生成时间: 2026年09月09日 14:16:48
重点关注论文数量: 0
了解领域论文数量: 3
不相关论文数量: 21
了解领域论文（摘要翻译）
1. 标量双曲守恒律的高阶间断切割有限元方法
High-Order Discontinuous Cut Finite Element Methods for Scalar Hyperbolic Conservation Laws
作者: Pei Fu, Gunilla Kreiss, Zelin Xin, Sara Zahedi
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08880v1
链接: http://arxiv.org/abs/2609.08880v1
摘要翻译
中文标题: 标量双曲守恒律的高阶间断切割有限元方法
摘要翻译: 本文针对复杂域上的标量双曲守恒律，提出了一族基于间断伽辽金（DG）框架的高阶切割有限元方法。在我们前期工作的基础上，我们发展了一种多维格式，将宏单元稳定化与通量限制相结合，以获得保持最大值原理且对背景网格的任意边界切割具有鲁棒性的格式。物理域嵌入到规则背景网格中，该网格可能产生任意小的切割单元。为了避免此类单元通常导致的严苛时间步长限制，我们在宏单元的内部面上添加了幽灵惩罚稳定项。所得方法在稳定性与精度方面与拟合网格上的标准DG方法类似。在周期和流入-流出边界条件下，我们推导了半离散格式的$L^2$稳定性结果。为强制最大值原理并抑制非物理振荡，我们将标准DG方法中的限制器技术推广到CutFEM设置中，通过在宏单元上定义限制参数来实现。特别地，我们提出了一种基于宏单元的参数化通量限制器，以及Zhang-Shu保界限制器和Barth-Jespersen斜率限制器的适配版本。二维和三维空间中的数值实验表明，即使对于涉及极小切割单元相交的具有挑战性的切割构型，该方法也能实现最优收敛阶、保持最大值原理，并在无伪振荡的情况下准确捕获激波。
2. 水下结构水弹性分析的间断有限元方法
A discontinuous finite element method for the hydroelastic analysis of submerged structures
作者: Zachary J. Wegert, Oriol Colomés, Michael H. Meylan, Ngamta Thamwattana, Vivien J. Challis
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08313v1
链接: http://arxiv.org/abs/2609.08313v1
摘要翻译
中文标题: 水下结构水弹性分析的间断有限元方法
摘要翻译: 本文针对水下弹性板水弹性建模中出现的波-结构相互作用问题，发展了一种有限元方法。该方法适用于二维情形和三维管道情形。对于问题中的流体部分，我们采用对称间断伽辽金格式，以捕捉势函数在板两侧的间断性。为了施加Sommerfeld辐射条件，我们借鉴Dirichlet-to-Neumann映射方法，利用半无限域中的解析解构造适当的非局部边界条件。对于板，我们使用连续/间断伽辽金方法，在不使用连续可微有限元的情况下求解4$^{ m th}$阶算子。我们证明了该方法的适定性，表明所得半双线性形式有界且满足Gårding不等式，从而保证解存在唯一且稳定。我们使用Julia语言中的Gridap包将所提格式实现为开源工具。我们将该方法与超奇异边界积分方法进行验证，结果吻合良好。通过对二维斜板和三维板几何体（包括中心矩形板、偏置矩形板和环形板）的数值模拟，展示了该方法的灵活性。本文提出的有限元方法可直接用于压电双晶片波能转换的建模。此外，该方法还可轻松扩展以考虑固定或刚性结构或变化底部地形的波散射，且不局限于水弹性应用。
3. GridapGeosciences.jl：用于一般流形上偏微分方程的 Julia 有限元软件包
GridapGeosciences.jl: A Julia finite element package for partial differential equations on general manifolds
作者: Tamara A. Tambyah, Alberto F. Martín, David Lee, Santiago Badia
类别: math.NA, math-ph
发布日期: 2026-09-07
arXiv ID: 2609.08036v1
链接: http://arxiv.org/abs/2609.08036v1
摘要翻译
中文标题: GridapGeosciences.jl：用于一般流形上偏微分方程的 Julia 有限元软件包
摘要翻译: 我们介绍了 GridapGeosciences.jl，这是一个用于一般流形上偏微分方程数值逼近的新的并行分布式内存 Julia 软件包。我们生成离散流形域的抽象方法总体上依赖于网格细化，并在 Gridap 有限元库中实现；该库的高级接口使得内蕴和外蕴变分公式能够无缝定义。GridapGeosciences.jl 以立方球流形为特色，本文用它来展示 GridapGeosciences.jl 在不同应用中的功能。第一个应用涉及标量输运，我们建立了常见稳定项的内蕴公式，并证明了这些公式与众所周知的外蕴稳定化公式等价。这些稳定项被用于建立包含迎风数值通量的二维热浅水方程的内蕴公式。最后一个应用是 Boussinesq 方程的线性化，我们展示了 GridapGeosciences.jl 在三维流形上捕捉表面动力学和垂直动力学的能力。
不相关论文（基本信息）
1. 含相关非高斯输入的不确定性量化的二次点估计法
Quadratic Point Estimate Method for Uncertainty Quantification with Dependent Non-Gaussian Inputs
作者: Minhyeok Ko, Konstantinos G. Papakonstantinou
类别: math.NA, math.PR, math.ST, stat.CO, stat.ME
发布日期: 2026-09-08
arXiv ID: 2609.09053v1
链接: http://arxiv.org/abs/2609.09053v1
