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MATHEMATICAL MODEL AND ITS FAST NUMERICAL METHOD FOR THE TUMOR GROWTH
- Authors
- Lee, Hyun Geun; Kim, Yangjin; Kim, Junseok
- Issue Date
- 12월-2015
- Publisher
- AMER INST MATHEMATICAL SCIENCES
- Keywords
- operator splitting method; multigrid method; Tumor growth; conservative Allen-Cahn equation
- Citation
- MATHEMATICAL BIOSCIENCES AND ENGINEERING, v.12, no.6, pp.1173 - 1187
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATICAL BIOSCIENCES AND ENGINEERING
- Volume
- 12
- Number
- 6
- Start Page
- 1173
- End Page
- 1187
- ISSN
- 1547-1063
- 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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