Hochschule Würzburg-Schweinfurt

Kai Diethelm

Anschrift:

Leistungsprofil:

• Numerische Mathematik
• Approximationstheorie
• Differentialgleichungen
• Integralgleichungen
• Hochleistungsrechnen, Parallele Algorithmen

• Advanced Soft Tissue Modeling for Telemedicine and Surgical Simulation (Partner: NASA Glenn Research Center und Cleveland Clinic) Skalierbare Infrastruktur zur automatischen Leistungsanalyse paralleler Codes (Partner: TU Dresden, RWTH Aachen, TU München, FZ Jülich) Leistungsdynamik massiv-paralleler Codes (Partner: TU Dresden, RWTH Aachen, TU München, FZ Jülich, German Research School for Simulation Sciences Aachen) Skalierbare Werkzeuge zur Energieanalyse und -optimierung im Höchstleistungsrechnen (Partner: TU Dresden, RWTH Aachen, TU München, FZ Jülich, German Research School for Simulation Sciences Aachen, TU Darmstadt) Automatisierung der Netzgenerierung mit Hilfe von auf geometrischen Eigenschaften basierenden Trajektorien (Partner: Beuth-Hochschule Berlin) Merkmalsbasierte Diskretisierung von Geometrien für Finite-Elemente-Berechnungen (Partner: Beuth-Hochschule Berlin) Run-time Exploitation of Application Dynamism for Energy Efficient Exascale Computing (Partner: TU Dresden, TU München, Irish Center for High-End Computing Dublin, Intel France, NTNU Trondheim, IT4Innovations Ostrava) Mittelflächengenerierung für Finite-Elemente-Berechnungen (Partner: Beuth-Hochschule Berlin) Prognosewerkzeuge für das mechanische Verhalten von Beton über lange Zeiträume zur Sicherheitsanalyse von Verschlusssystemen für Endlagerstätten (Partner: Universität Stuttgart) Advanced Numerical Investigations of the Long-Term Behaviour of the Solutions to Fractional Differential Equations (Partner: Mehran University of Engineering and Technology, Pakistan)

Publikationen:

