Mathematical model and its fast numerical method for the tumor growth
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 equatio...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2015-07-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1173 |
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| Summary: | 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. |
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| ISSN: | 1551-0018 |