correctors. D. Peterseim. In G. R. Barrenechea, F. Brezzi, A. Cangiani, and E. H. Georgoulis, editors, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, volume 114 of Lecture Notes in Computational Science and Engineering. Springer, may 2016. BibTeX PDF arXiv
  18. Relaxing the CFL condition for the wave equation on adaptive meshes. D. Peterseim and M. Schedensack. PAMM, 16(1):765–766, 2016. BibTeX DOI
  19. A multiscale method for porous microstructures. D. Brown and D. Peterseim. SIAM MMS, 14:1123–1152, 2016. BibTeX PDF arXiv
  20. Efficient implementation of the Localized Orthogonal Decomposition method. C. Engwer, P. Henning, A. Målqvist, and D. Peterseim. ArXiv e-prints, feb 2016. BibTeX arXiv
  21. Comparison results for the Stokes equations. C. Carstensen, K. Köhler, D. Peterseim, and M. Schedensack. Appl. Numer. Math., 95:118–129, 2015. BibTeX DOI arXiv
  22. The norm of a discretized gradient in H(div)∗{H}(div)^* for a posteriori finite element error analysis. C. Carstensen, D. Peterseim, and A. Schröder. Numer. Math., 132(3):519–539, 2015. BibTeX DOI
  23. Simulation of composite materials by a network fem with error control. M. Eigel and D. Peterseim. Computational Methods in Applied Mathematics (online), 15(1):21–37, 2015. BibTeX DOI
  24. Multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering. D. Gallistl and D. Peterseim. Oberwolfach Reports, 12(3):2580–2581, 2015. BibTeX
  25. Multiscale partition of unity. P. Henning, P. Morgenstern, and D. Peterseim. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, volume 100 of Lecture Notes in Computational Science and Engineering, pages 185–204. Springer International Publishing, 2015. BibTeX PDF DOI
  26. Analysis-suitable adaptive T-mesh refinement with linear complexity. P. Morgenstern and D. Peterseim. Computer Aided Geometric Design, 34:50–66, 2015. Also available as INS Preprint No. 1409. BibTeX PDF DOI
  27. Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering. D. Gallistl and D. Peterseim. Comp. Meth. Appl. Mech. Eng., 295:1–17, march 2015. BibTeX PDF DOI arXiv
  28. Two-level discretization for the Gross-Pitaevskii eigenvalue problem with a rough potential. P. Henning, A. Målqvist, and D. Peterseim. to appear in Oberwolfach Rep., 2014. BibTeX DOI
  29. Two-level discretization techniques for ground state computations of bose-einstein condensates. P. Henning, A. Målqvist, and D. Peterseim. SIAM J. Numer. Anal., 52(4):1525–1550, 2014. BibTeX PDF DOI
  30. A localized orthogonal decomposition method for semi-linear elliptic problems. P. Henning, A. Målqvist, and D. Peterseim. ESAIM: Math. Model. Numer. Anal., 48(05):1331–1349, 2014. BibTeX DOI
  31. Multiscale techniques for solving quadratic eigenvalue problems. A. Målqvist and D. Peterseim. to appear in Oberwolfach Rep., 2014. BibTeX DOI
  32. Computation of eigenvalues by numerical upscaling. A. Målqvist and D. Peterseim. Numer. Math., 130(2):337–361, 2014. BibTeX DOI arXiv
  33. Localization of elliptic multiscale problems. A. Målqvist and D. Peterseim. Math. Comp., 83(290):2583–2603, 2014. BibTeX DOI
  34. Composite finite elements for elliptic interface problems. D. Peterseim. Math. Comp., 83(290):2657–2674, 2014. BibTeX DOI
  35. Optimal adaptive nonconforming FEM for the Stokes problem. C. Carstensen, D. Peterseim, and H. Rabus. Numer. Math., 123(2):291–308, 2013. BibTeX DOI
  36. Oversampling for the multiscale finite element method. P. Henning and D. Peterseim. Multiscale Model. Simul., 11(4):1149–1175, 2013. BibTeX PDF DOI
