arXiv subjects

Ping Lin

Publications and source records attributed to Ping Lin.

At least 19 recordsLinked to original sources

arXiv2026

Asymptotically Compatible Variational Energy Dissipation Laws and Structure-Preserving Variable-Step Linear Relaxation Schemes for a Subdiffusive Tumor-Nutrient Model

In this work, we develop a mass-conservative subdiffusive tumor-nutrient model coupled through chemotaxis and memory-dependent reaction exchange, together with structure-preserving variable-step linear relaxation schemes. A weighted Riemann-Liouville identity is proved and used to construct a variational energy and the associated energy dissipation law for the proposed model. Both the model and the associated variational energy dissipation law are asymptotically compatible with their integer-order counterparts as the fractional order approaches one. For numerical approximation, we discretize the Riemann-Liouville fractional derivatives using the L1R formula on nonuniform time meshes and derive the associated discrete weighted inequality. We first construct a variable-step linear relaxation scheme for the subdiffusive model. Then, to mitigate alternating perturbations induced by the auxiliary-variable error and amplified by the L1R convolution at small fractional orders, we construct a temporally damped linear relaxation scheme. Since temporal damping leaves the auxiliary-variable recurrence unchanged, we further introduce an a posteriori relaxation correction to reduce alternating errors in the auxiliary variable. All three schemes preserve total mass, are proven to satisfy discrete variational energy dissipation laws using the discrete weighted inequality, and remain consistent with the integer-order limit. Several numerical examples are presented to validate the accuracy and stability of the proposed schemes.

math.NA↗

arXiv2026

A second-order energy-stable sequential regularization scheme for the Navier-Stokes equations

In this paper, we construct a second-order decoupled scheme for the Navier-Stokes equations based on the idea of the auxiliary variable and the sequential regularization method (SRM). The proposed scheme enjoys unconditional energy stability, which is generally unavailable for the existing SRM, while preserving its key advantage of avoiding artificial pressure boundary conditions and maintaining the original velocity boundary conditions. We establish a viscosity-independent low-order stability estimate and a higher-order stability estimate for the proposed scheme. Furthermore, we derive global-in-time second-order error estimates in two dimensions and corresponding local-in-time estimates in three dimensions, without imposing any time-step restrictions. A series of numerical experiments confirm the convergence and stability, and demonstrate improved accuracy and incompressibility control compared with the projection method and the conventional SRM. In particular, both high-Reynolds-number and three-dimensional numerical simulations further demonstrate the robustness and reliability of the proposed method for complex incompressible flows.

math.NA↗

arXiv2026

A Lattice Boltzmann Method with Adaptive Relaxation Parameter and Lax--Friedrichs-Type Equilibrium for Hyperbolic Systems

In this paper, a lattice Boltzmann method with an adaptive relaxation parameter and a Lax--Friedrichs-type equilibrium is proposed for hyperbolic systems with source terms. The equilibrium distribution recovers the conservative variables and physical fluxes while incorporating dissipation determined by characteristic-speed bounds. To balance accuracy and robustness, the relaxation parameter is selected from a local smoothness indicator based on characteristic projections. In smooth regions, the parameter approaches the low-dissipation limit, retaining second-order accuracy; near discontinuities, it is automatically reduced to introduce localized dissipation and suppress nonphysical oscillations. The stabilization acts directly through the local collision step and preserves the standard collide-and-stream structure, without a posteriori recomputation or interface-based limiting. Maxwell iteration establishes second-order consistency in smooth regions, and a weighted $L^2$-stability estimate is proved for linear hyperbolic systems with periodic boundary conditions under a standard CFL condition. Numerical experiments for scalar advection, Euler, shallow-water, and reactive Euler equations demonstrate the expected accuracy for smooth solutions and robust resolution of challenging one- and two-dimensional discontinuous problems, including wet--dry fronts and reactive discontinuities. A large-scale simulation of a 2D cellular detonation further demonstrates the capability of the method to resolve long-time multidimensional shock--reaction interactions.

math.NA↗

arXiv2026

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↗

arXiv2026

A Thermodynamically Consistent Cahn-Hilliard-Navier-Stokes Model for Tumor Growth