摘要: As an extension of the Point Estimate Method (PEM) to evaluate probabilistic moments of quantities of interest (QoI) in general $n$-dimensional spaces, the Quadratic Point Estimate Method (QPEM) has been recently developed. This new method is defined to fully represent up to fifth-order input moments in the Gaussian space, providing general analytical expressions for sample locations and weights, without requiring any numerical optimization. The QPEM can significantly improve the estimation accuracy of the output QoI moments, in relation to PEM-based methods whose numbers of sigma points grow linearly with the problem dimension, while at the same time having an affordable and competitive computational cost up to a considerable number of dimensions. The QPEM is further enhanced in this work by enabling copula integration into the framework, which enables effective modeling of the joint input probability density function by estimating marginals and the dependence structure of the involved random variables. The validity and efficient performance of the copula-based QPEM are showcased against numerous other sampling methods in various examples considering two practical scenarios: (i) when the joint dependence structure can be inferred from data, and (ii) when only marginal distributions and correlation matrices are known.
2. 薛定谔算子谱类型的最优计算界
Sharp Computational Bounds for Spectral Types of Schrödinger Operators
作者: Matthew J. Colbrook, George Coote
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08945v1
链接: http://arxiv.org/abs/2609.08945v1
摘要: We prove sharp bounds for determining the spectral-type decomposition of Schrödinger operators in the spirit of Smale’s program on the foundations of computation. For explicit one-dimensional self-adjoint Schrödinger operators $H=-{\mathrm d^2}/{\mathrm dx^2}+V$ on $L^2(\mathbb R)$, where $V\in C^\infty(\mathbb R;\mathbb R)$ is given by a finite description of all derivatives and derivative bounds, the pure point and absolutely continuous spectral sets cannot, in general, be recovered by any single limiting procedure. The singular continuous spectral set is strictly harder: it cannot, in general, be recovered by two nested limiting procedures. Analytic constructions of dichotomies realize the lower bounds: Gordon-type repetitions for pure point spectrum, high barriers for absolutely continuous spectrum, and an inverse spectral construction for singular continuous spectrum based on Riesz products, moment-killing perturbations, and a computational Gelfand–Levitan scheme. The finite-description framework also implies corresponding limitations on what can be certified in fixed formal systems (e.g., when used in computer-assisted proofs). Conversely, using wavelet-based certified computation, we prove matching upper bounds for broad classes of self-adjoint differential operators on $\mathbb R^d$ with coefficients of locally bounded variation and quantitative local variation control: two limits suffice for the pure point and absolutely continuous parts, and three for the singular continuous part. This provides a sharp hierarchy for spectral types.
