arXiv subjects

Yumiao Zhang

Publications and source records attributed to Yumiao Zhang.

4 recordsLinked to original sources

arXiv2026

A quasi-monolithic localized high-order ALE finite element method for multi-scale fluid-structure interaction problems

This paper presents a quasi-monolithic localized high-order arbitrary Lagrangian-Eulerian (qMLH-ALE) finite element method for multi-scale fluid-structure interaction (FSI) in microfluidic systems. The fluid momentum, the incompressible Neo-Hookean constitutive law, and the left Cauchy-Green tensor $\mathcal{B}$ are assembled into a single implicit system, while the harmonic mesh extension is updated explicitly in a staggered manner. Isoparametric $\mathcal{P}_2$ elements provide third-order geometric approximation of curved fluid-solid interfaces, and a second-order implicit-explicit partitioned Runge-Kutta scheme delivers second-order temporal accuracy without the dissipation of backward Euler. A localized updating strategy confines the moving mesh and the deformation history to a body-fitted sub-domain coupled with a precomputed steady background flow, bridging the scale disparity between local FSI dynamics and the macroscopic microchannel geometry. The Turek-Hron FSI3 benchmark, performed at unit fluid-solid density ratio, reproduces the reference beam-tip amplitude and frequency within $3\%$, confirming stability under the strong added-mass coupling that destabilizes conventional partitioned schemes. Three-dimensional particle-focusing simulations in spiral microchannels further illustrate the framework on long-range multi-scale problems.

math.NA↗

arXiv2026

High-order DLM-ALE discretizations with robust operator preconditioning for fluid-rigid-body interaction

Motivated by the design of deterministic lateral displacement (DLD) microfluidic devices, we develop a high-order numerical framework for fluid-rigid-body interaction on fitted moving meshes. Rigid-body motion is enforced by a distributed Lagrange multiplier (DLM) formulation, while the moving fluid domain is treated by an arbitrary Lagrangian-Eulerian (ALE) mapping. In space, we use isoparametric Taylor-Hood elements to achieve high-order accuracy and to represent curved boundaries and the fluid-particle interface. In time, we employ a high-order partitioned Runge-Kutta strategy in which the mesh motion is advanced explicitly and the coupled physical fields are advanced implicitly, yielding high-order accuracy for the particle trajectory. The fully coupled system is linearized into a generalized Stokes problem subject to distributed constraints of incompressibility and rigid-body motion. We establish well-posedness of this generalized Stokes formulation at both the continuous and discrete levels, providing the stability foundation for operator preconditioning that is robust with respect to key physical and discretization parameters. Numerical experiments on representative benchmarks, including a DLD case, demonstrate high-order convergence for the fluid solution and rigid-body dynamics, as well as robust iterative convergence of the proposed preconditioners.

math.NA↗

arXiv2025

DatawiseAgent: A Notebook-Centric LLM Agent Framework for Adaptive and Robust Data Science Automation

Existing large language model (LLM) agents for automating data science show promise, but they remain constrained by narrow task scopes, limited generalization across tasks and models, and over-reliance on state-of-the-art (SOTA) LLMs. We introduce DatawiseAgent, a notebook-centric LLM agent framework for adaptive and robust data science automation. Inspired by how human data scientists work in computational notebooks, DatawiseAgent introduces a unified interaction representation and a multi-stage architecture based on finite-state transducers (FSTs). This design enables flexible long-horizon planning, progressive solution development, and robust recovery from execution failures. Extensive experiments across diverse data science scenarios and models show that DatawiseAgent consistently achieves SOTA performance by surpassing strong baselines such as AutoGen and TaskWeaver, demonstrating superior effectiveness and adaptability. Further evaluations reveal graceful performance degradation under weaker or smaller models, underscoring the robustness and scalability.

cs.CL↗

arXiv2024

A Unified-Field Monolithic Fictitious Domain-Finite Element Method for Fluid-Structure-Contact Interactions and Applications to Deterministic Lateral Displacement Problems

Based upon two overlapped, body-unfitted meshes, a type of unified-field monolithic fictitious domain-finite element method (UFMFD-FEM) is developed in this paper for moving interface problems of dynamic fluid-structure interactions (FSI) accompanying with high-contrast physical coefficients across the interface and contacting collisions between the structure and fluidic channel wall when the structure is immersed in the fluid. In particular, the proposed novel numerical method consists of a monolithic, stabilized mixed finite element method within the frame of fictitious domain/immersed boundary method (IBM) for generic fluid-structure-contact interaction (FSCI) problems in the Eulerian-updated Lagrangian description, while involving the no-slip type of interface conditions on the fluid-structure interface, and the repulsive contact force on the structural surface when the immersed structure contacts the fluidic channel wall. The developed UFMFD-FEM for FSI or FSCI problems can deal with the structural motion with large rotational and translational displacements and/or large deformation in an accurate and efficient fashion, which are first validated by two benchmark FSI problems and one FSCI model problem, then by experimental results of a realistic FSCI scenario -- the microfluidic deterministic lateral displacement (DLD) problem that is applied to isolate circulating tumor cells (CTCs) from blood cells in the blood fluid through a cascaded filter DLD microchip in practice, where a particulate fluid with the pillar obstacles effect in the fluidic channel, i.e., the effects of fluid-structure interaction and structure collision, play significant roles to sort particles (cells) of different sizes with tilted pillar arrays.

math.NA↗