生成时间: 2026年05月15日 07:00:37

重点关注论文数量: 0

了解领域论文数量: 1

不相关论文数量: 17

了解领域论文（摘要翻译）

1. 基于T-E表述的薄高温超导壳磁化建模

T-E formulation-based modeling of thin HTS shell magnetization

作者: Leonid Prigozhin, Vladimir Sokolovsky

类别: cond-mat.supr-con, math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14818v1

链接: http://arxiv.org/abs/2605.14818v1

摘要翻译

中文标题: 基于T-E表述的薄高温超导壳磁化建模

摘要翻译: 薄膜磁化数值建模方法主要侧重于计算电流密度分布。II类超导体的高度非线性电流-电压特性使得电场的精确计算变得极为复杂。先前针对扁平超导薄膜推导的基于T-E表述的混合有限元方法，能够同时准确确定这两个变量。该方法的另一个优势是计算区域仅限于薄膜自身：无需对周围空间进行网格划分。薄壳近似将问题简化为二维问题。 本研究将T-E表述和数值方法推广至带金属基底的非扁平超导壳。我们通过若干测试算例（包括模拟球体磁化）验证了该方法。随后将该方法应用于一个圆柱形磁流体动力泵的现实模型，并计算了所产生的开路电压。

不相关论文（基本信息）

1. 粘弹性波导中稳健色散曲线计算的自适应同伦延拓方法：保证分支标识连续性

Adaptive homotopy continuation for robust dispersion curve computation in viscoelastic waveguides: guaranteed branch identity continuity

作者: Dong Xiao, Zahra Sharif Khodaei, M. H. Aliabadi

类别: math.NA, physics.comp-ph

发布日期: 2026-05-14

arXiv ID: 2605.15089v1

链接: http://arxiv.org/abs/2605.15089v1

摘要: This paper presents the first systematic application of a material homotopy continuation framework for efficient, automated computation of dispersion curves in viscoelastic waveguides of arbitrary cross-section. A material homotopy continuously maps the original lossy problem to an auxiliary lossless one via an attenuation parameter s in [0,1], addressing the core challenges of the non-Hermitian eigenvalue problem. Grounded in analytic perturbation theory, the method guarantees branch identity continuity–a one-to-one correspondence between solutions at s=0 and s=1–provided the real-parameter path does not cross any exceptional points. Under a Type I exceptional point topology, physical mode labels established at the elastic stage remain valid at the viscoelastic stage without post-processing, yielding the characteristic real-part veering with imaginary-part crossing. The decoupling strategy performs reliable mode tracking in the Hermitian regime via adaptive wavenumber refinement, then propagates a sparse set of key solutions to the target viscoelastic state through predictor-corrector homotopy continuation. Numerical examples across symmetric and unsymmetric laminates validate the framework’s robustness and efficiency, with the majority of cases verified at a loss factor of approximately 0.003 and a single symmetric laminate providing additional support at 0.02. For a challenging unsymmetric laminate at a loss factor of 0.05, the method still produces numerically accurate solutions; two complementary diagnostic signatures–an extremely sharp imaginary-part crossing and a discernible discrepancy between spectral group velocity and energy flux velocity–warn of potential label mismatch and guide further analysis.

2. 流形上的Nyström近似

Nyström Approximation on Manifolds

作者: Hantao Nie, Bin Gao, Andi Han, Pratik Jawanpuria, Bamdev Mishra, Zaiwen Wen

类别: math.NA, math.OC

发布日期: 2026-05-14

arXiv ID: 2605.14933v1

链接: http://arxiv.org/abs/2605.14933v1

摘要: Computations on a manifold often involve constructing an operator on the tangent space and computing its inverse, which can be time-consuming in many applications. In order to reduce the computational costs and preserve the benign properties of tangent operators, we develop the Riemannian Nyström approximation on manifolds, a low-rank approximation of tangent operators through subspace projections onto the tangent space. The developed approximation is intrinsically constructed and inherits desirable properties from the classical Nyström approximation, e.g., positive semidefiniteness and approximation errors. Instead of the Gaussian sketching, we introduce the Haar–Grassmann sketching condition with a coordinate-free representation, which remains compatible under isometric vector transport across tangent spaces. Moreover, we propose a randomized Newton-type method for optimization on manifolds in which the linear system is constructed via the Riemannian Nyström approximation. Numerical experiments on the SPD and Grassmann manifolds, together with principal geodesic analysis on real data, illustrate that the proposed approximation reduces the computational cost of operators while maintaining comparable accuracy.

