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A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia

Please always quote using this URN: urn:nbn:de:0297-zib-3785
  • 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.

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Author:Peter Deuflhard, Martin WeiserORCiD, Martin Seebass
Document Type:ZIB-Report
Tag:hyperthermia; multilevel FEM; nonlinear elliptic
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J60 Nonlinear elliptic equations
65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J15 Equations with nonlinear operators (do not use 65Hxx)
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C50 Medical applications (general)
Date of first Publication:1998/12/10
Series (Serial Number):ZIB-Report (SC-98-35)
Published in:Appeared under the title: "A New Nonlinear Elliptic Multilevel FEM in Clinical Cancer Therapy Planning" in: Comput Visual Sc 3 (2000) 115-120