3. 关于活动子空间方法的样本复杂度
On the sample complexity of the active subspace method
作者: Fabio Nobile, Matteo Raviola, Raúl Tempone
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08940v1
链接: http://arxiv.org/abs/2609.08940v1
摘要: Active subspaces identify low-dimensional linear structure in high-dimensional parameter-to-output maps by estimating the dominant eigenspace of a gradient covariance operator. In practice this covariance is replaced by a Monte Carlo estimator built from a limited number of gradient evaluations. Classical analyses based on controlling the covariance error in operator norm lead to sample-complexity estimates that can be substantially more pessimistic than the sampling rules commonly used in computations. This paper studies the empirical active subspace method directly in the projection-error metric relevant for ridge approximation. We derive non-asymptotic quasi-optimality bounds governed by a regularized inverse Christoffel function associated with the gradient field. Under a bounded-gradient assumption, the resulting estimates already improve the sample-complexity estimates obtained from operator-norm covariance bounds. We then show that additional smoothness of the gradient map, expressed through membership in a reproducing kernel Hilbert space, yields sharper coherence estimates and motivates tractable importance sampling from kernel diagonal measures. Furthermore, the same smoothness assumption yields a priori decay bounds for the population active subspace tail energy, which can be combined with our finite-sample estimate to prescribe rank, regularization scale, and sample size, allowing to fully characterize the a priori sample complexity. The abstract assumptions are verified for lognormal Gaussian and affine uniform parametric elliptic PDEs using weighted summability of Hermite and Legendre series expansions.
4. 关于悬索桥中经典Melan方程的适定性与高效逼近
On the well-posedness and efficient approximation for the classical Melan equation in suspension bridges
作者: Jinxiang Wang
类别: math.NA, math.CA
发布日期: 2026-09-08
arXiv ID: 2609.08912v1
链接: http://arxiv.org/abs/2609.08912v1
摘要: The classical Melan equation modeling suspension bridges is considered. We first study the explicit expression and global properties of the analytical solution for the simplified less stiff'' model, based on which we derive an a priori estimate for the original classical Melan equation and establish, under an explicit load condition, that it has a unique solution with nonnegative integral under downward live loads, thereby showing the uniqueness of the corresponding deflection curve in the engineering setting. We also develop an efficient iterative approximation method by taking the solution of the simplified less stiff’’ model as the first iterate, and prove its geometric convergence with explicit error estimates. The applicability and computational efficiency of the method are demonstrated through calculations for two actual bridges, which also quantify the influence of the nonlinear nonlocal term on the solution and clarify the relationship between the simplified and original models. Several engineering observations are verified and explained, and some related open problems are suggested.
5. 超线性双曲型SPDE的驯化指数欧拉格式的强收敛速率
Strong convergence rates of tamed exponential Euler schemes for superlinear hyperbolic SPDEs
作者: Katharina Klioba
类别: math.NA, math.AP, math.FA, math.PR
发布日期: 2026-09-08
arXiv ID: 2609.08872v1
链接: http://arxiv.org/abs/2609.08872v1
摘要: In this paper, we prove pathwise uniform convergence at rates up to $1/2$ for tamed exponential Euler schemes for semilinear hyperbolic stochastic evolution equations with superlinearly growing nonlinearities and multiplicative noise. We take the term hyperbolic to mean that the leading operator generates a contractive $C_0$-semigroup but no parabolic smoothing occurs. Under local Lipschitz, polynomial growth, coercivity, and monotonicity conditions on the nonlinearities, we establish pathwise uniform strong error estimates of the form \begin{equation*} \Big(\mathbb{E}\max_{0\le j \le N} |U(t_j)-U^j|_X^p\Big)^{1/p} \lesssim \sqrt{k} \end{equation*} on a Hilbert space $X$ for $p\in [2,\infty)$. Here, $U$ is the mild solution and $U^j$ is the tamed exponential Euler approximation at time $t_j=jk$ with step size $k>0$. This extends previous convergence results for non-parabolic SPDEs from globally to locally Lipschitz nonlinearities, allowing both drift and diffusion to grow polynomially. In a stochastic Kato framework, we further establish local and global well-posedness as well as uniform a priori estimates for the mild solution and its approximation. Applications to nonlinear stochastic transport, Airy, wave-type, and dissipatively damped nonlinear Schrödinger equations are included, covering different nonlinearities-stopped and fractionally tamed schemes. For the Klein-Gordon equation with cubic velocity damping, this complements previous results obtained for additive noise.
