2023/07/17 by Nunzio Dimola, Miroslav Kuchta, Dimola, Nunzio +5
Computer Science · Engineering · #65F08 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2307.08431
openalex publication_date 2023/07/17 · openalex created_date 2023/07/19 · openalex updated_date 2026/07/28
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.