3. 对流-扩散方程柯西问题的最小二乘弱Galerkin有限元格式

A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Convection–Diffusion

作者: Chunmei Wang, Shangyou Zhang

类别: math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14770v1

链接: http://arxiv.org/abs/2605.14770v1

摘要: We introduce and rigorously analyze a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem of convection–diffusion equations. The proposed framework utilizes weak derivatives defined on a class of discontinuous weak functions, enabling the natural treatment of complex boundary conditions and internal interfaces. A key advantage of the least-squares formulation is that it transforms the underlying non-self-adjoint operator into a discrete linear system that is inherently symmetric and positive definite (SPD). We demonstrate the geometric flexibility of the method on arbitrary polygonal and polyhedral partitions. Furthermore, we establish the uniqueness of the numerical solution and derive optimal-order error estimates in a carefully defined discrete energy norm. Extensive numerical tests are presented to confirm the theoretical convergence rates and highlight the algorithm’s robustness and efficiency compared to standard Galerkin approaches.

4. 对称正定张量的特征值界

Eigenbounds of symmetric positive definite tensors

作者: Snigdhashree Nayak, Hemant Sharma, Nachiketa Mishra

类别: math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14768v1

链接: http://arxiv.org/abs/2605.14768v1

摘要: This article introduces an algebraic framework for establishing eigenvalue bounds for symmetric positive definite tensors by leveraging intrinsic invariants, specifically the trace and determinant (resultant). We derive a hierarchy of inequalities via the Arithmetic Mean-Geometric Mean (AM-GM) inequality that yields progressively tighter upper and lower bounds for the tensor spectral radius and smallest eigenvalue. A comprehensive comparative analysis demonstrates that our invariant-based approach significantly outperforms classical coordinate-dependent methods such as the Gershgorin circle theorem. We explicitly show that our bounds remain robust and informative in scenarios where Gershgorin bounds fail, particularly for tensors with negative off-diagonal entries, where algebraic cancellations occur, and higher-order tensors, where combinatorial growth leads to loose estimates. Furthermore, we validate the practical utility of these bounds by applying them to certify the positive definiteness of Lyapunov functions in the stability analysis of nonlinear autonomous systems.

5. 计算三阶张量T-平方根的迭代方法

Iterative Methods for Computing the T-Square Root of Third-Order Tensors

作者: Hemant Sharma, Nachiketa Mishra

类别: math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14748v1

链接: http://arxiv.org/abs/2605.14748v1

摘要: We develop and analyze iterative methods for computing the principal square root of third-order tensors under the T-product framework. Tensor extensions of the Newton iteration (quadratic convergence) and the Denman–Beavers iteration (geometric convergence with simultaneous computation of the inverse square root) are proposed, with rigorous convergence guarantees established via the Fourier-domain block-diagonalization of the T-product. We apply these methods to image processing, introducing Tensor Decorrelated Grayscale conversion, T-Whitening, and optimal color transfer under the T-product geometry. We also formulate the Tensor Bures–Wasserstein distance and prove it defines a valid metric on the space of T-positive definite tensors. Numerical experiments confirm rapid convergence and demonstrate that the proposed tensor-based techniques offer improved structural preservation and cross-channel decorrelation compared to classical methods.

