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ペーター・ドイフルハード

出典: フリー百科事典『ウィキペディア(Wikipedia)』

ペーター・ドイフルハード(Peter Deuflhard、1944年5月3日 - 2019年9月22日)は、ドイツの数学者。専門は、数値解析ニュートン法常微分方程式の数値解法偏微分方程式の数値解法に関する著書で知られている。

著書

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  • Deuflhard, P., & Hairer, E. (1983). Numerical treatment of inverse problems in differential and integral equations: proceedings of an international workshop, Heidelberg, Fed. Rep. of Germany, August 30-September 3, 1982 (Vol. 2). Birkhäuser.
  • Deuflhard, P., & Engquist, B. (1987). Large scale scientific computing. Birkhäuser.
  • Deuflhard, P., & Hohmann, A. (1995). Numerical Analysis: A First Course in Scientific Computation. Walter de Gruyter & Co.
  • Deuflhard, P., & Hohmann, A. (2003). Numerical analysis in modern scientific computing: an introduction. New York: Springer.
  • Deuflhard, P., & Bornemann, F., Scientific computing with ordinary differential equations. en:Springer Science & Business Media.
  • Deuflhard, P. (2011). Newton methods for nonlinear problems: affine invariance and adaptive algorithms. en:Springer Science & Business Media.
  • Deuflhard, P., & Weiser, M. (2012). Adaptive numerical solution of PDEs. Walter de Gruyter.

代表的な論文

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単著

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  • A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting, P Deuflhard - en:Numerische Mathematik, 1974.
  • Deuflhard, P. (1979). A stepsize control for continuation methods and its special application to multiple shooting techniques. en:Numerische Mathematik, 33(2), 115-146.
  • Deuflhard, P. (1979). A study of extrapolation methods based on multistep schemes without parasitic solutions. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 30(2), 177-189.
  • Order and stepsize control in extrapolation methods, P Deuflhard - Numerische Mathematik, 1983.
  • Recent progress in extrapolation methods for ordinary differential equations, P Deuflhard - SIAM review, 1985.
  • Deuflhard, P. (1991). Global inexact Newton methods for very large scale nonlinear problems. IMPACT of Computing in Science and Engineering, 3(4), 366-393.
  • Deuflhard, P. (1994). Cascadic conjugate gradient methods for elliptic partial differential equations: algorithm and numerical results. Contemporary Mathematics, 180, 29-29.
  • Deuflhard, P. (2012). A short history of Newton’s method. Documenta Mathematica, Optimization stories, 25-30.

共著

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1970年代

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  • Deuflhard, P., Pesch, H. J., & Rentrop, P. (1976). A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques. en:Numerische Mathematik, 26(3), 327-343.
  • Affine invariant convergence theorems for Newton’s method and extensions to related methods, P Deuflhard, G Heindl - en:SIAM Journal on Numerical Analysis, 1979.

1980年代

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  • A semi-implicit mid-point rule for stiff systems of ordinary differential equations, G Bader, P Deuflhard - en:Numerische Mathematik, 1983.
  • A semi-implicit mid-point rule for stiff systems of ordinary differential equations, G Bader, P Deuflhard - en:Numerische Mathematik, 1983.
  • One-step and extrapolation methods for differential-algebraic systems, P Deuflhard, E Hairer, J Zugck - en:Numerische Mathematik, 1987.
  • Concepts of an adaptive hierarchical finite element code, P Deuflhard, P Leinen, H Yserentant - IMPACT of Computing in Science and Engineering, 1989.

1990年代

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  • Deuflhard, P., & Potra, F. A. (1992). Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem. en:SIAM Journal on Numerical Analysis, 29(5), 1395-1412.
  • Schmidt, F., & Deuflhard, P. (1995). Discrete transparent boundary conditions for the numerical solution of Fresnel's equation. Computers & Mathematics with Applications, 29(9), 53-76.
  • The cascadic multigrid method for elliptic problems, FA Bornemann, P Deuflhard - en:Numerische Mathematik, 1996.
  • Beck, R., Deuflhard, P., Hiptmair, R., Hoppe, R. H., & Wohlmuth, B. (1997). Adaptive multilevel methods for edge element discretizations of Maxwell's equations.
  • A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions, P Deuflhard, HW Engl, O Scherzer - Inverse problems, 1998.
  • A direct approach to conformational dynamics based on hybrid Monte Carlo, C Schütte, A Fischer, W Huisinga, P Deuflhard - Journal of Computational Physics, 1999.

2000年代

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  • Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains, P Deuflhard, W Huisinga, A Fischer, C Schütte - Linear Algebra and its Applications, 2000.
  • Robust Perron cluster analysis in conformation dynamics, P Deuflhard, M Weber - Linear algebra and its applications, 2005.
  • Weiser, M., Schiela, A., & Deuflhard, P. (2005). Asymptotic mesh independence of Newton's method revisited. en:SIAM Journal on Numerical Analysis, 42(5), 1830-1845.
  • Franzone, P. C., Deuflhard, P., Erdmann, B., Lang, J., & Pavarino, L. F. (2006). Adaptivity in space and time for reaction-diffusion systems in electrocardiology. en:SIAM Journal on Scientific Computing, 28(3), 942-962.
  • Weiser, M., Deuflhard, P., & Erdmann, B. (2007). Affine conjugate adaptive Newton methods for nonlinear elastomechanics. Optimisation Methods and Software, 22(3), 413-431.
  • Deuflhard, P., Huisinga, W., Jahnke, T., & Wulkow, M. (2008). Adaptive discrete Galerkin methods applied to the chemical master equation. en:SIAM Journal on Scientific Computing, 30(6), 2990-3011.

脚注

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外部リンク

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