Monotonicity-preserving interproximation of B-H-curves

Journal of Computational and Applied Mathematics

Volumn 196, Issue 1, 2006, Pages 45-57

  Pechstein, Clemens ^a   Jüttler, Bert ^a  

^a Institute of Applied Geometry   (Austria)

Author keywords

B H curves; Interproximation; Maxwell's equations; Monotonicity preserving approximation; Nonlinear field computations; Smoothing splines

Indexed keywords

COMPUTER SIMULATION; ELECTROMAGNETIC FIELD EFFECTS; FERROMAGNETIC MATERIALS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; NUMERICAL ANALYSIS; SPLINES;

B-H-CURVES; INTERPROXIMATION; MONOTONICITY-PRESERVING APPROXIMATION; NONLINEAR FIELD COMPUTATIONS; SMOOTHING SPLINES;

APPROXIMATION THEORY;

EID: 33745677836     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.08.021     Document Type: Article

References (28)

1. Berlotti G. Hysteresis in Magnetism: for Physicists, Materials Scientists, and Engineers (1998), Academic Press, New York
2. Cheng F., and Barsky B.A. Interproximation: interpolation and approximation using cubic spline curves. Comput.-Aided Design 23 (1991) 700-706
3. Dierckx P. Curve and Surface Fitting with Splines (1993), Oxford Science Publications, Oxford
4. Fredenhagen S., Oberle H.J., and Opfer G. On the construction of optimal monotone cubic spline interpolations. J. Approximation Theory 96 (1999) 182-201
5. Fritsch F.N., and Carlson R.E. Monotone piecewise cubic interpolation. SIAM J. Numer. Anal. 2 (1980) 235-246
6. Gill P.E., Murray W., and Wright M.H. Practical Optimization (1981), Academic Press, London, New York
7. Greiner G., Kolb A., and Riepl A. Scattered data interpolation using data dependant optimization techniques. Graph. Models 64 1 (2002) 1-18
8. B. Heise, Mehrgitter-Newton-Verfahren zur Berechnung nichtlinearer magnetischer Felder, Ph.D. Thesis, Technical University of Chemnitz, Germany, 1991.
9. Heise B. Analysis of a fully discrete finite element method for a nonlinear magnetic field problem. SIAM J. Numer. Anal. 31 (1994) 745-759
10. Ida N., and Bastos J.P.A. Electromagnetics and Calculation of Fields (1997), Springer, Berlin
11. Jackson J.D. Classical Electrodynamics. third ed. (1998), Wiley, New York
12. Jüttler B. Surface fitting using convex tensor-product splines. J. Comput. Appl. Math. 84 (1997) 23-44
13. Kaltenbacher M. Numerical Simulation of Mechatronic Sensors and Actuators (2004), Springer, Berlin, Heidelberg, New York
14. B. Kaltenbacher, M. Kaltenbacher, S. Reitzinger, Identification of nonlinear B-H curves based on magnetic field computations and multigrid methods for ill-posed problems, European J. Appl. Math. 14 (2003) 15-38.
15. Kopotun K., and Shadrin A. On k-monotone approximation by free knot splines. SIAM J. Math. Anal. 34 (2003) 901-924
16. V.G. Korneev, U. Langer, Approximate Solution of Plastic Flow Theory Problems, Teubner Texte zur Mathematik, B.G. Teubner, Leipzig, 1984.
17. 2 cubic splines. IMA J. Numer. Anal. 17 (1997) 305-320
18. Monk P. Finite Element Methods for Maxwell's Equations (2003), Oxford University Press, Oxford
19. Oja P. Low degree rational spline interpolation. BIT 37 (1997) 901-909
20. C. Pechstein, Multigrid-Newton-methods for nonlinear magnetostatic problems, Master Thesis, Johannes Kepler University Linz, Austria, 2004, available from 〈www.numa.uni-linz.ac.at/Teaching/Diplom/finished/pechstein.html〉.
21. Pinchukov V.I. A monotone nonlocal cubic spline. Comput. Math. Math. Phys. 41 (2001) 180-186
22. Qu R., and Sarfraz M. Efficient method for curve interpolation with monotonicity preservation and shape control. Neural Parallel Sci. Comput. 5 (1997) 275-288
23. Reinsch C.H. Smoothing by spline functions. Numer. Math. 10 (1967) 177-183
24. S. Reitzinger, B. Kaltenbacher, M. Kaltenbacher, A Note on the Approximation of B-H Curves for Nonlinear Computations, Report no. 02-30, SFB F013, Johannes Kepler University Linz, Austria, 2002, available from 〈www.sfb013.uni-linz.ac.at/sfb/reports/liste/trliste/trliste.html〉.
25. Volkov Yu.S. On monotone interpolation by cubic splines. Vychisl. Tekhnol. 6 (2001) 14-24
26. Zavyalov Yu.S., and Bogdanov V.V. Monotone and convex Hermite interpolation by generalized cubic splines. Siberian J. Comput. Math. 2 (1995) 15-32
27. Zeidler E. Applied functional analysis: applications to mathematical physics. Appl. Math. Sci. 108 (1986)
28. Zeidler E. Nonlinear Functional Analysis and Its Applications II/B: Nonlinear Monotone Operators (1995), Springer, Berlin