A new nonlinear elliptic multilevel FEM in clinical cancer therapy planning

Computing and Visualization in Science

Volumn 3, Issue 3, 2000, Pages 115-120

  Deuflhard, Peter ^a   Weiser, Martin ^a   Seebaß, Martin ^a  

^a ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; VISUALIZATION;

ADAPTIVE FEM; CANCER THERAPY; ELLIPTIC BOUNDARY VALUE PROBLEM; HELMHOLTZ; NON-STATIONARY MODEL; NUMERICAL EFFICIENCY; STATIONARY MODELS; VIRTUAL PATIENTS;

ONCOLOGY;

EID: 12244254037     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/PL00013546     Document Type: Article

References (14)

1. Bank, R.E.: PLTMG: A Software Package for Solving Elliptic Partial Differential Equations. User's Guide 8.0. SIAM, Philadelphia 1998
2. Bank, R.E., Rose, D.J.: Analysis of a multilevel iterative method for nonlinear finite element equations. Math. Comput. 39, 453-465 (1982)
3. Bastian, P., Birken, K., Johannsen, K., Lang, S., Neuss, N., Rentz- Reichert, H., Wieners, C.: UG - A Flexible Software Toolbox for Solving Partial Differential Equations. Comput. Visualization Sci. 1, 27-40 (1997)
4. Bastian, P., Wittum, G.: Adaptive multigrid methods: The UG concept. In: W. Hackbusch et al. (eds.), Adaptive methods - algorithms, theory and applications. Proceedings of the 9th GAMM-Seminar Kiel, Germany, January 22-24, 1993, Vol. 46 of Notes Numer. Fluid Mech. Braunschweig, Vieweg 1994, pp. 17-37
5. Beck, R., Erdmann, B., Roitzsch, R.: Kaskade 3.0, an object-oriented adaptive finite element code. Technical Report TR 95-4, ZIB 1995
6. Deuflhard, P., Seebaß, M.: Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyperthermia. In: Lai, C.-H., Bjørstad, P.E., Cross, M., Widlund, O.O., (eds.), Proc. of Eleventh International Conference on Domain Decomposition Methods, published by: DDM-org Press, Bergen, pp. 403-414, 1999
7. Deuflhard, P., Seebaß, M., Stalling, D., Beck, R., Hege, H.-C.: Hyperthermia Treatment Planning in Clinical Cancer Therapy: Modelling, Simulation and Visualization. In: Sydow, A. (ed.), Proc. of the 15th IMACS World Congress 1997 on Scientific Computation: Modelling and Applied Mathematics, Vol. 3, Wissenschaft und Technik Verlag 1997, pp. 9-17
8. Deuflhard, P., Weiser, M.: Local inexact Newton multilevel FEM for nonlinear elliptic problems. In: Bristeau, M.-O., Etgen, G., Fitzigibbon, W., Lions, J.-L., Periaux, J., Wheeler, M. (eds.), Computational science for the 21st century, Wiley 1997, pp. 129-138
9. Deuflhard, P., Weiser, M.: Global inexact Newton multilevel FEM for nonlinear elliptic problems. In Hackbusch,W., Wittum, G. Eds., Multigrid Methods V, Lecture Notes in Computational Science and Engineering, Springer 1998 pp. 71-89
10. Hackbusch, W., Reusken, A.: Analysis of a damped nonlinear multilevel method. Numer. Math. 55(2), 225-246 (1989)
11. Lang, J.: Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems. Theory, Algorithm, and Applications. Habilitation Thesis, Free University of Berlin 1999
12. Lang, J., Erdmann, B., Seebaß, M.: Impact of Nonlinear Heat Transfer on Temperature Control in Regional Hyperthermia. IEEE Trans. Biomed. Eng. appeared in: 46,1129-1138 (1999)
13. Pennes, H.H.: Analysis of tissue and arterial blood temperatures in the resting human forearm. J. Appl. Phys. 1, 93-122 (1948)
14. Song, C.W., Lokshina, A., Rhee, J.G., Patten, M., Levitt, S.H.: Implication of blood flow in hyperthermic treatment of tumors. IEEE Trans. Biomed. Eng. 31, 9-16 (1984)