Mathematical model and its fast numerical method for the tumor growth

Hyun Geun Lee, Yangjin Kim, Junseok Kim

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1173-1187
Number of pages15
JournalMathematical Biosciences and Engineering
Issue number6
Publication statusPublished - 2015 Dec 1


  • Conservative Allen-Cahn equation
  • Multigrid method
  • Operator splitting method
  • Tumor growth

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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