6. 高维偏微分方程的无偏且免二阶训练

Unbiased and Second-Order-Free Training for High-Dimensional PDEs

作者: Jaemin Seo, Surin Lee, Jae Yong Lee

类别: cs.LG, math.NA, math.OC

发布日期: 2026-05-14

arXiv ID: 2605.14643v1

链接: http://arxiv.org/abs/2605.14643v1

摘要: Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, BSDE approaches can avoid the curse of dimensionality and often admit second-order-free training objectives that do not require explicit Hessian evaluations. It has recently been established that the commonly used Euler-Maruyama (EM) time discretization induces an intrinsic bias in BSDE training losses. While high-order schemes such as Heun can fully eliminate this bias, such schemes re-introduce second-order spatial derivatives and incur substantial computational overhead. In this work, we provide a principled analysis of EM-induced loss bias and propose an unbiased, second-order-free training framework that preserves the computational advantages of BSDE methods. Our code is available at https://github.com/seojaemin22/Un-EM-BSDE.

7. 基于光滑余因子方法的直线剖分上样条空间维数计算

Dimension Calculation for Spline Spaces over Rectilinear Partitions via Smoothing Cofactor Method

作者: Bingru Huang, Falai Chen

类别: math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14577v1

链接: http://arxiv.org/abs/2605.14577v1

摘要: This paper presents a general framework for calculating the dimension of spline spaces over arbitrary rectilinear partitions using the smoothing cofactor method. The approach extends existing dimension theory for polynomial splines over T-meshes by introducing the concept of TE-connected components, reducing the problem to the rank computation of explicitly constructible conformality matrices. Furthermore, a new class of rectilinear partitions, termed partitions with disjoint truncated l-edges, is introduced. It is proven that under specific conditions, the dimension of the corresponding spline space attains Schumaker’s lower bound. This shows that the lower bound is attainable for arbitrary degree d and smoothness order mu in certain partition configurations. Numerical examples, including the Morgan-Scott and Yuan-Stillman partitions, validate the effectiveness and generality of the framework for both triangular and non-triangular rectilinear partitions.

8. 基于对称Strang分裂的各向异性孔隙弹性波模拟互易性验证

Verification of reciprocity in anisotropic poroelastic wave simulation using symmetric Strang splitting

作者: Morten Jakobsen, Jose Carcione

类别: math.NA, physics.flu-dyn, physics.geo-ph

发布日期: 2026-05-14

arXiv ID: 2605.14576v1

链接: http://arxiv.org/abs/2605.14576v1

摘要: Poroelastic wave simulations are important for many applications relating fluid flow and wave characteristics in porous rock formations. Reciprocity is a key physical property of wave propagation in porous media that is important for such applications, even when viscous dissipation is present. However, numerical poroelastic simulations often fail to reproduce reciprocal responses because the discretization does not preserve the balance between reversible wave dynamics and irreversible fluid-solid drag. To address this, we formulate the Biot equations in terms of a continuous evolution operator split into a reversible (skew-adjoint) wave part and an irreversible (self-adjoint, non-positive) Darcy part, including the leading-order Johnson-Koplik-Dashen correction. This structure clarifies why reciprocity holds in the continuous equations and how it is easily broken in discrete form. Guided by this interpretation, we construct a symmetric second-order Strang-splitting scheme with half-step source injection. The method conserves energy in the reversible subsystem, treats Darcy dissipation unconditionally stably, and retains Courant limits similar to elastic solvers. Using a staggered pseudo-spectral discretization, we model multimode propagation in 2D VTI media and obtain cross-component reciprocity with a relative L2 misfit approaching machine precision, demonstrating that the discrete scheme inherits the symmetry properties of the continuous evolution operator.

