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math.GT2025
On Topology of Three-dimensional Continua with Singular Points
Hao Liang, Yunhao Qiu, Yan Tan +1
We propose to model the topology of three-dimensional (3D) continua by Yin sets, regular open semianalytic sets with bounded boundary. Our model differs from manifold-based models…
math.NA2025
On Convergence of the Secant Method
Yan Tan, Chenhao Ye, Qinghai Zhang +1
The secant method, as an important approach for solving nonlinear equations, is introduced in nearly all numerical analysis textbooks. However, most textbooks only briefly address…
math.NA2025
A multiphase cubic MARS method for fourth- and higher-order interface tracking of two or more materials with arbitrary topology and geometry
Yan Tan, Yixiao Qian, Zhiqi Li +1
For interface tracking of an arbitrary number of materials in two dimensions, we propose a multiphase cubic MARS method that (a) represents the topology and geometry of the interfa…