This work develops a thermodynamically consistent phase-field model for tumor growth based on the energetic variational framework. The model couples the Cahn-Hilliard equations for tumor evolution and nutrient transport with the incompressible Navier-Stokes equations. A first-order time discretization scheme based on the Multiple Scalar Auxiliary Variables (MSAV) approach together with a pressure-correction strategy is proposed to efficiently handle the nonlinear and coupled structure of the system. The proposed scheme is rigorously proved to be unconditionally energy stable and mass conservative. Furthermore, optimal first-order temporal error estimates are established for the tumor phase-field variable, the nutrient concentration, and the fluid velocity. Finally, numerical experiments demonstrate the effectiveness and robustness of the proposed method and verify the theoretical convergence rates.

math.NA↗

arXiv2026

Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth

We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient concentration and admits a dissipative energy law at the continuous level. For the discretisation, we employ a scalar auxiliary variable (SAV) formulation together with a mixed finite element method for the Cahn--Hilliard part and standard conforming finite elements for the reaction-diffusion equation in space, combined with a first-order Euler time-stepping scheme. The resulting method is unconditionally energy-stable, mass-preserving, and inherits a discrete energy dissipation law associated with the SAV-based approximate energy functional, while requiring the solution of only linear systems at each time step. Under suitable regularity assumptions on the exact solution, we derive rigorous error estimates in $L^2$, $H^1$, and $L^\infty$ norms, establishing first-order accuracy in time and optimal-order accuracy in space. A key step in this analysis is the proof of boundedness of the numerical solutions in $L^\infty$. Numerical experiments validate the theoretical convergence rates and demonstrate the robustness of the method in capturing characteristic phenomena such as aggregation and chemotactic tumour growth.

math.NA↗

arXiv2026

Bridging What the Model Thinks and How It Speaks: Expressive Speech Generation via Self-Aware Intent-Realization Alignment

Speech Language Models (SLMs) exhibit strong semantic understanding, yet often fail to translate this capacity into expressive acoustic realization, producing speech with flattened prosody and misaligned emotion. We identify this mismatch as the semantic understanding-acoustic realization gap. Existing approaches typically rely on externally specified proxies, such as emotion labels or style prompts, which require annotations and struggle to capture dynamically evolving expressive intent throughout dialogue. To overcome these limitations, we propose SASLM (Self-Aware Speech Language Model), a proxy-free framework that bridges what the model thinks and how it speaks through self-aware intent-realization alignment: (1) Intent-Aware Bridging self-distills expressive intent from the model's own evolving semantic generation states via a Variational Information Bottleneck (VIB), thereby guiding expressive speech realization without external expressive supervision; while (2) Realization-Aware Alignment reflectively aligns generated acoustics with intended expression through self-reward optimization, progressively improving intent-realization consistency during speech generation. Despite using only 3B parameters and 800 hours of expressive speech data, SASLM achieves state-of-the-art performance on EchoMind among open-source systems, surpassing models over 10 times larger and approaching commercial systems.

cs.CL↗

arXiv2026

A Regularized Auxiliary Variable (RAV) Approach for Gradient Flows

In this paper, we propose a regularized auxiliary variable (RAV) approach and construct accurate and robust time-discrete schemes for a large class of gradient flows. By introducing an auxiliary variable $r=0$ and constructing an auxiliary equation that naturally fits into the energy relation, the numerical solution $r^{n+1}$ of the auxiliary variable is corrected at each time step to preserve consistency with the original system. The developed RAV scheme satisfies unconditional energy stability with respect to the original variables, and in certain cases the original energy law can be directly recovered. Furthermore, we obtain a uniform bound on the norm of the numerical solution, which allows us to establish the optimal error estimate in $L^\infty(0,T;H^2)$ for the second-order scheme without any restriction on the time step. We present ample numerical results, including comparisons with the scalar auxiliary variable (SAV) approach, to demonstrate the accuracy and effectiveness of the proposed RAV approach.

math.NA↗

arXiv2026

A Scalable Benchmark for Repository-Oriented Long-Horizon Conversational Context Management