6. 稀疏有限孔径数据下基于Hankel补全的离网点散射体定位
Off-Grid Point-Scatterer Localization from Sparse Limited-Aperture Data via Hankel Completion
作者: Jingzhi Li, Xiliang Lu, Juntao You
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08665v1
链接: http://arxiv.org/abs/2609.08665v1
摘要: We study the localization of $s$ distinct planar point scatterers from sparsely sampled single-incidence, single-frequency acoustic far-field data over a limited receiver aperture. Under the first Born approximation, the coherent data form a two-dimensional off-grid exponential sum and admit a low-rank Hankel representation. A limited aperture generally admits multiple aperture-admissible Hankel pencils with different lifted dimensions, sampling multiplicities, and Vandermonde conditioning. Hence, the choice of the Hankel pencil affects both data completion and subsequent localization. In this work, we introduce a unified framework for structured completion and off-grid localization based on general aperture admissible Hankel pencils. We establish exact recovery in the noiseless case and stable recovery under bounded noise from a number of random aperture samples that is linear in $s$, up to factors determined by the pencil geometry, source conditioning, and logarithmic terms, together with an explicit localization bound in terms of the completion error. The analysis separates the contribution of the pencil geometry from the conditioning induced by the source configuration and provides verifiable sufficient conditions for stable completion and MUSIC resolution. These results yield quantitative criteria for selecting sample efficient Hankel pencils under a prescribed physical aperture. Numerical experiments on connected and disconnected apertures demonstrate the effects of pencil geometry, sampling, and noise.
7. 使用GenEO谱粗空间的全对偶区域分解方法用于极限学习机
A Fully Dual Domain Decomposition Method for Extreme Learning Machines Using GenEO Spectral Coarse Spaces
作者: Chang-Ock Lee, Byungeun Ryoo
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08630v1
链接: http://arxiv.org/abs/2609.08630v1
摘要: Extreme learning machines (ELMs) are a class of machine learning algorithms that randomly intialize and subsequently fix the hidden layer parameters, and solve for the last layer coefficients using a least squares method. ELMs have been successfully applied to the solution of various partial differential equations, but the cost of solving large least squares problems limits their use in large scale problems or when high accuracy is desired. To address this limitation, domain decomposition methods (DDMs) have been developed for ELMs, reducing training times via parallel computation. Yet these methods, even those incorporating a coarse space, have struggled with scalability. This paper introduces a novel nonoverlapping DDM for ELMs that treats and enforces continuity and flux conditions equally. Additive Schwarz preconditioners and GenEO (Generalized Eigenvalues problems in the Overlaps) coarse spaces are constructed to accelerate the method. Numerical experiments show the new method outperforms previous DDMs for ELMs in both iteration count and accuracy, especially for the Stokes and wave equations. Furthermore, weak scalability has been observed in up to 4,096 subdomains when employing GenEO coarse spaces.
8. 采用基于THB样条的局部自适应等几何分析的肿瘤生长Cahn-Hilliard相场建模
Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines
作者: Dhiraj S. Bombarde, Carlotta Giannelli, Alessandro Reali, Guillermo Lorenzo
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08479v1
链接: http://arxiv.org/abs/2609.08479v1
摘要: Predicting tumor dynamics in biological systems under physiologically relevant conditions using mathematical and computational models remains a challenging problem. Continuum models based on phase-field (diffuse-interface) formulations have proven to be an effective modeling strategy to govern tumor dynamics and interactions of multiple species. Within this framework, the present work investigates a tumor growth model based on the Cahn-Hilliard (CH) equation. The formulation involves a fourth-order differential operator that imposes higher continuity requirement on approximation spaces for a well-defined primal variational formulation. To address this challenge, we use isogeometric analysis (IGA), which inherently satisfies this requirement through spline-based basis functions and eliminates the need for mixed or auxiliary-variable approaches commonly used in standard finite element discretizations. Additionally, a locally adaptive IGA scheme with truncated hierarchical B-splines (THB-splines) is used to reduce computational cost while maintaining accuracy. The model is first evaluated on standard benchmark cases and then applied to an organ-scale, patient-specific geometric model of the breast reconstructed from magnetic resonance imaging (MRI) data. Our results show that the model reproduces known tumor morphologies, ranging from a spheroidal pattern to fingered growth. A series of numerical experiments further shows the diversity of tumor dynamics produced by different model parameter choices. Our findings demonstrate the predictive potential of the CH-based phase-field tumor growth model integrated with a locally adaptive IGA framework.
