arXiv subjects

Haijun Wu

Publications and source records attributed to Haijun Wu.

At least 19 recordsLinked to original sources

arXiv2026

Polynomial preserving recoveries of edge element method on Cartesian grids for the time-harmonic Maxwell equations with large wave number

This paper considers the lowest-order first type N\'{e}d\'{e}lec edge element method (EEM) on Cartesian grids for the three-dimensional time-harmonic Maxwell equations with a large wave number. New polynomial preserving recovery (PPR) operators are proposed for the curl of the edge element solution and for the solution itself, respectively. Under the condition that $\kappa^3 h^2 C_{\mathrm{sol}}$ is sufficiently small, second-order superconvergence estimates are proved for both the recovered curl and the recovered solution, where $\kappa$ is the wave number, $h$ is the mesh size, and $C_{\mathrm{sol}}$ is a stability constant associated with the Maxwell solution operator. In particular, the analysis shows that the proposed PPR procedures cannot mitigate the well-known pollution effect inherent to the EEM. To reduce the pollution error, we further propose a new continuous interior penalty edge element method (CIP-EEM) that incorporates an additional normal-jump penalty term. It is shown that by appropriately choosing the penalty parameters, the new CIP-EEM can improve the phase error by two orders in $\kappa h$. Numerical experiments are presented to confirm the theoretical superconvergence results and to demonstrate that the CIP-EEM can effectively reduce the pollution error in the high-frequency regime.

math.NA↗

arXiv2026

Mr.LHDR: A Benchmark for Multimodal Real-World Long-Horizon Deep Research Agents

Deep research agents are increasingly capable of web search, tool use, multimodal evidence analysis, and information synthesis. However, existing benchmarks mainly evaluate medium-horizon exploration and rarely test whether agents can sustain long, dependency-heavy research processes. We introduce Mr.LHDR (Multimodal real-world Long-Horizon Deep Research), a benchmark for evaluating real-world deep research over long, irreducible chains of interdependent evidence across eight categories. Each question is constructed from a hidden Node-Relation graph and requires an average of 12.1 necessary intermediate conclusions with a mean dependency depth of 10.4 before reaching a short, unique, and verifiable answer. Questions incorporate multimodal evidence, including images, maps, PDFs, logos, charts, tables, and video frames, with at least one non-text element that changes the reasoning state. Mr.LHDR evaluates both final answers and the correctness of intermediate conclusions under annotated dependencies. We evaluate general models, deep research systems, and agent frameworks using Overall Accuracy (OA), Strict Accuracy (SA), Checklist Score (CS), and Dependency-Aware Checklist Score (DACS). Results show that even the strongest system achieves only 43.1% OA and 34.3% SA, indicating that final-answer accuracy substantially overestimates complete research success. Removing images reduces DACS by 12.6 points, demonstrating the importance of multimodal evidence, while SA consistently declines as reasoning chains become longer. These findings reveal sustained, dependency-consistent evidence integration, rather than isolated fact retrieval, as a key bottleneck for current deep research agents.

cs.AI↗

arXiv2026

The effect of numerical integration in the FEM for elliptic problems with mixed boundary conditions

This paper investigates the impact of quadrature accuracy for volume and face integrals in the finite element method using $p$-th order polynomial shape functions for elliptic problems with mixed Dirichlet and Robin boundary conditions. The optimal $p$-th order $H^1$-convergence is maintained when numerical integration with algebraic precision at least $2p-2$ for volume terms and at least $2p-1$ for face terms is adopted. For $L^2$-error, we achieve optimal $O(h^{p+1})$ convergence when using quadrature rules of precision no less than $\max\{p,2p-2\}$ for volume terms and no less than $2p-1$ for face terms. Of particular significance, we present two examples to show that the above result on $L^2$-error is sharp for the linear FEM ($p=1$). When reduced to the case of Dirichlet boundary condition, our results yield improved dependence on the given data compared to the classical results established by Ciarlet, \textit{et al}. Numerical experiments are provided to illustrate the theoretical findings and confirm the necessity of specified quadrature accuracy and data regularity.