In recent years, large language models (LLMs) have advanced rapidly, substantially enhancing their code understanding and generation capabilities and giving rise to powerful code assistants. However, in practical repository development, excessively long-horizon conversational context may overwhelm models, causing the loss of critical information and degraded performance, thereby limiting the utility of code assistants. Existing context management methods proposed to mitigate this context dilemma primarily target general-purpose conversations, while repository-oriented solutions remain largely unexplored, which is largely due to the lack of reliable evaluation benchmarks. To bridge this gap, we present LoCoEval, the first long-horizon conversational context management benchmark tailored to repository-oriented development scenarios. Adhering to three key principles, LoCoEval is constructed via an LLM-driven pipeline that generates realistic and diverse repository-oriented conversations, capturing key interaction patterns such as iterative requirements, noisy input, and retrospective questions. We evaluate 7 baselines, including 4 representative context management methods, using 3 advanced backbone LLMs on LoCoEval. The results reveal substantial challenges faced by standalone LLMs and existing approaches, especially memory systems, in repository-oriented conversational scenarios. To address these limitations, we further propose an improved method integrating conversational and repository information into a unified memory, which outperforms all baselines (*Oracle* excluded) and demonstrates robustness. Additionally, we investigated the impact of various factors on method performance, providing actionable insights for future research.

cs.SE↗

arXiv2025

Unconditionally stable Gauge-Uzawa finite element schemes for the chemo-repulsion-Navier-Stokes system

This paper investigates a Gauge-Uzawa finite element method (GU-FEM) for the two-dimensional chemo-repulsion-Navier-Stokes (CRNS) system. The proposed approach establishes a fully discrete projection framework that integrates the advantages of both canonical and Uzawa-type formulations while preserving variational consistency. The method possesses two notable advantages: (1) it requires no initial pressure value; (2) it avoids artificial pressure boundary conditions and thus reduces computational cost. Furthermore, the scheme is shown to be unconditionally energy stable, and we establish unique solvability together with optimal error estimates for cell density, chemical concentration, and fluid velocity. Finally, several numerical experiments are provided to validate the accuracy, stability, and efficiency of the proposed method.

math.NA↗

arXiv2025

Fully discrete finite element approximation for the projection method to solve the Chemotaxis-Fluid System

In this paper, we investigate a chemotaxis-fluid interaction model governed by the incompressible Navier-Stokes equations coupled with the classical Keller-Segel chemotaxis system. To numerically solve this coupled system, we develop a pressure-correction projection finite element method based on a projection framework. The proposed scheme employs a backward Euler method for temporal discretization and a mixed finite element method for spatial discretization. Nonlinear terms are treated semi-implicitly to enhance computational stability and efficiency. We further establish rigorous error estimates for the fully discrete scheme, demonstrating the convergence of the numerical method. A series of numerical experiments are conducted to validate the stability, accuracy, and effectiveness of the proposed method. The results confirm the scheme's capability to capture the essential dynamical behaviors and characteristic features of the chemotaxis-fluid system.

math.NA↗

arXiv2025

A Phase-Field Model for Vesicle Membranes Incorporating Area-Difference Elasticity

This paper presents a phase-field model for simulating the three-dimensional deformation of vesicle membranes, incorporating area-difference elasticity, with constraints on bulk volume and surface area. We develop efficient numerical schemes based on the Fourier-spectral method for spatial discretization and temporal evolution. The model successfully captures a wide variety of steady-state vesicle shapes. The numerical experiments demonstrate that by tuning the simulation parameters, the vesicle can transition from a simple discocyte shape to a complex, multi-armed starfish-like and nested configuration. These results highlight the crucial role of area-difference elasticity in determining vesicle morphology.

math.NA↗

arXiv2025

Feedback approximate controllability of blowup points for the heat equation with anti-interference blowup profile

This paper is concerned with a feedback approximate controllability problem of blowup points for the heat equation. We show that the system is approximately controllable for blowup points with feedback controls and the feedback operator is bounded at any time before blowup. It is also proved that the blowup profile for feedback controllability of blowup points is stable with respect to initial data. That is, suppose that the initial data has a very small perturbation, the blowup profiles also have tiny changes. More precisely, it just undergoes a tiny translation in space and time. This means that our feedback strategy is anti-interference.

math.OC↗

arXiv2025

Linear Relaxation Schemes with Asymptotically Compatible Energy Law for Time-Fractional Phase-Field Models

