Journal
MATHEMATICAL BIOSCIENCES AND ENGINEERING
Volume 12, Issue 6, Pages 1173-1187Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2015.12.1173
Keywords
Tumor growth; conservative Allen-Cahn equation; operator splitting method; multigrid method
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Funding
- Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Education [2009-0093827]
- Basic Science Research Program through the National Research Foundation of Korea, Ministry of Education and Technology [2012R1A1A1043340]
- National Research Foundation of Korea (NRF) - Korea government(MSIP) [NRF-2014R1A2A2A01003683]
- National Research Foundation of Korea [2012R1A1A1043340] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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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