9. 基于学习误差门控的选择性边界条件约化
Selective boundary condition reduction via learned error gating
作者: Daniel Fernández, Dominik Penk, Dominik Riedelbauch
类别: math.NA, cs.LG
发布日期: 2026-09-08
arXiv ID: 2609.08461v1
链接: http://arxiv.org/abs/2609.08461v1
摘要: Parametric PDEs can admit different boundary conditions with different accuracy and computational cost. We introduce a framework for learning when one reduced boundary condition can replace another: paired solutions train a neural network to estimate the resulting domain and boundary errors, and the simpler condition is used only when both predicted errors meet prescribed tolerances. We focus on singular limits in applications, in which a stiff Robin or nonlinear boundary law is replaced by its limiting Dirichlet form. We evaluate the method on a galvanic corrosion problem and other nonlinear stationary and evolution problems.
10. 爱因斯坦方程中特征初值问题的Picard迭代
Picard Iteration for the Characteristic Initial Value Problem in Einstein Equations
作者: Shengrong Wu
类别: gr-qc, math.NA, physics.comp-ph
发布日期: 2026-09-08
arXiv ID: 2609.08421v1
链接: http://arxiv.org/abs/2609.08421v1
摘要: We present an iteration algorithm for vacuum and Einstein scalar-field equations in double-null gauge, which transform the non-linear PDE into systems of ODE. The numerical realization combines characteristic constraint solves, LGL spectral elements, pole-free spherical operators, Galerkin projection, and independent first-order residual and consistency checks.
11. 一种用于具有Kelvin-Voigt阻尼的内禀梁模型的间断Galerkin方法
A Discontinuous Galerkin Method for the Intrinsic Beam Model with Kelvin-Voigt Damping
作者: Shivam Sundriyal, Christian Bleffert, Lukas Dreyer, Melven Röhrig-Zöllner, Gregor Gassner, Vadym Aizinger
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08397v1
链接: http://arxiv.org/abs/2609.08397v1
摘要: We present an energy-stable discontinuous Galerkin (DG) spatial discretization of the intrinsic beam equations with Kelvin-Voigt damping. We reformulate the governing equations by splitting the total sectional resultants into elastic and viscous parts, thereby exposing a mixed system without mixed space-time derivatives. For homogeneous cantilever boundary data, the continuous system obeys an energy dissipation identity. With characteristic upwinding and alternating auxiliary traces the DG discretization is energy stable at the semidiscrete level for the stated homogeneous split boundary closure. The method is implemented in the Julia-based simulation framework Trixi.jl. A physically compatible manufactured solution with all state and viscous components active assesses convergence, while a rotating-beam test verifies the analytic constant-spin branch and the actuated energy balance.
12. 具有朗缪尔吸附的多组分输运问题的紧凑隐式高分辨率数值格式
Compact implicit high-resolution numerical scheme for multicomponent transport problems with Langmuir sorption
作者: Dagmar Zakova, Peter Frolkovic
类别: math.NA, math.AP
发布日期: 2026-09-08
arXiv ID: 2609.08320v1
链接: http://arxiv.org/abs/2609.08320v1
摘要: We present a compact implicit high-resolution finite volume scheme for one-dimensional multicomponent transport problems with nonlinear Langmuir sorption. The method combines a second order compact implicit discretization with WENO reconstruction and a time limiter for the treatment of steep gradients and discontinuities. A special attention is given to the Courant number used in the limiter, where local characteristic Courant numbers based on the eigenvalues of the inverse retardation matrix are considered. The compact implicit schemes are compared with analogous explicit first and second order methods. Numerical experiments show second order convergence for smooth solutions and demonstrate that the implicit approach can be used with significantly larger Courant numbers. The method is also applied to a three-component displacement chromatography problem with sharp concentration fronts.
