Jürgen Dölz

Dr. Jürgen Dölz

Dolivostraße 15
64293 Darmstadt

Raum: S4|10 103

+49 6151 16-23162


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Independent DAMS-PostDoc within the group Numerical Analysis and Scientific Computing.

Research Interests

  • Numerical Solution of PDE
  • Uncertainty Quantification of PDE with Random Input Data
  • Fast Treatment of non-local Operators
  • Isogeometric Analysis
  • Numerical Methods for Maxwell's Equations

Preprints

  1. J. Dölz. A higher order perturbation approach for electromagnetic scattering problems on random domains. arXiv:1907.05501.
  2. J. Dölz, H. Harbrecht, S. Kurz, M.D. Multerer, S. Schöps, and F. Wolf. Bembel: The fast isogeometric boundary element C++ library for Laplace, Helmholtz, and electric wave equation. arXiv:1906.00785.

Publications

  1. A. Buffa, J. Dölz, S. Kurz, S. Schöps, R. Vázques and F. Wolf. Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis, 2018 (to appear in Numer. Math.).
  2. J. Dölz, S. Kurz, S. Schöps and F. Wolf. A Numerical Comparison of an Isogeometric and a Classical Higher-Order Approach to the Electric Field Integral Equation, 2018 (to appear in IEEE Transactions on Antennas and Propagation).
  3. J. Dölz, S. Kurz, S. Schöps and F. Wolf. Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples. SIAM J. Sci. Comput. 41 (5), B983-B1010, 2019.
  4. J. Dölz and T. Gerig, M. Lüthi, H. Harbrecht and T. Vetter. Error-Controlled Model Approximation for Gaussian Process Morphable Models. Journal of Mathematical Imaging and Vision, 61(4), 443–457, 2019.
  5. J. Dölz, H. Harbrecht and M.D. Multerer. On the best approximation of the hierarchical matrix product. SIAM J. Matrix Anal. Appl., 40(1), 147–174, 2019.
  6. J. Dölz and H. Harbrecht. Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains. J. Comput. Phys., 371:506-527, 2018.
  7. J. Dölz, H. Harbrecht, S. Kurz, S. Schöps, and F. Wolf. A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems. Comput. Methods Appl. Mech. Engrg., 330:83-101, 2018.
  8. J. Dölz, H. Harbrecht, and M. Peters. H-matrix based second moment analysis for rough random fields and finite element discretizations. SIAM J. Sci. Comput., 39(4):B618-B639, 2017.
  9. J. Dölz, H. Harbrecht, and C. Schwab. Covariance regularity and H-matrix approximation for rough random fields. Numer. Math., 135(4):1045-1071, 2017.
  10. J. Dölz, H. Harbrecht, and M. Peters. An interpolation-based fast multipole method for higher order boundary elements on parametric surfaces. Int. J. Numer. Meth. Eng., 108(13):1705-1728, 2016.
  11. J. Dölz, H. Harbrecht, and M. Peters. H-matrix accelerated second moment analysis for potentials with rough correlation. J. Sci. Comput., 65(1):387-410, 2015.

Thesis

J. Dölz. Hierarchical matrix techniques for partial differential equations with random input data. 2017, Doctoral Thesis, University of Basel, Faculty of Science.

Software

We made our higher-order/isogeometric boundary element code with H2-compression available as open source. You can download it here.

Projects

1.10.2017 – 30.9.2018: Early Postdoc.Mobility, project 174987 from the Swiss National Science Foundation.

Teaching

At Darmstadt
  • WS19/20: Computational Inverse Problems (Lecturer, together with H. Egger)
  • SS19: Numerische Lineare Algebra (Lecturer)
  • WS18/19: Seminar: Nonstandard Finite Element Methods
At Basel
  • FS17: Seminar: Methoden des Computer Aided Designs
  • HS16: Numerik der Differentialgleichungen
  • FS16: Nichtkonforme und gemischte Finite-Element-Methoden
  • HS15: Numerik der partiellen Differentialgleichungen
  • FS15: Einführung in die Numerik
  • HS14: Numerik der Differentialgleichungen
  • FS14: Praktikum II
  • HS13: Praktikum I
  • FS13: Lineare Algebra II
  • HS12: Reelle Analysis
  • FS12: Mathematische Methoden 4
  • HS11: Mathematische Methoden 3