Tootfinder

Noticed the SVG spec saves me from having to jump through hoops fixing an implementation detail. Phew. Thank goodness. 😅
https://stackoverflow.com/questions/16890292/why-nest-an-svg-element-inside-another-svg-element

Why nest an
Why would a demo such as this: http://jsbin.com/ejorus/2/edit, have an

A general kinematic theory of fluid-element rotation and intrinsic vorticity decompositions
Tao Chen, Jie-Zhi Wu, Feng Mao, Tianshu Liu
https://arxiv.org/abs/2509.00372 https://…

A general kinematic theory of fluid-element rotation and intrinsic vorticity decompositions
The present study proposes a general kinematic theory for fluid-element rotation and intrinsic vorticity decompositions within the context of vorticity and vortex dynamics. Both the angular velocities of material line and surface elements comprise a classical contribution driven by volume-element rotation (equal to half the local vorticity), and a strain-rate-induced specific angular velocity. Then, two direction-dependent vorticity decompositions (DVDs) are constructed, revealing the rigid rot…

Analysis of A Mixed Finite Element Method for Poisson's Equation with Rough Boundary Data
Huadong Gao, Yuhui Huang, Wen Xie
https://arxiv.org/abs/2507.00697

Analysis of A Mixed Finite Element Method for Poisson's Equation with Rough Boundary Data
This paper is concerned with finite element methods for Poisson's equation with rough boundary data. Conventional methods require that the boundary data $g$ of the problem belongs to $H^{1/2} (\partial Ω)$. However, in many applications one has to consider the case when $g$ is in $L^2(\partial Ω)$ only. To this end, very weak solutions are considered to establish the well-posedness of the problem. Most previously proposed numerical methods use regularizations of the boundary data. The main pu…

Now that's a new one, Element "misconfigured".

On Euclidean Algorithms for oriented linear Grassmanians
Arnold Maxim, Karpenkov Oleg
https://arxiv.org/abs/2509.01733 https://arxiv.org/pdf/2509.01733

On Euclidean Algorithms for oriented linear Grassmanians
In this paper we study Euclidean algorithms and the corresponding continued fractions for oriented linear Grassmanians $G(k,n)$. We propose two algorithms: Maximal Element Elimination algorithm and Minimal Element Elimination algorithm. The first algorithm reduces the absolute maximal value of the Plücker coordinates; the algorithm works only in $G(2,n)$. The second algorithm eliminates the Plücker coordinate with the smallest absolute values, while all other coordinates may increase; the alg…

ConamArray: A 32-Element Broadband MEMS Ultrasound Transducer Array
Dennis Laurijssen, Rens Baeyens, Walter Daems, Jan Steckel
https://arxiv.org/abs/2509.01372 https://

ConamArray: A 32-Element Broadband MEMS Ultrasound Transducer Array
This paper presents the ConamArray, a compact broadband ultrasound transducer array composed of 32 MEMS loudspeakers. Unlike conventional broadband transducers, which are typically large and require high driving voltages, the proposed array combines small form factor MEMS devices in a staggered two-row configuration to enable beam steering across a wide ultrasonic band. A dual-microcontroller back-end with synchronized multi-DAC outputs provides flexible waveform generation and runtime steering…

Bryne: sustainable prototyping of finite element models
Benjamin Terschanski, Robert Kl\"ofkorn, Andreas Dedner, Julia Kowalski
https://arxiv.org/abs/2509.02378 https://

Bryne: sustainable prototyping of finite element models
Open-source simulation frameworks are evolving rapidly to provide accessible tools for the numerical solution of partial differential equations. Modern finite element (FEM) software such as FEniCS, Firedrake, or dune-fem alleviates the need for modelers to recode the discretization and linear solver backend for each application and enables rapid prototyping of solvers. However, while it has become easier to build prototype FEM models, creating a solver reusable beyond its specific initial simul…

