Mathematical model and its fast numerical method for the tumor growth
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Updated: Mar 27, 2026

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
Published on: December 1, 2023
Hyun Geun Lee1, Yangjin Kim, Junseok Kim
1Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, South Korea.
Abstract:
In this paper, we reformulate the diffuse interface model of the tumor growth (S.M. Wise et al., Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524--543). In the new proposed model, we use the conservative second-order Allen--Cahn equation with a space--time dependent Lagrange multiplier instead of using the fourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, we apply a recently developed hybrid numerical method. We perform various numerical experiments. The computational results demonstrate that the new model is not only fast but also has a good feature such as distributing excess mass from the inside of tumor to its boundary regions.
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