math.NA↗

arXiv2026

HeadRank: Decoding-Free Passage Reranking via Preference-Aligned Attention Heads

Decoding-free reranking methods that read relevance signals directly from LLM attention weights offer significant latency advantages over autoregressive approaches, yet suffer from attention score homogenization: middle-context documents receive near-identical scores, destroying the fine-grained distinctions required for ranking. We propose HeadRank, a framework that lifts preference optimization from discrete token space into the continuous attention domain through entropy-regularized head selection, hard adjacent-level preference pairs, and a distribution regularizer that jointly sharpen discriminability in the homogenized middle zone. Depth truncation at the deepest selected layer further reduces inference to $\mathcal{O}(1)$ forward passes. Across 14 benchmarks on three Qwen3 scales (0.6B--4B) using only 211 training queries, HeadRank achieves the highest average NDCG@10 at every scale, outperforming both generative and decoding-free baselines on the majority of benchmarks with 100\% formatting success. At 4B, 57.4\% of relevant middle-zone documents reach the top quartile versus 14.2\% for irrelevant ones -- a 43-percentage-point selectivity gap that demonstrates the effectiveness of attention-space preference alignment for listwise reranking.

cs.IR↗

arXiv2025

When & How to Write for Personalized Demand-aware Query Rewriting in Video Search

In video search systems, user historical behaviors provide rich context for identifying search intent and resolving ambiguity. However, traditional methods utilizing implicit history features often suffer from signal dilution and delayed feedback. To address these challenges, we propose WeWrite, a novel Personalized Demand-aware Query Rewriting framework. Specifically, WeWrite tackles three key challenges: (1) When to Write: An automated posterior-based mining strategy extracts high-quality samples from user logs, identifying scenarios where personalization is strictly necessary; (2) How to Write: A hybrid training paradigm combines Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO) to align the LLM's output style with the retrieval system; (3) Deployment: A parallel "Fake Recall" architecture ensures low latency. Online A/B testing on a large-scale video platform demonstrates that WeWrite improves the Click-Through Video Volume (VV$>$10s) by 1.07% and reduces the Query Reformulation Rate by 2.97%.

cs.IR↗

arXiv2025

Tailoring ultra-high-order optical skyrmions

Skyrmions, as quasiparticles with topological spin textures, has recently garnered great attention for both condensed matter and structured wave communities, promising next-generation large-density robust information technologies. However, a big challenge to this end is that the generation of high-order skyrmions is elusive in any physical systems. Here, we propose the method to create and control ultra-high-order skyrmions (skyrmion number up to $400^{th}$) in a structured light system. We also experimentally control the topological state transition between bimeron and skyrmion, arbitrarily tailor the transverse size of an arbitrary-order skyrmionic beam independent of topological number, and ensure the topological stability upon propagation. Our work offers solutions for topologically resilient communication and memory with much enhanced information capacity.

physics.optics↗

arXiv2025

Preasymptotic error estimates of higher-order EEM for the time-harmonic Maxwell equations with large wave number

The time-harmonic Maxwell equations with impedance boundary condition and large wave number are discretized using the second-type N\'{e}d\'{e}lec's edge element method (EEM). Preasymptotic error bounds are derived, showing that, under the mesh condition $\kappa^{2p+1}h^{2p}$ being sufficiently small, the error of the EEM of order $p$ in the energy norm is bounded by $\mathcal{O}\big(\kappa^{p}h^p + \kappa^{2p+1}h^{2p}\big)$, while the error in the $\kappa$-scaled $\boldsymbol{L}^2$ norm is bounded by $\mathcal{O}\big((\kappa h)^{p+1} + \kappa^{2p+1} h^{2p}\big)$. Here, $\kappa$ is the wave number and $h$ is the mesh size. Numerical tests are provided to illustrate our theoretical results.

math.NA↗

arXiv2025

Super-resolution optical trapping of multiple cold atoms

Arrays of optical tweezers form the backbone of neutral atoms analog and digital quantum processors. However, the inter-trap distance remains generally much larger than the size of the tweezers to avoid interference-induced trap distortions, limiting the trap density. Here, we report single-atom trapping in four super-resolved tweezers, meaning with a separation below the Sparrow diffraction limit. The optical pattern is generated using superoscillatory phenomenon leading to subwavelength traps with full control of the trap relative phases. We investigate two sets of relative phases that impede or allow the hopping and the reshuffling of atoms. We envision that superoscillatory light structuring will bridge the gap between large-distance traps generated by tweezer arrays and short-distance traps formed with optical lattices.

physics.atom-ph↗

arXiv2025

Optical skyrmion lattices accelerating in free space

Generation and propagation of optical skyrmions provide a versatile plalform for topologically nontrivial optical informatics and light-matter interactions, but their acceleration along curved trajectories is to be studied. In this study, we experimentally demonstrate the first accelerating skyrmion lattices conveyed by Airy structured light, characterized by topologically stable skyrmion textures with self-acceleration along parabolic trajectories. We show that the skyrmion unit cell can maintain a Skyrme number $|N_\text{sk}|>0.9$ within a propagation range of $\pm1.22\ z_R$ upon parabolic acceleration. Notably, the meron structure remains $|N_\text{sk}|$ stable within $0.5\pm0.02$ over a significantly extended range of $\pm3.06\ z_R$. Our work provides a new potential carrier for topologically robust information distribution, particle sorting and manipulation.

