Parallel splitting solvers for the isogeometric analysis of the Cahn-Hilliard equation
| Autor: | Marcin Łoś, Maciej Paszyński, Witold Dzwinel, Vladimir Puzyrev, Victor M. Calo, Grzegorz Gurgul |
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| Rok vydání: | 2019 |
| Předmět: |
Computer science
0206 medical engineering Biomedical Engineering Numerical Analysis Computer-Assisted Bioengineering 030229 sport sciences 02 engineering and technology General Medicine Isogeometric analysis Models Biological 020601 biomedical engineering Computer Science Applications Human-Computer Interaction 03 medical and health sciences 0302 clinical medicine Neoplasms Humans Applied mathematics Tumor growth Linear solver Cahn–Hilliard equation Algorithms Cell Proliferation |
| Zdroj: | Computer Methods in Biomechanics and Biomedical Engineering. 22:1269-1281 |
| ISSN: | 1476-8259 1025-5842 |
| DOI: | 10.1080/10255842.2019.1661388 |
| Popis: | Modeling tumor growth in biological systems is a challenging problem with important consequences for diagnosis and treatment of various forms of cancer. This growth process requires large simulation complexity due to evolving biological and chemical processes in living tissue and interactions of cellular and vascular constituents in living organisms. Herein, we describe with a phase-field model, namely the Cahn-Hilliard equation the intricate interactions between the tumors and their host tissue. The spatial discretization uses highly-continuous isogeometric elements. For fast simulation of the time-dependent Cahn-Hilliard equation, we employ an alternating directions implicit methodology. Thus, we reduce the original problems to Kronecker products of 1 D matrices that can be factorized in a linear computational cost. The implementation enables parallel multi-core simulations and shows good scalability on shared-memory multi-core machines. Combined with the high accuracy of isogeometric elements, our method shows high efficiency in solving the Cahn-Hilliard equation on tensor-product meshes. |
| Databáze: | OpenAIRE |
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