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MATHEMATICAL MODEL AND ITS FAST NUMERICAL METHOD FOR THE TUMOR GROWTH
- MATHEMATICAL MODEL AND ITS FAST NUMERICAL METHOD FOR THE TUMOR GROWTH
- Lee, Hyun Geun; Kim, Yangjin; Kim, Junseok
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- MATHEMATICAL BIOSCIENCES AND ENGINEERING
- 1547-1063; 1551-0018
- vol. 12, no. 6, pp. 1173 - 1187
- Tumor growth; conservative Allen-Cahn equation; operator splitting method; multigrid method
- AMER INST MATHEMATICAL SCIENCES
- SCIE; 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.
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