• The Analysis of Fractional Differential Equations — An application-oriented exposition using differential operators of Caputo type. Springer, Berlin (2010), viii+247 pp., ISBN 978-3-642-14573-5. (mit D. Baleanu, E. Scalas and J. J. Trujillo) Fractional Calculus — Models and numerical methods. First edition, World Scientific Publ. Comp., Singapore (2012), xxiv+400 pp., ISBN 978-981-4355-20-9. Second edition, World Scientific Publ. Comp., Singapore (2016), xxviii+448 pp., ISBN 978-981-3140-03-5. Gemeinschaftliches Entscheiden — Untersuchung von Entscheidungsverfahren mit mathematischen Hilfsmitteln. Springer, Berlin (2016), ix+138 pp., ISBN 978-3-662-48779-2.
• Modified Compound Quadrature Rules for Strongly Singular Integrals. Computing 52 (1994), 337-354. Non-Optimality of Certain Quadrature Rules for Cauchy Principal Value Integrals. Z. Angew. Math. Mech. 74 (1994), T689-T690. Uniform Convergence of Optimal Order Quadrature Rules for Cauchy Principal Value Integrals. J. Comput. Appl. Math. 56 (1994), 321-329. Error Estimates for a Quadrature Rule for Cauchy Principal Value Integrals. Proc. Sympos. Appl. Math. 48 (1994), 287-291. The Order of Convergence of Modified Interpolatory Quadratures for Singular Integrals of Cauchy Type. Z. Angew. Math. Mech. 75 (1995), S621-S622. Gaussian Quadrature Formulae of the Third Kind for Cauchy Principal Value Integrals: Basic Properties and Error Estimates. J. Comput. Appl. Math. 65 (1995), 97-114. Asymptotically Sharp Error Bounds for a Quadrature Rule for Cauchy Principal Value Integrals Based on Piecewise Linear Interpolation. Approx. Theory Appl. (N. S.) 11 (1995), No. 4, 78-89. Peano Kernels and Bounds for the Error Constants of Gaussian and Related Quadrature Rules for Cauchy Principal Value Integrals. Numer. Math. 73 (1996), 53-63. A Definiteness Criterion for Linear Functionals and its Application to Cauchy Principal Value Quadrature. J. Comput. Appl. Math. 66 (1996), 167-176. Error Bounds for Compound Quadratures for Hadamard-Type Finite-Part Integrals. In G. Alefeld, J. Herzberger (Eds.): Numerical Methods and Error Bounds. Akademie-Verlag, Berlin (1996), 58-63. Definite Quadrature Formulae for Cauchy Principal Value Integrals. Bolyai Soc. Math. Stud. 5 (1996), 175-186. An Algorithm for the Numerical Solution of Differential Equations of Fractional Order. Elec. Transact. Numer. Anal. 5 (1997), 1-6. Generalized Compound Quadrature Formulae for Finite-Part Integrals. IMA J. Numer. Anal. 17 (1997), 479-493. Peano Kernels of Non-Integer Order. Z. Anal. Anwendungen 16 (1997), 727-738. New Error Bounds for Modified Quadrature Formulas for Cauchy Principal Value Integrals. J. Comput. Appl. Math. 82 (1997), 93-104. A Fractional Version of the Peano-Sard Theorem. Numer. Funct. Anal. Optim. 18 (1997), 745-757. (mit G. Walz) Numerical Solution of Fractional Order Differential Equations by Extrapolation. Numer. Algorithms 16 (1997), 231-253. Error Bounds for Spline-Based Quadrature Methods for Strongly Singular Integrals. J. Comput. Appl. Math. 89 (1998), 257-261. Erratum: J. Comput. Appl. Math. 142 (2002), 449-450. Fractional Error Constants for Quadrature Formulas. In C. K. Chui, L. L. Schumaker (eds.): Approximation Theory IX, Vol. 1. Vanderbilt University Press, Nashville, TN (1998), 113-118. Existence and Construction of Definite Estimation Functionals. Studia Sci. Math. Hungar. 35 (1999), 217-236. (mit A. D. Freed) On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity. In F. Keil, W. Mackens, H. Voß, J. Werther (eds.): Scientific Computing in Chemical Engineering II. Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties. Springer-Verlag, Heidelberg (1999), 217-224. (mit S. B. Damelin) Interpolatory Product Quadratures for Cauchy Principal Value Integrals with Freud Weights. Numer. Math. 83 (1999), 87-105. (mit A. D. Freed) The FracPECE Subroutine for the Numerical Solution of Differential Equations of Fractional Order. In S. Heinzel, T. Plesser (eds.): Forschung und wissenschaftliches Rechnen: Beiträge zum Heinz-Billing-Preis 1998. Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen (1999), 57-71. A Method for the Practical Evaluation of the Hilbert Transform on the Real Line. J. Comput. Appl. Math. 112 (1999), 45-53. Estimation of Quadrature Errors in Terms of Caputo-Type Fractional Derivatives. Fract. Calc. Appl. Anal. 2 (1999), 313-327. (mit P. Köhler) Asymptotic Behaviour of Fixed-Order Error Constants of Modified Quadrature Formulae for Cauchy Principal Value Integrals. J. Inequal. Appl. 5 (2000), 167-190. (mit K. Murawski) Randomly Generated Spectrum of the Solar f-Mode. Astronomy and Astrophysics 358 (2000), P 753-758. Two General Methods for the Numerical Approximation of Multidimensional Cauchy Principal Value Integrals. ANZIAM J. 42 (2000), E1-E26. (mit S. B. Damelin) Boundedness and Uniform Numerical Approximation of the Weighted Hilbert Transform on the Real Line. Numer. Funct. Anal. Optim. 