13. 三类具有自由边界的反应扩散方程的有限差分方法
Finite difference methods for three kinds of reaction-diffusion equations with free boundaries
作者: Caiyun Huang, Weizhi Liao, Weiping Bu
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08212v1
链接: http://arxiv.org/abs/2609.08212v1
摘要: This work considers to numerically solve three kinds of reaction-diffusion equations with free boundaries. First, the popular front-fixing method is used to transform the considered free boundary problems into fixed boundary problems. Then, by employing the finite difference method, numerical schemes with $\mathrm{M}$-matrices as their coefficient matrices are developed for these transformed fixed-boundary problems. Next, for the developed numerical schemes, we establish numerical theory involving positivity preservation, monotonicity preservation, and stability. It is noteworthy that, unlike some existing works that impose tight restrictions on the time step-size to discuss the numerical theory, the proposed numerical schemes require only a mild restriction. Finally, numerical examples are provided to test the developed numerical schemes and to confirm the theoretical results.
14. 带正且有界校正函数的三阶Halley型迭代法
Third-order Halley-type iterative method with positive and bounded correction function
作者: Hirai Mukasa
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08110v1
链接: http://arxiv.org/abs/2609.08110v1
摘要: In this paper, we propose a new one-point iterative method for finding simple roots of nonlinear equations by modifying Halley’s method. Its correction function is positive and bounded on $\mathbb{R}$ and matches the local expansion of Halley’s correction function near a simple root. The method avoids the singularity and sign reversal of Halley’s correction function while retaining at least third-order local convergence. We also establish sufficient conditions for global convergence. Numerical experiments show that the proposed method achieves high convergence success rates and favorable iteration counts over a wide range of initial guesses. Further experiments near the singularity of Halley’s correction function demonstrate robust convergence behavior of the proposed method. An application to the van der Waals equation illustrates the effectiveness of the proposed method.
15. 有限精度对称Krylov方法：精确舍入示例、块Paige恒等式与变块Lanczos模型
Finite-Precision Symmetric Krylov Methods: Exact Rounding Examples, Block Paige Identities,and a Variable-Block Lanczos Model
作者: Mohit Sinha
类别: math.NA
发布日期: 2026-09-08
arXiv ID: 2609.08066v1
链接: http://arxiv.org/abs/2609.08066v1
摘要: Short-recurrence Krylov methods that are equivalent in exact arithmetic often diverge in floating-point arithmetic. To illustrate this, we provide an exactly representable two-cycle for steepest descent with a recursively updated residual. A complementary convergence theorem gives a sufficient condition under which the stored residual decreases geometrically. We then show that a second positive definite family yields different outcomes for a Hestenes–Stiefel Conjugate Gradient (CG) implementation and a direct Lanczos–Galerkin approach. CG finds the exact solution after four updates, whereas the two-step projected system becomes inconsistent. Under stated perturbation and transfer hypotheses, a common spectral enclosure gives comparable convergence bounds. For a dense, left-to-right evaluation order, we prove a sufficient precision bound for a prescribed backward error within $n$ updates for an $n\times n$ matrix, together with a computable stopping test and specified exponent-range assumptions. We use polynomial estimates and numerical experiments to examine the trade-off between working precision and the number of CG iterations needed to achieve a prescribed backward error. We also compare results on inexact matrix-vector products and preconditioning with the frameworks of Paige and Greenbaum. For block Lanczos, we analyze Householder orthogonalization and singular-value truncation as the block size changes. Under componentwise and normwise error bounds, the computed coefficients satisfy a controlled local recurrence and an exact block Lanczos relation for a nearby symmetric problem in a larger space. A block form of Paige’s identity bounds the overlap with a Ritz vector along its residual coordinate direction. An inter-block recurrence describes the evolution of overlap, and a Gram-matrix argument gives a count of additional nearby Ritz values.