physics.optics↗

arXiv2024

Photonic torons, topological phase transition and tunable spin monopoles

Creation and control of topological complex excitations play crucial roles in both fundamental physics and modern information science. Torons are a sophisticated class of 3D chiral polar topological structures with both skyrmionic quasiparticle textures and monopole point defects, so far only observed in liquid crystal nonpolar models. Here, we experimentally construct torons with the photonic spin of vector structured light and demonstrate the topological phase transitions among diverse topological states: torons, hopfions, skyrmioniums and monopole pairs. We can also continually tune the toron's chirality and the helical spin textures of emerging monopole pairs. The birth of photonic torons and tunable monopoles opens a flexible platform for studying nontrivial light-matter interaction and topological informatics.

physics.optics↗

arXiv2024

Spintwistronics: Photonic bilayer topological lattices tuning extreme spin-orbit interactions

Twistronics, the manipulation of Moir\'e superlattices via the twisting of two layers of two-dimensional (2D) materials to control diverse and nontrivial properties, has recently revolutionized the condensed matter and materials physics. Here, we introduce the principles of twistronics to spin photonics, coining this emerging field spintwistronics. In spintwistronics, instead of 2D materials, the two layers consist of photonic topological spin lattices on a surface plasmonic polariton (SPP) platform. Each 2D SPP wave supports the construction of topological lattices formed by photonic spins with stable skyrmion topology governed by rotational symmetry. By introducing spintwistronics into plasmonics, we demonstrate theoretically and experimentally that two layers of photonic spin lattices can produce Moir\'e spin superlattices at specific magic angles. These superlattices, modulated periodically by the quantum number of total angular momentum, exhibit novel properties-including new quasiparticle topologies, multiple fractal patterns, extremely slow-light control, and more-that cannot be achieved in conventional plasmonic systems. As a result, they open up multiple degrees of freedom for practical applications in quantum information, optical data storage and chiral light-matter interactions.

physics.optics↗

arXiv2024

Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number

Preasymptotic error estimates are derived for the linear edge element method (EEM) and the linear $\boldsymbol{H}(\boldsymbol{\mathrm{curl}})$-conforming interior penalty edge element method (CIP-EEM) for the time-harmonic Maxwell equations with large wave number. It is shown that under the mesh condition that $\kappa^3 h^2$ is sufficiently small, the errors of the solutions to both methods are bounded by $\mathcal{O} (\kappa h + \kappa^3 h^2 )$ in the energy norm and $\mathcal{O} (\kappa h^2 + \kappa^2 h^2 )$ in the $\boldsymbol{L}^2$ norm, where $\kappa$ is the wave number and $h$ is the mesh size. Numerical tests are provided to verify our theoretical results and to illustrate the potential of CIP-EEM in significantly reducing the pollution effect.

math.NA↗

arXiv2024

Adaptive Finite Element Method for a Nonlinear Helmholtz Equation with High Wave Number

A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for the NLH problem, a priori stability and error estimates are established for the FEM on shape regular meshes including the case of locally refined meshes. Then a posteriori upper and lower bounds using a new residual-type error estimator, which is equivalent to the standard one, are derived for the FE solutions to the NLH problem. These a posteriori estimates have confirmed a significant fact that is also valid for the NLH problem, namely the residual-type estimator seriously underestimates the error of the FE solution in the preasymptotic regime, which was first observed by Babu\v{s}ka et al. [Int J Numer Methods Eng 40 (1997)] for a one-dimensional linear problem. Based on the new a posteriori error estimator, both the convergence and the quasi-optimality of the resulting adaptive finite element algorithm are proved the first time for the NLH problem, when the initial mesh size lying in the preasymptotic regime. Finally, numerical examples are presented to validate the theoretical findings and demonstrate that applying the continuous interior penalty (CIP) technique with appropriate penalty parameters can reduce the pollution errors efficiently. In particular, the nonlinear phenomenon of optical bistability with Gaussian incident waves is successfully simulated by the adaptive CIPFEM.

