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Dirk Praetorius

Dirk Praetorius

D-Index & Metrics

Mathematics

D-Index
30
Citations
3283
World Ranking
3551
National Ranking
44

Overview

Dirk Praetorius is affiliated with TU Wien in Austria. Their research focuses primarily on the field of engineering, with a strong emphasis on computational mechanics and numerical analysis.

Their work spans multiple subfields of study, including:

  • Computational Mechanics
  • Computational Theory and Mathematics
  • Numerical Analysis
  • Mechanics of Materials
  • Electrical and Electronic Engineering

Praetorius's main research topics cover advanced numerical methods and mathematical modeling in engineering, concentrating on:

  • Advanced Numerical Methods in Computational Mathematics
  • Advanced Mathematical Modeling in Engineering
  • Numerical Methods for Differential Equations
  • Numerical Methods in Engineering
  • Electromagnetic Simulation and Numerical Methods
  • Magnetic Properties of Thin Films
  • Model Reduction and Neural Networks

Among their recent papers are:

  • "Magnetostatics and micromagnetics with physics informed neural networks," 2022, Journal of Magnetism and Magnetic Materials
  • "Dörfler marking with minimal cardinality is a linear complexity problem," 2020, Mathematics of Computation
  • "Rate optimality of adaptive finite element methods with respect to overall computational costs," 2021, Mathematics of Computation
  • "Mathematical Foundations of Adaptive Isogeometric Analysis," 2022, Archives of Computational Methods in Engineering
  • "Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver," 2021, Numerische Mathematik

Praetorius collaborates frequently with several researchers, including:

  • Michael Innerberger
  • Michele Ruggeri
  • Julian Streitberger
  • Maximilian Brunner
  • Gregor Gantner

Their publications are often found in venues such as:

  • arXiv (Cornell University)
  • Computational Methods in Applied Mathematics
  • Computers & Mathematics with Applications
  • Mathematics of Computation
  • Numerische Mathematik

Best Publications

  • Convergence of adaptive BEM for some mixed boundary value problem

    M. Aurada;S. Ferraz-Leite;P. Goldenits;M. Karkulik

  • Axioms of adaptivity

    C. Carstensen;M. Feischl;M. Page;D. Praetorius

  • Efficient implementation of adaptive P1-FEM in Matlab

    Stefan A. Funken;Dirk Praetorius;Philipp Wissgott

  • On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H 1-Stability of L 2-Projection

    Michael Karkulik;David Pavlicek;Dirk Praetorius

  • Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems

    Michael Feischl;Thomas Führer;Dirk Praetorius

  • Quasi-optimal convergence rate for an adaptive boundary element method

    Michael Feischl;Michael Karkulik;Jens Markus Melenk;Dirk Praetorius

  • Simple a posteriori error estimators for the h -version of the boundary element method

    S. Ferraz-Leite;D. Praetorius

  • Averaging Techniques for the Effective Numerical Solution of Symm's Integral Equation of the First Kind

    Carsten Carstensen;Dirk Praetorius

  • On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H1-Stability of L2-Projection

    Michael Karkulik;David Pavlicek;Dirk Praetorius

  • Estimator reduction and convergence of adaptive BEM

    Markus Aurada;Samuel Ferraz-Leite;Dirk Praetorius

  • Residual-based a posteriori error estimate for hypersingular equation on surfaces

    Carsten Carstensen;M. Maischak;D Praetorius;E. P. Stephan

  • Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity

    Markus Aurada;Michael Feischl;Thomas Führer;Michael Karkulik

  • Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods

    Markus Aurada;Michael Feischl;Thomas Führer;Michael Karkulik

  • A three-dimensional spin-diffusion model for micromagnetics.

    Claas Abert;Michele Ruggeri;Florian Bruckner;Christoph Vogler

  • Magnetostatics and micromagnetics with physics informed neural networks.

    Alexander Kovacs;Lukas Exl;Alexander Kornell;Johann Fischbacher

  • Energy norm based a posteriori error estimation for boundary element methods in two dimensions

    C. Erath;S. Ferraz-Leite;S. Funken;D. Praetorius

  • Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems

    Alex Bespalov;Alexander Haberl;Dirk Praetorius

  • Adaptive FEM with optimal convergence rates for a certain class of non-symmetric and possibly non-linear problems

    Michael Feischl;Thomas Führer;Dirk Praetorius

  • An abstract analysis of optimal goal-oriented adaptivity

    Michael Feischl;Dirk Praetorius;Kristoffer George van der Zee

  • Energy norm based error estimators for adaptive BEM for hypersingular integral equations

    Markus Aurada;Michael Feischl;Thomas Führer;Michael Karkulik

  • Spin-polarized transport in ferromagnetic multilayers: An unconditionally convergent FEM integrator.

    Claas Abert;Gino Hrkac;Marcus Page;Dirk Praetorius

  • Dörfler marking with minimal cardinality is a linear complexity problem

    Carl-Martin Pfeiler;Dirk Praetorius

  • Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations.

    Michael Feischl;Gregor Gantner;Dirk Praetorius

  • Rate optimal adaptive FEM with inexact solver for nonlinear operators

    Gregor Gantner;Alexander Haberl;Dirk Praetorius;Bernhard Stiftner

  • 3D FEM-BEM-Coupling Method to solve Magnetostatic Maxwell Equations

    Florian Bruckner;Christoph Vogler;Michael Feischl;Dirk Praetorius

  • Convergence of simple adaptive Galerkin schemes based on h − h /2 error estimators

    S. Ferraz-Leite;C. Ortner;D. Praetorius

  • Residual-based a posteriori error estimate for hypersingular equation on surfaces Dedicated to W. L. Wendland on the occasion of his 65th birthday

    Carsten Carstensen;M. Maischak;D. Praetorius;E. P. Stephan

Frequent Co-Authors

Carsten Carstensen
Carsten Carstensen Humboldt-Universität zu Berlin
Ernst P. Stephan
Ernst P. Stephan University of Hannover
Christoph Ortner
Christoph Ortner University of Warwick
Annalisa Buffa
Annalisa Buffa École Polytechnique Fédérale de Lausanne
Martin Vohralík
Martin Vohralík French Institute for Research in Computer Science and Automation - INRIA
Barbara Wohlmuth
Barbara Wohlmuth Technical University of Munich
Stefan Katzenbeisser
Stefan Katzenbeisser University of Passau
Roy W. Chantrell
Roy W. Chantrell University of York

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