22 (2001), 13-54. (mit N. J. Ford) Numerical Solution Methods for Distributed Order Differential Equations. Fract. Calc. Appl. Anal. 4 (2001), 531-542. (mit N. J. Ford) Analysis of Fractional Differential Equations. J. Math. Anal. Appl. 265 (2002), 229-248. (mit N. J. Ford und A. D. Freed) A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations. Nonlinear Dynamics 29 (2002), 3-22. (mit N. J. Ford) Numerical Solution of the Bagley-Torvik Equation. BIT 42 (2002), 490-507. Predictor-Corrector Strategies for Single- and Multi-Term Fractional Differential Equations. In E. A. Lipitakis (ed.): Proceedings of the 5th Hellenic-European Conference on Computer Mathematics and its Applications. LEA Press, Athens (2002), 117-122. Efficient Solution of Multi-Term Fractional Differential Equations using P(EC)mE methods. Computing 71 (2003), 305-319. (mit M. Weilbeer) A Numerical Approach for Joulin’s Model of a Point Source Initiated Flame. Fract. Calc. Appl. Anal. 7 (2004), 191-212. (mit N. J. Ford und A. D. Freed) Detailed Error Analysis for a Fractional Adams Method. Numer. Algorithms 36 (2004), 31-52. Monotonicity Results for a Compound Quadrature Method for Finite-Part Integrals. J. Inequal. Pure Appl. Math. 5 (2004), article 44. (mit N. J. Ford) Multi-Order Fractional Differential Equations and Their Numerical Solution. Appl. Math. Comput. 154 (2004), 621-640. (mit M. Weilbeer) Initial-Boundary Value Problems for Time-Fractional Diffusion-Wave Equations and Their Numerical Solution. In A. Le Méhauté, J. A. Tenreiro Machado, J. C. Trigeassou, J. Sabatier (Eds.): Proceedings of the 1st IFAC Workshop on Fractional Differentiation and its Applications. ENSEIRB, Bordeaux (2004), 551-557. (mit S. B. Damelin) Numerical Approximation and Stability of Singular Integral Equations for Freud Exponential Weights on the Line. J. Integral Equations Appl. 16 (2004), 273-292. A Note on the Midpoint Rectangle Formula for Riemann-Stieltjes Integrals. J. Stat. Comput. Simulation 74 (2004), 920-922. (mit Y. Luchko) Numerical Solution of Linear Multi-Term Initial Value Problems of Fractional Order. J. Comput. Anal. Appl. 6 (2004), 243-263. (mit S. B. Damelin) Weighted Polynomial Approximation and Hilbert Transforms: Their Connections to the Numerical Solution of Singular Integral Equations. In Proceedings of the 4th International Conference on Dynamic Systems and Applications. Dynamic Publishers, Atlanta (2004), 20-26. (mit J. M. Ford, N. J. Ford und M. Weilbeer) A Comparison of Backward Differentiation Approaches for Ordinary and Partial Differential Equations of Fractional Order. In A. Le Méhauté, J. A. Tenreiro Machado, J. C. Trigeassou, J. Sabatier (Eds.): Fractional Differentiation and its Applications. Ubooks, Neusäß (2005), 557-569. (mit A. D. Freed) Tensor Fields for Use in Fractional-Order Viscoelasticity. In A. Le Méhauté, J. A. Tenreiro Machado, J. C. Trigeassou, J. Sabatier (Eds.): Fractional Differentiation and its Applications. Ubooks, Neusäß (2005), 169-182. (mit N. J. Ford, A. D. Freed und Y. Luchko) Algorithms for the Fractional Calculus: A Selection of Numerical Methods. Comput. Methods Appl. Mech. Eng. 194 (2005), 743-773. (mit K. Radtke) Rückfederungsberechnung mit INDEED. In K. Pöhlandt (Ed.): 8. Workshop über Simulation in der Umformtechnik. Universität Stuttgart (2005), Paper 2.7. (mit A. D. Freed) An Efficient Algorithm for the Evaluation of Convolution Integrals. Computers Math. Applic., 51 (2006), 51-72. (mit A. D. Freed) Fractional Calculus in Biomechanics: A 3D Viscoelastic Model Using Regularized Fractional-Derivative Kernels with Application to the Human Calcaneal Fat Pad. Biomechanics and Modeling in Mechanobiology, 5 (2006), 203-215. (mit J. M. Ford, N. J. Ford und M. Weilbeer) Pitfalls in Fast Numerical Solvers for Fractional Differential Equations. J. Comput. Appl. Math. 186 (2006), 482-503. Smoothness Properties of Solutions of Caputo-type Fractional Differential Equations. Fract. Calc. Appl. Anal. 10 (2007), 151-160. (mit A. D. Freed) Caputo Derivatives in Viscoelasticity: A Non-linear Finite-deformation Theory for Tissue. Fract. Calc. Appl. Anal. 10 (2007), 219-248. An Investigation of Some Nonclassical Methods for the Numerical Approximation of Caputo-Type Fractional Derivatives. Numer. Algorithms 47 (2008), 361-390. Multi-Term Fractional Differential Equations, Multi-Order Fractional Differential Systems and Their Numerical Solution. J. Europ. Syst. Autom. 