In this paper, we propose a variable time-step linear relaxation scheme for time-fractional phase-field equations with a free energy density in general polynomial form. The $L1^{+}$-CN formula is used to discretize the fractional derivative, and an auxiliary variable is introduced to approximate the nonlinear term by directly solving algebraic equations rather than differential-algebraic equations as in the invariant energy quadratization (IEQ) and the scalar auxiliary variable (SAV) approaches. The developed semi-discrete scheme is second-order accurate in time, and the inconsistency between the auxiliary and the original variables does not deteriorate over time. Furthermore, we take the time-fractional volume-conserved Allen-Cahn equation, the time-fractional Cahn-Hilliard equation, and the time-fractional Swift-Hohenberg equation as examples to demonstrate that the constructed schemes are energy stable and that the discrete energy dissipation law is asymptotically compatible with the classical one when the fractional-order parameter $α\rightarrow 1^{-}$. Several numerical examples demonstrate the effectiveness of the proposed scheme. In particular, numerical results confirm that the auxiliary variable remains well aligned with the original variable, and the error between them does not continue to increase over time before the system reaches steady state.

math.NA↗

arXiv2025

Second-Order Linear Relaxation Schemes for Time-Fractional Phase-Field Models

This work uses a linear relaxation method to develop efficient numerical schemes for the time-fractional Allen-Cahn and Cahn-Hilliard equations. The L1+-CN formula is used to discretize the fractional derivative, and an auxiliary variable is introduced to approximate the nonlinear term by solving an algebraic equation rather than a differential equation as in the invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches. The proposed semi-discrete scheme is linear, second-order accurate in time, and the inconsistency between the auxiliary and the original variables does not deteriorate over time. Furthermore, we prove that the scheme is unconditionally energy stable. Numerical results demonstrate the effectiveness of the proposed scheme.

math.NA↗

arXiv2025

A thermodynamically consistent phase-field model for mass transport with interfacial reaction and deformation

In this paper, a thermodynamically consistent phase-field model is proposed to describe the mass transport and reaction processes of multiple species in a fluid. A key feature of this model is that reactions between different species occur only at the interface, and may induce deformation of the interface. For the governing equations derived based on the energy variational method, we propose a structure-preserving numerical scheme that satisfies the mass conservation and energy dissipation laws at the discrete level. Furthermore, we carry out a rigorous error analysis of the time-discrete scheme for a simplified case. A series of numerical experiments are conducted to validate the effectiveness of the model as well as the accuracy and stability of the scheme. In particular, we simulate microvessels with straight and bifurcated structures to illustrate the risk of microaneurysm formation.

math.NA↗

arXiv2024

Homogenization principle and numerical analysis for fractional stochastic differential equations with different scales

This work is concerned with fractional stochastic differential equations with different scales. We establish the existence and uniqueness of solutions for Caputo fractional stochastic differential systems under the non-Lipschitz condition. Based on the idea of temporal homogenization, we prove that the homogenization principle (averaging principle) holds in the sense of mean square ($L^2$ norm) convergence under a novel homogenization assumption. Furthermore, an Euler-Maruyama scheme for the non-autonomous system is constructed and its numerical error is analyzed. Finally, two numerical examples are presented to verify the theoretical results. Different from the existing literature, we demonstrate the computational advantages of the homogenized autonomous system from a numerical perspective.

math.NA↗

arXiv2024

Revisiting AGN Placement on the BPT Diagram: A Spectral Decomposition Approach

Traditional single-fibre spectroscopy provides a single galaxy spectrum, forming the basis for crucial parameter estimation. However, its accuracy can be compromised by various sources of contamination, such as the prominent \Ha~emission line originating from both Star-Forming (SF) regions and non-Star-Forming regions (NonSF), including Active Galactic Nuclei (AGN). The potential to dissect a spectrum into its SF and NonSF constituents holds the promise of significantly enhancing precision in parameter estimates. In contrast, Integral Field Unit (IFU) surveys present a solution to minimize contamination. These surveys examine spatially localized regions within galaxies, reducing the impact of mixed sources. Although an IFU survey's resulting spectrum covers a smaller region of a galaxy than single-fibre spectroscopy, it can still encompass a blend of heterogeneous sources. Our study introduces an innovative model informed by insights from the MaNGA IFU survey. This model enables the decomposition of galaxy spectra, including those from the Sloan Digital Sky Survey (SDSS), into SF and NonSF components. Applying our model to these survey datasets produces two distinct spectra, one for SF and another for NonSF components, while conserving flux across wavelength bins. When these decomposed spectra are visualized on a BPT diagram, interesting patterns emerge. There is a significant shift in the placement of the NonSF decomposed spectra, as well as the emergence of two distinct clusters in the LINER and Seyfert regions. This shift highlights the key role of SF `contamination' in influencing the positioning of NonSF spectra within the BPT diagram.

astro-ph.GA↗