Analysis of the operator Δ-1div arising in magnetic models

Zeitschrift für Analysis und ihre Anwendungen

Volumn 23, Issue 3, 2004, Pages 589-605

  Praetorius, Dirk ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Calder n Zygmund kernel; Hierarchical matrices; Integral representation; Laplace equation; Magnetic potential; Micromagnetics; Panel clustering

Indexed keywords

EID: 8844259734     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/1212     Document Type: Article

References (22)

1. Agmon, S.: Lectures on Elliptic Boundary Value Problems. Princeton: Van Nostrand 1965.
2. Börm, S., Grasedyck, L. and W. Hackbusch: Introduction to hierarchical matrices with applications. Engin. Anal. with Boundary El. 27 (2003), 405-422.
3. Brown, W. F.: Micromagnetism. New York: Interscience 1963.
4. Carstensen, C. and D. Praetorius: A posteriori error control in adaptive qualocation boundary element analysis for a logarithmic-kernel integral equation of the first kind. SIAM J. Sci. Comp. 25 (2004), 259-283.
5. Carstensen, C. and D. Praetorius: Numerical analysis for a macroscopic model in micromagnetics. To appear in SIAM J. Numer. Anal. (2004). Preprint at http://www.anum.tuwien.ac.at/~dirk/download
6. Carstensen, C. and D. Praetorius: Effective simulation of a macroscopic model in micromagnetics. To appear in Comput. Meth. Appl. Mech. Engrg. (2004). Preprint at http://www.anum.tuwien.ac.at/~dirk/download
7. DeSimone, A.: Energy minimizers for large ferromagnetic bodies. Arch. Rational Mech. Anal. 125 (1993), 99-143.
8. Gilbarg, D. and N. S. Trudinger: Elliptic Partial Differential Equations of Second Order (Grundlehren der Mathematischen Wissenschaften: Vol. 224). Berlin et al.: Springer-Verlag 1977.
9. Hackbusch, W.: Direct integration of the Newton potential over cubes including a program description. Computing 68 (2002), 193-216.
10. -1div. In preparation 2003.
11. Hubert, A. and R. Schäfer: Magnetic Domains. Berlin - Heidelberg - New York: Springer-Verlag 1998.
12. James, R. D. and D. Kinderlehrer: Frustration in ferromagnetic materials. Continuum Mech. Thermodyn. 2 (1990), 215-239.
13. Lions, P. L.: Mathematical Topics in Fluid Mechanics. Volume 1: Incompressible Models (Oxford Lecture Series in Mathematics and its Applications: Vol. 3). Oxford: Clarendon Press 1996.
14. Luskin, M. and L. Ma: Analysis of the finite element approximation of microstructure in micromagnetics. SIAM J. Numer. Anal. 29 (1992), 320-331.
15. Ma, L.: Analysis and Computation for a Variational Problem in Micromagnetics. Ph.D. Thesis. University of Minnesota 1991.
16. Maischak, M.: The analytical computation of the Galerkin elements for the Laplace, Lamé and Helmholtz equation. Technical report ifam48: 2D BEM. Technical report ifam50: 3D BEM. Inst. Angew. Math., Univ. Hannover 1999 and 2000.
17. McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge: Univ. Press 2000.
18. Popović, N. and D. Praetorius: Applications of H-matrix techniques in micromagnetics. To appear in Computing (2004). Preprint available at http://www.anum.tuwien.ac.at/~dirk/download
19. Praetorius, D.: Analysis, Numerik und Simulation eines relaxierten Modell-problems zum Mikromagnetismus. Doctoral Thesis. Vienna Univ. of Technology 2003. Thesis at http://www.anum.tuwien.ac.at/~dirk/download
20. Rudin, W.: Functional Analysis (2-nd ed.). New York: McGraw-Hill 1991.
21. Rudin, W.: Real and Complex Analysis (3-rd ed.). New York: McGraw-Hill 1987.
22. Stein, E. M.: Singular Integrals and Differentiability Properties of Functions (Princeton Mathematical Series: Vol. 30). Princeton: Univ. Press 1970.