Robust preconditioning of multiphysics problems and interstitial fluid flow
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- Institutt for informatikk [4956]
Sammendrag
In the natural sciences, there are many examples of physical systems which can be modeled by differential equations, such as the flow of water through soil or the deformation of a bridge under load. By developing mathematical techniques for solving the resulting equations with a computer, we can use these models to answer questions such as how much weight a bridge can support before collapsing. Complex systems often involve multiple interdependent kinds of physical behavior. An example is the brain, where water movement occurs both inside blood vessels and in the surrounding brain tissue. Because the two kinds of flow affect each other through interchange across the vessel walls, a model of water movement in the brain must account for both. However, even when there are methods for solving either subproblem individually, coupling them together in a robust manner is not always straightforward, and the focus of this thesis. Robustness means that the method should run in a reasonable amount of time, both for complex problems with many unknowns and for all values of the problem parameters, even the very large or very small. This property is crucial for applications in biomechanics.Artikkelliste
Paper I: Holter, et al. Holter, Kehlet, Devor, Sejnowski, Dale, Omholt, Ottersen, Nagelhus, Mardal and Pettersen. ‘Interstitial solute transport in 3D reconstructed neuropil occurs by diffusion rather than bulk flow’. In: Proceedings of the National Academy of Sciences 114.37 (2017), pp. 9894-9899. DOI: 10.1073/pnas.1706942114. The article is included in the thesis. Also available at: https://doi.org/10.1073/pnas.1706942114 |
Paper II: Holter, Kuchta, and Mardal. ‘Sub-voxel perfusion modeling in terms of coupled 3d-1d problem’. arXiv: 1803.04896. In: ENUMATH 2017 Proceedings. Lecture Notes in Computational Science and Engineering, 126, 2019. DOI: 10.1007/978-3-319-96415-7_2. The article is included in the thesis. Also available at: https://doi.org/10.1007/978-3-319-96415-7_2 |
Paper III: Holter, Kuchta, and Mardal. ‘Robust preconditioning of monolithically coupled multiphysics problems’. arXiv: 2001.05527 In submission. To be published. The paper is not available in DUO awaiting publishing. |
Paper IV: Holter, Kuchta, and Mardal. ‘Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form’. arXiv: 2001.05529. In: Computers & Mathematics with Applications, 2021, vol 91, 53-66. DOI: 10.1016/j.camwa.2020.08.021. The article is included in the thesis. Also available at: https://doi.org/10.1016/j.camwa.2020.08.021 |