9. DiffPhD: 面向弹性动力学中含丰富接触的投影异质材料的GPU加速统一可微求解器

DiffPhD: A Unified Differentiable Solver for Projective Heterogeneous Materials in Elastodynamics with Contact-Rich GPU-Acceleration

作者: Shih-Yu Lai, Sung-Han Tien, Jui-I Huang, Yen-Chen Tseng, Yi-Ting Chiu, Siyuan Luo, Ziqiu Zeng, Fan Shi, Peter Yichen Chen, Tiantian Liu, Yu-Lun Liu, Bing-Yu Chen

类别: cs.GR, cs.DC, cs.RO, math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14526v1

链接: http://arxiv.org/abs/2605.14526v1

摘要: Differentiable simulation of soft bodies is a foundation for system identification, trajectory optimization, and Real2Sim transfer. Yet, existing methods such as the differentiable Projective Dynamics (DiffPD) struggle when faced with heterogeneous materials with extreme stiffness contrasts, hyperelasticity under large deformations, and contact-rich interactions, which are common scenarios in the real world. We present DiffPhD, a unified GPU-accelerated differentiable Projective Dynamics framework for heterogeneous materials that tackles these intertwined challenges simultaneously. Our key insight is a careful integration of: (i) stiffness-aware projective weights to embed heterogeneity into the global system; (ii) trust-region eigenvalue filtering lifted to the backward pass for stable hyperelastic gradients and a type-II Anderson Acceleration scheme with dual-gate convergence to stabilize forward iteration under large stiffness contrasts; and (iii) a unified GPU pipeline that reuses a single sparse factor across forward, backward, and contact computations, with stiffness-amplified Rayleigh damping folded into the same factor for heterogeneity-aware dissipation at zero recurring cost. DiffPhD achieves strict gradient accuracy while delivering up to an order-of-magnitude speedup over prior differentiable solvers on heterogeneous, hyperelastic, contact-rich benchmarks. Crucially, this speedup does not come at the cost of stability: DiffPhD remains convergent on stiffness contrasts up to 100x where prior PD solvers degrade. This unlocks end-to-end gradient-based optimization on regimes previously bottlenecked by either solver fragility or per-iteration cost – shell–joint composite creatures, soft characters wielding stiff weapons, and soft-gripper robotic manipulation – all handled within a single forward–backward pass.

10. 奇异摄动的神经网络——有限正则性

Neural Networks for Singular Perturbations – Finite Regularity

作者: F. Rohner, Ch. Schwab, C. Xenophontos

类别: math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14459v1

链接: http://arxiv.org/abs/2605.14459v1

摘要: We study finite-element and deep feedforward neural network (DNN for short) expressivity rate bounds for solution sets of a model linear, second order singularly perturbed, elliptic two-point boundary value problem, in Sobolev norms on a bounded interval $(-1,1)$, with explicit dependence on the singular perturbation parameter $\e\in (0,1]$. Emphasis is on low Sobolev regularity of the data, i.e., source term $f$ and reaction coefficient $b$. A proof of $\e$-explicit solution regularity based on exponentially weighted energy-norm bounds is developed, and \emph{$\e$-robust, algebraic expression rate bounds} in Sobolev norms for $\mathbb{P}_1$ Finite-Elements on exponential and Shishkin type meshes is proved. Expression rates for shallow (fixed depth) $\ReLU$-NNs are shown which are robust w.r. to $\e$ and explicit in terms of the NN size. Robust NN expression rate bounds are further studied for deep feedforward DNNs with ReLU and tanh-activations. As in \cite{OSX24_1085}, tanh- and sigmoid-activated sub-NNs allow to include exponential boundary layer functions exactly into the NN feature space, leading to reduced NN sizes. Recent bitstring encoding techniques for deep NNs with ReLU activations afford, still under low data regularity $f,b \in H^1(I)$ \emph{twice the (robust) convergence rate of $\mathbb{P}_1$ Finite-Elements} achievable with ``eXp’’ or Shishkin meshes.

