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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| Format: | Article |
| Language: | English |
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AIMS Press
2015-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1173 |
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| _version_ | 1832590105952387072 |
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| author | Hyun Geun Lee Yangjin Kim Junseok Kim |
| author_facet | Hyun Geun Lee Yangjin Kim Junseok Kim |
| author_sort | Hyun Geun Lee |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-30791a66637343c1a6fa2e4f2c57d727 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-30791a66637343c1a6fa2e4f2c57d7272025-01-24T02:33:57ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-07-011261173118710.3934/mbe.2015.12.1173Mathematical model and its fast numerical method for the tumor growthHyun Geun Lee0Yangjin Kim1Junseok Kim2Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750Department of Mathematics, Konkuk University, Seoul 143-701Department of Mathematics, Korea University, Seoul 136-713In 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.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1173conservative allen--cahn equationtumor growthoperator splitting methodmultigridmethod. |
| spellingShingle | Hyun Geun Lee Yangjin Kim Junseok Kim Mathematical model and its fast numerical method for the tumor growth Mathematical Biosciences and Engineering conservative allen--cahn equation tumor growth operator splitting method multigridmethod. |
| title | Mathematical model and its fast numerical method for the tumor growth |
| title_full | Mathematical model and its fast numerical method for the tumor growth |
| title_fullStr | Mathematical model and its fast numerical method for the tumor growth |
| title_full_unstemmed | Mathematical model and its fast numerical method for the tumor growth |
| title_short | Mathematical model and its fast numerical method for the tumor growth |
| title_sort | mathematical model and its fast numerical method for the tumor growth |
| topic | conservative allen--cahn equation tumor growth operator splitting method multigridmethod. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1173 |
| work_keys_str_mv | AT hyungeunlee mathematicalmodelanditsfastnumericalmethodforthetumorgrowth AT yangjinkim mathematicalmodelanditsfastnumericalmethodforthetumorgrowth AT junseokkim mathematicalmodelanditsfastnumericalmethodforthetumorgrowth |