Mathematical model and its fast numerical method for the tumor growth - Hyun Geun Lee; Yangjin Kim; Junseok Kim (Mathematical Biosciences and Engineering)
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-orderAllen--Cahn equation with a space--time dependent Lagrange multiplier instead of using thefourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, weapply a recently developed hybrid numerical method. We perform various numerical experiments. Thecomputational results demonstrate that the new model is not only fast but also has a good featuresuch as distributing excess mass from the inside of tumor to its boundary regions.