42 (2008), 665-676. On the Separation of Solutions of Fractional Differential Equations. Fract. Calc. Appl. Anal. 11 (2008), 259-268. (mit N. J. Ford) Numerical Analysis for Distributed-Order Differential Equations. J. Comput. Appl. Math. 225 (2009), 96-104. An Improvement of a Nonclassical Numerical Method for the Computation of Fractional Derivatives. J. Vibration Acoustics 131 (2009), article 014502. (mit K. Kassem-Manthey, F. Thilo und M. Grauer) On the Application of Computational Optimization Methods to Increase the Efficiency of Metal Forming Processes. Proceedings of the IVth European Conference on Computational Mechanics. Paris (2010), Paper 937. (mit M.-F. Danca) Fractional-Order Attractors Synthesis via Parameter Switchings. Commun. Nonlinear Sci. Numer. Simul. 15 (2010), 3745-3753. An Efficient Parallel Algorithm for the Numerical Solution of Fractional Differential Equations. Fract. Calc. Appl. Anal. 14 (2011), 475-490. (mit D. an Mey, S. Biersdorf, C. Bischof, D. Eschweiler, M. Gerndt, A. Knüpfer, D. Lorenz, A. Malony, W. E. Nagel, Y. Oleynik, C. Rössel, P. Saviankou, D. Schmidl, S. Shende, M. Wagner, B. Wesarg und F. Wolf) Score-P — A Unified Performance Measurement System for Petascale Applications. In C. Bischof, H.-G. Hegering, W. E. Nagel and G. Wittum (Eds.): Competence in High Performance Computing 2010. Springer, Heidelberg (2012), 85-97. The Limits of Reproducibility in Numerical Simulation. Computing in Science & Engineering 14 (2012), No. 1, 64-71. (with N. J. Ford) Volterra Integral Equations and Fractional Calculus: Do Neighboring Solutions Intersect? J. Integral Equations Appl. 24 (2012), 25-37. The Mean Value Theorems and a Nagumo-Type Uniqueness Theorem for Caputo’s Fractional Calculus. Fract. Calc. Appl. Anal. 15 (2012), 304-313. Erratum: Fract. Calc. Appl. Anal. 20 (2017), 1567-1570. (mit A. Knüpfer, C. Rössel, D. an Mey, S. Biersdorf, D. Eschweiler, M. Geimer, M. Gerndt, D. Lorenz, A. Malony, W. E. Nagel, Y. Oleynik, P. Philippen, P. Saviankou, D. Schmidl, S. Shende, R. Tschüter, M. Wagner, B. Wesarg und F. Wolf) Score-P — A joint performance measurement run-time infrastructure for Periscope, Scalasca, TAU, and Vampir. In H. Brunst, M. Müller, W. E. Nagel, M. M. Resch (Eds.): Tools for High Performance Computing 2011. Springer, Heidelberg (2012), 79-91. A Fractional Calculus Based Model for the Simulation of an Outbreak of Dengue Fever. Nonlinear Dynamics 71 (2013), 613-619. Error Bounds for the Numerical Integration of Functions with Limited Smoothness. SIAM J. Numer. Anal. 52 (2014), 877-879. An Extension of the Well-Posedness Concept for Fractional Differential Equations of Caputo’s Type. Applicable Analysis 93 (2014), 2126-2135. Increasing the Efficiency of Shooting Methods for Terminal Value Problems of Fractional Order. J. Comput. Phys. 293 (2015), 135-141. Monotonicity of Functions and Sign Changes of Their Caputo Derivatives. Fract. Calc. Appl. Anal. 19 (2016), 561-566. Properties of the Solutions to “Fractionalized” ODE Systems, with Applications to Processes Arising in the Life Sciences. In D. T. Spasic, N. Grahovac, M. Zigic, M. Rapaic, T. M. Atanackovic (Eds.): Proceedings of the International Conference on Fractional Differentiation and its Applications 2016, Vol.1. Faculty of Technical Sciences, Novi Sad (2016), 32-44. Tools for Assessing and Optimizing the Energy Requirements of High Performance Scientific Computing Software. Proc. Appl. Math. Mech. 16 (2016), 837-838. (mit J. Schuchart, M. Gerndt, P. G. Kjeldsberg, M. Lysaght, D. Horák, L. Ríha, A. Gocht, M. Sourouri, M. Kumaraswamy, A. Chowdhury, M. Jahre, O. Bouizi, U. S. Mian, J. Kruzík, R. Sojka, M. Beseda, V. Kannan, Z. Bendifallah, D. Hackenberg und W. E. Nagel) The READEX Formalism for Automatic Tuning for Energy Efficiency. Computing 99 (2017), 727-745. (mit S. Siegmund und H. T. Tuan) Asymptotic behavior of solutions of linear multi-order fractional differential equation systems. Fract. Calc. Appl. Anal. 20 (2017), 1165-1195. (mit N. J. Ford) A Note on the Well-posedness of Terminal Value Problems for Fractional Differential Equations. J. Integral Equations Appl. 30 (2018), 371-376. Numerical Methods for the Fractional Differential Equations of Viscoelasticity. In H. Altenbach, A. Öchsner (Eds.): Encyclopedia of Continuum Mechanics. Springer, Berlin, 2018.

Kooperationsangebot für die Wirtschaft / Praxis:

• Portugiesische Stiftung für Forschung und Technologie, 2009-2013