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- W4384648122 abstract "In the context of micro-circulation, the coexistence of two distinct length scales - the vascular radius and the tissue/organ scale - with a substantial difference in magnitude, poses significant challenges. To handle slender inclusions and simplify the geometry involved, a technique called topological dimensionality reduction is employed, which suppresses manifold dimensions associated with the smaller characteristic length. However, the resulting discretized system's algebraic structure presents a challenge in constructing efficient solution algorithms. This chapter addresses this challenge by developing a robust preconditioner for the 3d-1d problem using the operator preconditioning technique. Robustness of the preconditioner is demonstrated with respect to problem parameters, except for the vascular radius. The vascular radius, as demonstrated, plays a fundamental role in mathematical well-posedness of the problem and the preconditioner's effectiveness." @default.
- W4384648122 created "2023-07-19" @default.
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- W4384648122 date "2023-07-17" @default.
- W4384648122 modified "2023-09-25" @default.
- W4384648122 title "Robust Preconditioning of mixed-dimensional PDEs on 3d-1d domains coupled with Lagrange multipliers" @default.
- W4384648122 doi "https://doi.org/10.48550/arxiv.2307.08431" @default.
- W4384648122 hasPublicationYear "2023" @default.
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