16. 考虑焦耳热的电-热-力接触的第三介质方法
A third-medium approach for electro-thermo-mechanical contact considering Joule heating
作者: Maximilian Vorwerk
类别: math.NA
发布日期: 2026-09-07
arXiv ID: 2609.08031v1
链接: http://arxiv.org/abs/2609.08031v1
摘要: Connectors are ubiquitous in technical systems and frequently combine mechanical contact with electric current transfer and heat generation. To capture these interacting processes, an electro-thermo-mechanical contact formulation based on the third-medium concept is proposed. Mechanical contact, electric current flow, and heat conduction are represented within a unified finite element framework without explicit contact-surface tracking. Deformation-dependent switching functions govern the onset of electrical and thermal transport during interface closure. Electrical conduction is coupled to the transient thermal problem through Joule heating, while the temperature dependence of the electrical conductivity provides the corresponding feedback on the current flow. The coupled displacement, electric potential, and temperature fields are solved monolithically and combined with an independently interpolated deformation-gradient-like field for robust third-medium regularization under severe compression. Numerical examples demonstrate contact-induced current transfer, subsequent Joule heating and transient temperature evolution, as well as localized current paths during progressive closure of rough interfaces.
17. 加速Fourier-Motzkin消去：冗余消除与变量消去顺序的选择
Accelerating Fourier–Motzkin elimination: redundancy removal and the choice of variable elimination order
作者: Shashaank Khanna
类别: cs.CC, math.CO, math.NA, math.OC, quant-ph
发布日期: 2026-09-07
arXiv ID: 2609.07960v1
链接: http://arxiv.org/abs/2609.07960v1
摘要: Fourier-Motzkin elimination computes an inequality description of the projection of a polyhedron onto a subset of its coordinates by eliminating one variable at a time. It is used in several areas of optimisation and computer science, and it is a standard way of obtaining the entropic constraints of a causal structure, where the marginalisation over the latent variables produces such a projection. Its limitation is the growth of the intermediate systems of inequalities, which can be doubly exponential in the number of eliminated variables even though the projection itself grows only as a single exponential. In practice the computational overload of the method therefore depends on two choices: how the redundant inequalities are removed after each step, and the order in which the variables are eliminated. We consider both. We first show, by an explicit example, that Imbert’s redundancy test cannot be interleaved with redundancy removal by linear programming. We show that the two methods, however, can be combined soundly if the derivation records used by Imbert’s test are re-initialised after every step at which linear programming is used. We then propose a rule for choosing the elimination order of the variables that gives a significant computational advantage, however, at the cost of increased resource usage. We demonstrate this advantage on some random polytopes, where the rule reduces the running time by factors of between 6 and 25 compared with the same elimination under a fixed order. For entropic descriptions of causal structures, with more than 250 inequalities and more than 100 variables to eliminate, our rule keeps the number of inequalities handled at each step one to two orders of magnitude lower than a fixed order.
18. 关于Laplace双层算子Kenig猜想的一个反例
A counterexample to Kenig’s conjecture for the Laplace double-layer operator
作者: Matthew J. Colbrook, Siavash Sadeghi
类别: math.AP, math-ph, math.NA, math.SP
发布日期: 2026-09-07
arXiv ID: 2609.07947v1
链接: http://arxiv.org/abs/2609.07947v1
摘要: Layer potentials provide a classical approach to boundary value problems for Laplace’s equation on Lipschitz domains. Kenig’s 1994 spectral-radius conjecture for the double-layer operator would ensure operator-norm convergence of the associated Neumann series on mean-zero $L^2$ densities when the boundary is connected. We disprove this conjecture by constructing a bounded simply connected planar Lipschitz domain whose double-layer operator on arclength $L^2$ has essential spectral radius strictly greater than $1/2$. More precisely, for every $t>1/2$ sufficiently close to $1/2$, we obtain such a domain with $\pm i t$ in its Fredholm essential spectrum. The construction starts from smooth graphs whose shapes repeat under translation. In the limit of separated scales, refinement makes solutions of adjoint resolvent equations grow with fixed forcing. The graph slopes remain uniformly bounded. A computer-assisted certificate proves this growth through an inequality for Hermitian $2\times2$ matrices. Its strict margin at $- i/2$ persists at nearby spectral parameters. Normalisation and a Floquet transform then give compactly supported densities with small residuals on the full graphs. We insert rescaled segments of successive graphs into one bounded boundary, where these densities form a weakly null sequence of approximate eigenvectors. The same spectral conclusion holds on a single periodic Lipschitz graph. The certificate combines continuous estimates, exact rational arithmetic and rigorous interval enclosures.