  37. Numerical upscaling of eigenvalue problems. A. Målqvist and D. Peterseim. Oberwolfach Rep., 10(1):402–405, 2013. BibTeX DOI
  38. Spectrum-preserving two-scale decompositions with applications to numerical homogenization and eigensolvers. D. Peterseim and A. Målqvist. Oberwolfach Rep., 10(1):850–853, 2013. BibTeX DOI
  39. Finite element network approximation of conductivity in particle composites. D. Peterseim and C. Carstensen. Numer. Math., 124(1):73–97, 2013. BibTeX DOI
  40. Convergence of a discontinuous galerkin multiscale method. D. Elfverson, E. H. Georgoulis, A. Målqvist, and D. Peterseim. SIAM J. Numer. Anal., 51(6):3351–3372, 2013. BibTeX PDF DOI
  41. Comparison results of finite element methods for the Poisson model problem. C. Carstensen, D. Peterseim, and M. Schedensack. SIAM J. Numer. Anal., 50(6):2803–2823, 2012. BibTeX PDF DOI
  42. Finite element discretization of multiscale elliptic problems. A. Målqvist and D. Peterseim. Oberwolfach Rep., 9(1):516–519, 2012. BibTeX DOI
  43. Comparison of finite element methods for the Poisson model problem. D. Peterseim, C. Carstensen, and M. Schedensack. Oberwolfach Rep., 9(1):584–587, 2012. BibTeX DOI
  44. Finite Elements for Elliptic Problems with Highly Varying, Nonperiodic Diffusion Matrix. D. Peterseim and S. Sauter. Multiscale Model. Simul., 10(3):665–695, 2012. BibTeX PDF DOI
  45. Robustness of Finite Element Simulations in Densely Packed Random Particle Composites. D. Peterseim. Netw. Heterog. Media, 2012. BibTeX PDF DOI
  46. Comparison results for first-order FEMs. M. Schedensack, C. Carstensen, and D. Peterseim. Oberwolfach Rep., 9(1):495–497, 2012. BibTeX DOI
  47. Parallel multistep methods for linear evolution problems. L. Banjai and D. Peterseim. IMA J. Numer. Anal., 32(3):1217–1240, 2011. BibTeX DOI
  48. Finite element methods for the Stokes problem on complicated domains. D. Peterseim and S. A. Sauter. Comp. Meth. Appl. Mech. Eng., 200(33-36):2611–2623, 2011. BibTeX DOI
  49. Composite finite elements for elliptic interface problems. D. Peterseim. PAMM, 10(1):661–664, 2010. BibTeX DOI
  50. Generalized delaunay partitions and composite material modeling. D. Peterseim. Matheon Preprint, 2010. BibTeX Publisher
  51. Triangulating a system of disks. D. Peterseim. Proc. 26th European Workshop on Computational Geometry (EWCG), pages 241–244, 2010. BibTeX Publisher
  52. Finite element analysis of particle-reinforced composites. D. Peterseim. Oberwolfach Rep., 6(2):1597–1665, 2009. BibTeX DOI
  53. Recent advances in composite finite elements. D. Peterseim and S. A. Sauter. Oberwolfach Rep., 5(2):1233–1293, 2008. BibTeX DOI
  54. The composite mini element – coarse mesh computation of Stokes flows on complicated domains. D. Peterseim and S. A. Sauter. SIAM J. Numer. Anal., 46(6):3181–3206, 2008. BibTeX DOI Link
  55. The Composite Mini Element: A mixed FEM for the Stokes equations on complicated domains. D. Peterseim. PhD thesis, Universität Zürich, 2007. BibTeX
  56. The composite mini element: a new mixed FEM for the Stokes equations on complicated domains. D. Peterseim and S. A. Sauter. PAMM, 7(1):2020101–2020102, 2007. BibTeX DOI
  57. Numerische Analyse parameterabhängiger periodischer Orbits nichtlinearer dynamischer Systeme mittels Mehrzielmethode und effizienter Fortsetzungstechniken. D. Peterseim. Master's thesis, IfMath, TU Ilmenau, 2004. BibTeX