AI 中文总结
本研究针对两种扩散界面肿瘤生长模型，提出基于舒尔补近似的块预处理子，结合自适应有限元离散化，实现了二维及三维场景下的稳健肿瘤生长数值模拟，经实验验证其收敛特性良好。
AI 中文摘要
肿瘤生长的计算模型是当代研究领域，扩散界面模型已被提出作为癌症建模的重要工具。本研究针对两种基于扩散界面模型的肿瘤生长模型的数值模拟，设计了预处理子。为提升数值效率，提出依赖有效舒尔补近似的块预处理子。结合最先进的自适应有限元离散化，该方法在二维和三维场景中实现了稳健模拟。大量数值实验表明，所提方法具有稳健的收敛特性。
英文摘要
Computational models of tumor growth form a contemporary area of study. Diffuse interface models have been proposed as an important tool for cancer modeling. In this work, we consider preconditioners for numerical simulations of two tumor growth models based on diffuse interface models. For numerical efficiency, we propose block preconditioners that rely on using effective Schur-complement approximations. We show that these methods combined with state-of-the-art adaptive finite element discretizations lead to robust simulations in two and three dimensions. In extensive numerical experiments, we show that the proposed methods show robust convergence behavior.
Comments26 pages, 18 figures, 4 tables
