SC 98-35 Peter Deuflhard, Martin Weiser, Martin Seebaß: A New Nonlinear Elliptic Multilevel FEM Applied to Regional
Hyperthermia
Abstract: In the clinical cancer therapy of regional hyperthermia
nonlinear perfusion effects inside and outside the tumor
seem to play a not negligible role. A stationary model
of such effects leads to a nonlinear Helmholtz term
within an elliptic boundary value problem. The present
paper reports about the application of a recently
designed adaptive multilevel FEM to this problem.
For several 3D virtual patients, nonlinear versus
linear model is studied. Moreover, the numerical
efficiency of the new algorithm is compared with a
former application of an adaptive FEM to the
corresponding instationary model PDE.
Keywords: hyperthermia,
nonlinear elliptic,
multilevel FEM
MSC: 92C50, 65J15, 35J60, 56N55