math.NA↗

arXiv2023

An Unfitted Interface Penalty DG--FE Method for Elliptic Interface Problems

We propose an unfitted interface penalty Discontinuous Galerkin-Finite Element Method (UIPDG-FEM) for elliptic interface problems. This hybrid method combines the interior penalty discontinuous Galerkin (IPDG) terms near the interface-enforcing jump conditions via Nitsche method-with standard finite elements away from the interface. The UIPDG-FEM retains the flexibilities of IPDG, particularly simplifying mesh generation around complex interfaces, while avoiding its drawback of excessive number of global degrees of freedom. We derive optimal convergence rates independent of interface location and establish uniform flux error estimates robust to discontinuous coefficients. To deal with conditioning issues caused by small cut elements, we develop a robust two-dimensional merging algorithm that eliminates such elements entirely, ensuring the condition number of the discretized system remains independent of interface position. A key feature of the algorithm is a novel quantification criterion linking the threshold for small cuts to the product of the maximum interface curvature and the local mesh size. Numerical experiments confirm the theoretical results and demonstrate the effectiveness of the proposed method.

math.NA↗

arXiv2023

Higher-order FEM and CIP-FEM for Helmholtz equation with high wave number and perfectly matched layer truncation

The high-frequency Helmholtz equation on the entire space is truncated into a bounded domain using the perfectly matched layer (PML) technique and subsequently, discretized by the higher-order finite element method (FEM) and the continuous interior penalty finite element method (CIP-FEM). By formulating an elliptic problem involving a linear combination of a finite number of eigenfunctions related to the PML differential operator, a wave-number-explicit decomposition lemma is proved for the PML problem, which implies that the PML solution can be decomposed into a non-oscillating elliptic part and an oscillating but analytic part. The preasymptotic error estimates in the energy norm for both the $p$-th order CIP-FEM and FEM are proved to be $C_1(kh)^p + C_2k(kh)^{2p} +C_3 E^{\rm PML}$ under the mesh condition that $k^{2p+1}h^{2p}$ is sufficiently small, where $k$ is the wave number, $h$ is the mesh size, and $E^{\rm PML}$ is the PML truncation error which is exponentially small. In particular, the dependences of coefficients $C_j~(j=1,2)$ on the source $f$ are improved. Numerical experiments are presented to validate the theoretical findings, illustrating that the higher-order CIP-FEM can greatly reduce the pollution errors.

math.NA↗

arXiv2022

Finite Element Method for a Nonlinear PML Helmholtz Equation with High Wave Number

A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM). Wave-number-explicit stability and regularity estimates and the exponential convergence are proved for the nonlinear truncated PML problem. Preasymptotic error estimates are obtained for the FEM, where the logarithmic factors in h required by the previous results for the NLH with impedance boundary condition are removed in the case of two dimensions. Moreover, local quadratic convergences of the Newton's methods are derived for both the NLH with PML and its FEM. Numerical examples are presented to verify the accuracy of the FEM, which demonstrate that the pollution errors may be greatly reduced by applying the interior penalty technique with proper penalty parameters to the FEM. The nonlinear phenomenon of optical bistability can be successfully simulated.

math.NA↗

arXiv2022

Topological Transformation and Free-Space Transport of Photonic Hopfions

Structured light fields embody strong spatial variations of polarisation, phase and amplitude. Understanding, characterization and exploitation of such fields can be achieved through their topological properties. Three-dimensional (3D) topological solitons, such as hopfions, are 3D localized continuous field configurations with nontrivial particle-like structures, that exhibit a host of important topologically protected properties. Here, we propose and demonstrate photonic counterparts of hopfions with exact characteristics of Hopf fibration, Hopf index, and Hopf mapping from real-space vector beams to homotopic hyperspheres representing polarisation states. We experimentally generate photonic hopfions with on-demand high-order Hopf indices and independently controlled topological textures, including N\'eel-, Bloch-, and anti-skyrmionic types. We also demonstrate a robust free-space transport of photonic hopfions, thus, showing potential of hopfions for developing optical topological informatics and communications.

physics.optics↗

arXiv2022

Dispersion Analysis of CIP-FEM for Helmholtz Equation

When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number $k$ increases, known as `pollution effect' which is directly related to the phase difference between the exact and numerical solutions, caused by the numerical dispersion. In this paper, we propose a dispersion analysis for the continuous interior penalty finite element method (CIP-FEM) and derive an explicit formula of the penalty parameter for the $p^{\rm th}$ order CIP-FEM on tensor product (Cartesian) meshes, with which the phase difference is reduced from $\mathcal{O}\big(k(kh)^{2p}\big)$ to $\mathcal{O}\big(k(kh)^{2p+2}\big)$. Extensive numerical tests show that the pollution error of the CIP-FE solution is also reduced by two orders in $kh$ with the same penalty parameter.

math.NA↗