arXiv subjects

Shihan Guo

Publications and source records attributed to Shihan Guo.

4 recordsLinked to original sources

arXiv2026

Neural enrichment finite element method: A hybrid framework for problems with strong oscillations or interface problems

We propose a hybrid method, the Neural Enrichment Finite Element Method (NEFEM), designed for problems involving strong oscillations or interface problems with weak discontinuities. This method is based on the stable generalized finite element method (SGFEM) framework, wherein neural networks (NNs) are introduced as enrichment functions for adaptivity, and the Ritz functional is applied for the training process. This works makes two main contributions. First, the method constructs local subspaces with superior approximation properties, significantly reducing the required number of degrees of freedom (DoFs). Second, minimal \emph{a priori} knowledge is required to define enrichment functions, as the NNs evolve heuristically during training. Furthermore, for smooth problems, we provide a residual-based error estimator and prove both its reliability and efficiency. For interface problems, a theoretical analysis on the optimal convergence of the SGFEM is studied, notably without imposing additional regularity assumptions. These analytic results guide the network architecture design and training strategies. The performance and effectiveness of the proposed method is validated through several numerical experiments.

math.NA↗

arXiv2025

An Unconditionally Stable Explicit Robin-Robin Partitioned Scheme for Fluid-Structure Interaction

We propose a parallelizable partitioned (loosely coupled) scheme for fluid structure interaction (FSI) problems, specifically designed for efficient computation in modern engineering simulations. The FSI problem under consideration involves an incompressible viscous fluid, governed by the Navier--Stokes equations, with a thick linear elastic structure. The scheme adopts a Robin--Robin coupling condition, evaluating the right-hand side of the Robin boundary terms at each time step solely from the previous-step solutions. This explicit scheme allows the fluid and structure subproblems to be solved entirely independently within each time step, eliminating the need for staggered coupling or costly sub-iterations, and thus enabling their concurrent computation. Various numerical experiments demonstrate the stability, accuracy, and computational efficiency of the proposed approach, highlighting its potential for large-scale parallel FSI computations in engineering applications.

math.NA↗

arXiv2024

Extended one-dimensional reduced model for blood flow within a stenotic artery

In this paper, we introduce an adapted one-dimensional (1D) reduced model aimed at analyzing blood flow within stenosed arteries. Differing from the prevailing 1D model \cite{Formaggia2003, Sherwin2003_2, Sherwin2003, Quarteroni2004, 10.1007/978-3-642-56288-4_10}, our approach incorporates the variable radius of the blood vessel. Our methodology begins with the non-dimensionalization of the Navier-Stokes equations for axially symmetric flow in cylindrical coordinates and then derives the extended 1D reduced model, by making additional adjustments to accommodate the effects of variable radii of the vessel along the longitudinal direction. Additionally, we propose a method to extract radial velocity information from the 1D results during post-processing, enabling the generation of two-dimensional (2D) velocity data. We validate our model by conducting numerical simulations of blood flow through stenotic arteries with varying severities, ranging from 23% to 50%. The results were compared to those from the established 1D model and a full three-dimensional (3D) simulation, highlighting the potential and importance of this model for arteries with variable radius. All the code used to generate the results presented in the paper is available at https://github.com/qcutexu/Extended-1D-AQ-system.git.

math.NA↗

arXiv2024

A Fully Parallelizable Loosely Coupled Scheme for Fluid-Poroelastic Structure Interaction Problems

We investigate the fluid-poroelastic structure interaction problem in a moving domain, governed by Navier-Stokes-Biot (NSBiot) system. First, we propose a fully parallelizable, loosely coupled scheme to solve the coupled system. At each time step, the solution from the previous time step is used to approximate the coupling conditions at the interface, allowing the original coupled problem to be fully decoupled into seperate fluid and structure subproblems, which are solved in parallel. Since our approach utilizes a loosely coupled scheme, no sub-iterations are required at each time step. Next, we conduct the energy estimates of this splitting method for the linearized problem (Stokes-Biot system), which demonstrates that the scheme is unconditionally stable without any restriction of the time step size from the physical parameters. Furthermore, we illustrate the first-order accuracy in time through two benchmark problems. Finally, to demonstrate that the proposed method maintains its excellent stability properties also for the nonlinear NSBiot system, we present numerical results for both $2D$ and $3D$ NSBiot problems related to real-world physical applications.

math.NA↗