ペーター・ドイフルハード

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

• 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

単著

• 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

1970年代

• 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

• 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

• 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

• 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.

外部リンク

• Peter Deuflhard, Emi Norris, 加古孝, コンラッド・ツーゼ・ベルリン情報技術研究所(ZIB)(海外情報)」『応用数理』 1994年 4巻 4号 p.377-383, 日本応用数理学会, doi:10.11540/bjsiam.4.4_377
• ペーター・ドイフルハードの出版物 - Google Scholar
• ペーター・ドイフルハード - Mathematics Genealogy Project