19. 亚扩散晶粒生长的阈值动力学
Threshold dynamics for subdiffusive grain growth
作者: Marvin Fritz
类别: math.NA
发布日期: 2026-09-07
arXiv ID: 2609.07938v1
链接: http://arxiv.org/abs/2609.07938v1
摘要: We propose a new fractional threshold-dynamics algorithm for subdiffusive interface motion and apply it to multiphase grain-growth simulations. The method combines the L1 discretization of the Caputo time derivative with a Helmholtz-resolvent thresholding step. At each time level, the L1 convolution produces a convex history average of the previously thresholded states; this history-dependent field is then propagated by a Helmholtz diffusion solve and projected back to pure phases by thresholding. For $α=1$, the method reduces to a Helmholtz-resolvent analogue of the Merriman-Bence-Osher scheme, whereas for $0<α<1$ it introduces a subdiffusive temporal memory. We establish a variational characterization, maximum and comparison principles, and stability for the continuous Helmholtz diffusion step. We also derive a memory-tail estimate and a finite-dimensional pinning criterion under an explicit resolvent-contraction hypothesis. The equal-tension multiphase scheme is implemented on periodic grids. The numerical experiments investigate the joint influence of the L1 history and the smoothing length. The fixed-step runs show faster coarsening for smaller fractional orders in the tested regime, while a comparison at fixed smoothing length examines the influence of the L1 history on successive updates.
20. 使用极小极大凹和加权 $\ell_1$ 罚的泊松图像去噪：非盲与盲方法
Poisson Image Denoising Using Minimax Concave and Reweighted $\ell_1$ Penalties: Nonblind and Blind Approaches
作者: Reza Parvaz
类别: cs.CV, math.NA
发布日期: 2026-09-07
arXiv ID: 2609.07916v1
链接: http://arxiv.org/abs/2609.07916v1
摘要: Images are important tools in various sciences. Despite the development of photo-taking tools, creating clear and image without noise remains challenging in practice. In particular, Poisson noise has an effect on medical and astronomical images, and reduces their quality. Additionally, blur is another factor that has an effect on image quality. The problem of image restoration becomes very complicated when we have no information about the Point Spread Function (PSF). These types of problems are known as blind case. However, in some images, such as some astronomical images, the type of PSF can be specified, and these types of problems are known as nonblind problems. Total Variation (TV) is a widely used method for solving such inverse problems, where the selection of the penalty function is the most critical factor that affects the method’s performance. In this paper, to improve edge preservation, we employ a reweighted $\ell_1$-regularization of the fractional order derivative. Furthermore, we propose a nonblind and blind image deblurring approach under Poisson noise using the Minimax Concave Penalty (MCP), which is a continuous, sparsity promoting, and nearly unbiased regularizer. This formulation leads to a nonconvex optimization model. To solve the proposed model, we introduce an efficient numerical algorithm based on the Alternating Direction Method of Multipliers (ADMM) and provide an analysis of its convergence. Finally, the effectiveness of the proposed algorithm are demonstrated through extensive experiments on various images.
21. LoCCA：基于节点扰动稳定性的核矩阵分解的局部切比雪夫交叉逼近
LoCCA: Localized Chebyshev Cross Approximation for Kernel Matrix Factorization via Nodal Perturbation Stability
作者: Sumit Singh, Shrirup Dutta, Sivaram Ambikasaran
类别: math.NA
发布日期: 2026-09-07
arXiv ID: 2609.07882v1
链接: http://arxiv.org/abs/2609.07882v1
摘要: We propose Local Chebyshev Cross-Approximation (LoCCA), a data-driven framework that bridges smooth polynomial interpolation with flexible matrix factorizations. LoCCA dynamically maps ideal grid nodes to their nearest physical neighbors within unstructured point sets. We support this framework with a new perturbation theory, proving that displacing Chebyshev nodes onto physical data points retains mathematical stability and accuracy without explosive error growth. Numerically, LoCCA provides strict, reliable error control even on irregular geometries where standard grid-based methods fail, achieving substantial speedups and near-optimal matrix compression.