8 papers
Bifurcation Analysis Reveals Solution Structures of Phase Field Models
Xinyue Evelyn Zhao, Long-Qing Chen, Wenrui Hao +1
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new ana…
A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations
Wenrui Hao, Chunyue Zheng
The homotopy continuation method has been widely used in solving parametric systems of nonlinear equations. But it can be very expensive and inefficient due to singularities during…
Projection based model reduction for the immersed boundary method
Yushuang Luo, Xiantao Li, Wenrui Hao
Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the i…
Convergence analysis of neural networks for solving a free boundary system
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Free boundary problems deal with systems of partial differential equations, where the domain boundaries are apriori unknown. Due to this special characteristic, it is challenging t…
Bifurcation analysis of a free boundary model of plaque formation associated with the cholesterol ratio
Wenrui Hao, Chunyue Zheng
The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol ratio has been shown a high correlation with the cardiovascular risk assessment. Is it possible to quan…
An adaptive homotopy method for computing bifurcations of nonlinear parametric systems
Wenrui Hao, Chunyue Zheng
In this paper, we present an adaptive step-size homotopy tracking method for computing bifurcation points of nonlinear systems. There are four components in this new method: 1) an…