11. 已有不连续面上流体驱动摩擦与拉伸破裂的三维模拟

Three dimensional simulation of fluid-driven frictional and tensile ruptures on existing discontinuities

作者: Brice Lecampion, Sylvain Brisson, Antareep Sarma, Ankit Gupta, Alexis Sáez, Regina Fakhretdinova

类别: physics.geo-ph, math.NA, physics.comp-ph, physics.flu-dyn

发布日期: 2026-05-14

arXiv ID: 2605.14397v1

链接: http://arxiv.org/abs/2605.14397v1

摘要: We present an implicit, fully-coupled hydro-mechanical solver for the three dimensional simulation of fluid-driven rupture propagation along existing discontinuities. The solver handles simultaneously frictional slip (shear failure) and tensile opening (hydraulic fracture) along arbitrary intersecting fractures and faults in a linearly elastic and impermeable rock matrix. The spatial discretization combines a collocation displacement discontinuity boundary element method for quasi-static elasticity with a Galerkin finite element method for nonlinear pore-fluid diffusion along the discontinuities. Frictional and tensile failure are governed by a poro-elastoplastic cohesive zone like interface law with slip-weakening friction, dilatancy, and tensile strength degradation, integrated via an elastic predictor-plastic corrector scheme. The strong nonlinear coupling between mechanical deformation and fracture permeability is handled via adaptive implicit time-stepping. Efficient block preconditioning of the coupled tangent system, leveraging hierarchical matrix representations of the boundary element operator, is essential to achieve robustness across the full range of fracture behaviors. Accuracy and convergence are demonstrated against a comprehensive suite of analytical and semi-analytical solutions of increasing complexity: fluid-driven frictional ruptures under constant and slip-weakening friction, dilatant ruptures with permeability changes, and penny shaped hydraulic fractures spanning the viscosity-to-toughness transition. The solver is further assessed on two multi-fracture configurations: injection into three intersecting fractures, and a height-confined hydraulic fracture intersecting a strike-slip fault. The proposed framework simultaneously captures frictional slip, dilatancy, permeability evolution, and tensile opening.

12. 凸向量优化中$\ell_p$范数极小化的收敛速率

Convergence Rates for $\ell_p$ Norm Minimization in Convex Vector Optimization

作者: Mohammed Alshahrani

类别: math.OC, math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14324v1

链接: http://arxiv.org/abs/2605.14324v1

摘要: We analyze convergence rates of norm-minimization-based outer approximation algorithms for convex vector optimization when the scalarization uses an $\ell_p$ norm with $p \in (1,\infty)$. While the Euclidean case ($p=2$) achieves the optimal rate $O(k^{2/(1-q)})$, the behavior under general $\ell_p$ norms has remained open. A direct approach via the modulus of smoothness yields only the weaker exponent $\min(p,2)$, which degrades for $1 < p < 2$. We prove that the Hausdorff approximation error satisfies $δ_H(P_k, A) = O(k^{2/(1-q)})$ for \emph{every} $p \in (1,\infty)$, where $q$ is the number of objectives and $k$ is the iteration count. The proof introduces a Euclidean intermediary technique that exploits the ambient inner product structure of $\R^q$ to obtain a quadratic bound on the hyperplane distance, bypassing the $\ell_p$ smoothness limitation; norm equivalence then converts this to any $\ell_p$ metric at the cost of only a dimension-dependent constant, not a loss of exponent. Numerical experiments confirm the $p$-independent rate predicted by the theory.

13. 凸向量优化中基于范数极小化的外部逼近的自适应度量

Adaptive Metrics for Norm-Minimization-Based Outer Approximation in Convex Vector Optimization

作者: Mohammed Alshahrani

类别: math.OC, math.NA

发布日期: 2026-05-14

arXiv ID: 2605.14320v1

链接: http://arxiv.org/abs/2605.14320v1

摘要: We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation error in a fixed Euclidean norm. This enables the algorithm to exploit problem geometry dynamically. Our approach rests on two theoretical foundations. First, we prove that the improved Euclidean convergence rate $O(k^{2/(1-q)})$ – previously known only for the standard $\ell_2$ norm – extends to all fixed inner-product norms. Second, we establish a dispersion theorem showing that the cut normals generated by the algorithm naturally spread across all directions when the upper image has a strictly convex boundary with bounded curvature. This geometric condition guarantees that the adaptive metric remains well-conditioned throughout execution. Building on these results, we derive explicit convergence bounds that quantify how metric conditioning influences the Hausdorff error estimates. Numerical experiments validate the theoretical rates and demonstrate that adaptive metrics achieve 31–33% fewer iterations than the fixed Euclidean norm on problems with curved Pareto fronts. Our results provide a rigorous foundation for adaptive metric selection in convex vector optimization.

