arXiv subjects

Maosheng Jiang

Publications and source records attributed to Maosheng Jiang.

8 recordsLinked to original sources

arXiv2026

GradAgent: A Knowledge-Guided Multi-Agent System for Structure-Preserving Gradient-Flow Computation with an Application to Multicomponent Vesicle Dynamics

High-order differential operators and nonlinear coupling make it challenging to construct conservative and energy-stable schemes for coupled gradient-flow systems. We present GradAgent, a knowledge-guided multi-agent system that coordinates three agents across model analysis, algorithm design and proofs, and numerical implementation and validation. Independent audits strengthen reliability by uncovering mathematical errors and proof gaps, guiding revisions, and maintaining consistency across stages. In Reconstruction Mode, GradAgent reconstructs 20 published studies and organizes audited knowledge in an extensible knowledge graph (KG), GradAgent-KG, linking model structures, discretization strategies and proofs, implementations, and numerical evidence. In Design Mode, the agents assess the applicability of retrieved knowledge and develop new schemes informed by relevant discretization strategies. Applied to the fully coupled multicomponent vesicle phase-field-fluid model, GradAgent yields three first-order and three second-order schemes across three algorithmic families, including four linear, decoupled schemes. Under stated assumptions, all six schemes conserve membrane component mass and vesicle volume and dissipate their respective temporally discrete energies unconditionally. Comparisons with and without GradAgent-KG show that it promotes diversity in structure-preserving scheme design for this target model. Numerical tests confirm second-order spatial accuracy, the expected temporal orders, conservation, and temporally discrete energy dissipation, while three-dimensional shear-flow simulations agree qualitatively with experiments. These results demonstrate GradAgent's ability to combine reusable knowledge, coordinated reasoning, and independent auditing to develop and validate structure-preserving algorithms for complex coupled systems.

math.NA↗

arXiv2026

A novel energy-conservation Crank-Nicolson finite element method for generalized Klein-Gordon-Zakharov equations

This article focuses on an energy-conservation Galerkin finite element method (FEM) for the generalized Klein-Gordon-Zakharov (KGZ) equations. This method combines the bilinear finite element method for spatial discretization with the Crank-Nicolson (CN) scheme for temporal discretization, thereby guaranteeing exact conservation of the discrete energy functional. A rigorous theoretical analysis is devoted to deriving error bounds for the fast-time-scale electronic field $u$ and the ion density deviation $φ$. By systematically integrating interpolation estimates, Ritz projection, and a postprocessing technique, the superclose error estimates and global superconvergence are established for $u$ in the $H^1$-norm, even under weakened regularity assumptions on the exact solution. Concurrently, we prove $H^1$-norm superconvergence for the auxiliary variable $ϕ$ ($-Δϕ= φ_t$) and optimal-order $L^2$-norm error estimates for the auxiliary variable $p$ ($p=u_t$) and $φ$. Numerical examples are provided to confirm theoretical results.

math.NA↗

arXiv2024

A Thermodynamically Consistent Phase-Field Model and an Entropy Stable Numerical Method for Simulating Two-Phase Flows with Thermocapillary Effects

In this study, we have derived a thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects. This model accommodates variations in physical properties such as density, viscosity, heat capacity, and thermal conductivity between the two components. The model equations encompass a Cahn-Hilliard equation with the volume fraction as the phase variable, a Navier-Stokes equation, and a heat equation, and meanwhile maintains mass conservation, energy conservation, and entropy increase simultaneously. Given the highly coupled and nonlinear nature of the model equations, we developed a semi-decoupled, mass-preserving, and entropy-stable time-discrete numerical method. We conducted several numerical tests to validate both our model and numerical method. Additionally, we have investigated the merging process of two bubbles under non-isothermal conditions and compared the results with those under isothermal conditions. Our findings reveal that temperature gradients influence bubble morphology and lead to earlier merging. Moreover, we have observed that the merging of bubbles slows down with increasing heat Peclect number PeT when the initial temperature field increases linearly along the channel, while bubbles merge faster with heat Peclect number PeT when the initial temperature field decreases linearly along the channel.

physics.flu-dyn↗

arXiv2022

Numerical analysis of growth-mediated autochemotactic pattern formation in self-propelling bacteria

In this paper, a decoupled characteristic Galerkin finite element procedure is provided for simulating growth-mediated autochemotactic pattern formation in self-propelling bacteria. In this procedure, a modified characteristic Galerkin method is established to solve the bacterial density equation, while the classical finite element procedure is considered for the self-secreted chemical density and polarization dynamics equations system. The convergence of this proposed method is considered under some regularity assumptions and the corresponding error estimate is derived. Numerical experiments are carried out to support the theoretical analysis. Furthermore, several new wave type pattern formations are found.

math.NA↗

arXiv2022

Hybrid mixed discontinuous Galerkin finite element method for incompressible miscible displacement problem

A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve pressure and velocity equations, and a new hybrid mixed discontinuous Galerkin procedure is constructed to solve the concentration equation with upwind technique. Compared with other traditional discontinuous Galerkin methods, the new method can reach global systems with less unknowns and sparser stencils. The consistency and conservation of the method are analyzed, the stability and optimal error estimates are also derived by the new technique.

math.NA↗

arXiv2021

Energy exchange in a dual flow diffusion process that consists of particles of the same nature divided into two different microstates

This article presents a new approach to the dynamics of a particle system, divided into two distinct microstates spreading out in a homogeneous medium. The particles belonging to the main microstate spread according to classical Fick's law and the complementary set moves excitedly by a new potential. Each set is associated with a certain energy level. The particles can move between the two sets, introducing a third flow that is internal to the system. The governing equation is a fourth order PDE containing two new parameters, which can be time-dependent functions, in addition to the classical diffusion constant. It is shown that the solutions can avoid violations of the mass conservation requirements.

physics.flu-dyn↗

arXiv2021

Improving the Accuracy and Consistency of the Scalar Auxiliary Variable (SAV) Method with Relaxation

The scalar auxiliary variable (SAV) method was introduced by Shen et al. and has been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar auxiliary variables, the original PDE problems are reformulated into equivalent PDE problems. The advantages of the SAV approach, such as linearity, unconditionally energy stability, and easy-to-implement, are prevalent. However, there is still an open issue unresolved, i.e., the numerical schemes resulted from the SAV method preserve a "modified" energy law according to the auxiliary variables instead of the original variables. Truncation errors are introduced during numerical calculations so that the numerical solutions of the auxiliary variables are no longer equivalent to their original continuous definitions. In other words, even though the SAV scheme satisfies a modified energy law, it does not necessarily satisfy the energy law of the original PDE models. This paper presents one essential relaxation technique to overcome this issue, which we named the relaxed-SAV (RSAV) method. Our RSAV method penalizes the numerical errors of the auxiliary variables by a relaxation technique. In general, the RSAV method keeps all the advantages of the baseline SAV method and improves its accuracy and consistency noticeably. Several examples have been presented to demonstrate the effectiveness of the RSAV approach.

math.NA↗

arXiv2015

Link Prediction in Networks with Nodes Attributes by Similarity Propagation

The problem of link prediction has attracted considerable recent attention from various domains such as sociology, anthropology, information science, and computer sciences. A link prediction algorithm is proposed based on link similarity score propagation by a random walk in networks with nodes attributes. In the algorithm, each link in the network is assigned a transmission probability according to the similarity of the attributes on the nodes connected by the link. The link similarity score between the nodes are then propagated via the links according to their transmission probability. Our experimental results show that it can obtain higher quality results on the networks with node attributes than other algorithms.

cs.SI↗