14. 基于小波的 Koopman 分析观测量：一个扩展的动态模式分解框架

Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework

作者: Cankat Tilki, Serkan Gugercin

类别: math.NA, cs.AI, math.DS, math.FA

发布日期: 2026-05-14

arXiv ID: 2605.14224v1

链接: http://arxiv.org/abs/2605.14224v1

摘要: We present an in-depth analysis of the Koopman semigroup via wavelet transform. Towards this goal, we start by introducing the wavelet-based observables and show that they are eigenfunctions of the Koopman semigroup when this semigroup is considered over the Banach space of continuous functions on a compact forward-invariant set endowed with the supremum norm. We then construct closed-form expressions of the action of the Koopman semigroup and its resolvent in terms of these observables. To approximate the action of Koopman semigroup numerically, we combine Extended Dynamic Mode Decomposition (EDMD) with the proposed wavelet-based observables leading to the Wavelet Dynamic Mode Decomposition via Continuous Wavelet Transform (cWDMD) algorithm. We validate our theoretical results on two numerical examples.

15. 双鞍点系统的分类

Classification of Double Saddle-Point Systems

作者: Susanne Bradley, Chen Greif

类别: math.NA

发布日期: 2026-05-13

arXiv ID: 2605.14157v1

链接: http://arxiv.org/abs/2605.14157v1

摘要: We offer a classification of a broad and practically relevant class of symmetric double saddle-point system. At the core of the paper is the division of the associated matrices into block-arrow'' and block-tridiagonal’’ forms. We describe relevant applications, invertibility conditions, spectral properties, and block preconditioners. Our discussion is kept within a general framework rather than tailored to specific applications.

16. 面向目标的指标1线性端口哈密顿微分-代数方程的时间自适应

Goal-Oriented Time Adaptivity for Linear Port-Hamiltonian Differential-Algebraic Equations of Index~1

作者: Aashutosh Sharma, Andreas Bartel, Manuel Schaller

类别: math.NA

发布日期: 2026-05-13

arXiv ID: 2605.14082v1

链接: http://arxiv.org/abs/2605.14082v1

摘要: Port-Hamiltonian systems provide a highly-structured framework for modeling of physical systems. By definition, they encode a balance equation relating energy changes to supplied and dissipated energy. Capturing this energy balance in discrete approximations is a fundamental challenge and often has been achieved by designing particular schemes such as discrete gradient methods. In this work, we propose an approach that controls the energy balance violation for port-Hamiltonian differential algebraic equations via time adaptivity using a posteriori grid refinement techniques based on the dual weighted residual method. In particular, we show how one may leverage the port-Hamiltonian structure to efficiently compute the error estimators using a dissipativity-exploiting block-Jacobi approximation. We illustrate the efficacy of the method by means of simulations of electrical circuit models.

17. $\ell$FEM：等参体与面有限元的高效无循环 Matlab 实现

$\ell$FEM: An efficient loop-free Matlab implementation of isoparametric bulk and surface finite elements

作者: Balázs Kovács, Michael Lantelme

类别: math.NA

发布日期: 2026-05-13

arXiv ID: 2605.14035v1

链接: http://arxiv.org/abs/2605.14035v1

摘要: The $\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB’s paged operators and therefore completely loop-free. We give a short and conscious description of high-order isoparametric surface finite elements, which is then used to describe the assembly process and the implementation. We report on relevant numerical experiments (runtime comparisons, modifications for non-linear problems, etc.), and on additional functions, examples, and a testing unit which are all part of the $\ell$FEM package.