Feasibility of spectral-element modeling of wave propagation through the anatomy of marine mammals
Carlos Garc\'ia A., Vladimiro Boselli, Aida Hejazi Nooghabi, Andrea Colombi, Lapo Boschi
https://arxiv.org/abs/2506.22944

Feasibility of spectral-element modeling of wave propagation through the anatomy of marine mammals
This study introduces the first 3D spectral-element method (SEM) simulation of ultrasonic wave propagation in a bottlenose dolphin (Tursiops truncatus) head. Unlike traditional finite-element methods (FEM), which struggle with high-frequency simulations due to costly linear-system inversions and slower convergence, SEM offers exponential convergence and efficient parallel computation. Using Computed Tomography (CT) scan data, we developed a detailed hexahedral mesh capturing complex anatomical …

Props to the people working on @… and @… for making Element Call.
I deployed the LiveKit backend on my Matrix server which was, frankly, quite tricky.
Once it's set up, though, it works super well. I've been…

Friedrich Merz, wenn die Bosse ihre 5 Milliarden wollen.

Non-Identical Diffusion Models in MIMO-OFDM Channel Generation
Yuzhi Yang, Omar Alhussein, M\'erouane Debbah
https://arxiv.org/abs/2509.01641 https://a…

Non-Identical Diffusion Models in MIMO-OFDM Channel Generation
We propose a novel diffusion model, termed the non-identical diffusion model, and investigate its application to wireless orthogonal frequency division multiplexing (OFDM) channel generation. Unlike the standard diffusion model that uses a scalar-valued time index to represent the global noise level, we extend this notion to an element-wise time indicator to capture local error variations more accurately. Non-identical diffusion enables us to characterize the reliability of each element (e.g., …

Probing Optical Vortex Beams via a Controllable Anisotropic Diffractive Phase Element
Ali Mardan Dezfouli, Mario Raki\'c, Hrvoje Skenderovi\'c
https://arxiv.org/abs/2509.01334

Probing Optical Vortex Beams via a Controllable Anisotropic Diffractive Phase Element
In this work, we investigate the diffraction of optical vortex beams through a tunable elliptical Fresnel phase mask (TEFPM). The resulting diffraction patterns are influenced by both the topological charge of the beam and the ellipticity of the mask, exhibiting characteristic intensity distributions that allow direct determination of the magnitude and sign of the topological charge. Requiring only a single controllable parameter, the TEFPM offers a simple and adaptable approach for vortex char…

On Fine-Grained Distinct Element Estimation
Ilias Diakonikolas, Daniel M. Kane, Jasper C. H. Lee, Thanasis Pittas, David P. Woodruff, Samson Zhou
https://arxiv.org/abs/2506.22608 …

On Fine-Grained Distinct Element Estimation
We study the problem of distributed distinct element estimation, where $α$ servers each receive a subset of a universe $[n]$ and aim to compute a $(1+\varepsilon)$-approximation to the number of distinct elements using minimal communication. While prior work establishes a worst-case bound of $Θ\left(α\log n+\fracα{\varepsilon^2}\right)$ bits, these results rely on assumptions that may not hold in practice. We introduce a new parameterization based on the number $C = \fracβ{\varepsilon^2}$ …

On injective endomorphisms of the semigroup $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $\omega$
Oleg Gutik, Inna Pozdniakova
https://arxiv.org/abs/2508.21387

On injective endomorphisms of the semigroup $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$
We describe injective endomorphisms of the semigroup $\boldsymbol{B}_{Z\mathbb{}}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$. In particular we show that every injective endomorphism $\mathfrak{e}$ of $\boldsymbol{B}_{Z\mathbb{}}^{\mathscr{F}^2}$ is presented in the form $\mathfrak{e}=\mathfrak{e}_0\mathfrak{a}$, where $\mathfrak{e}_0$ is an injective $(0,0,[0))$-endomorphism of $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ and $\mathfrak{a…

Adaptive finite element convergence analysis of AT1 phase-field model for quasi-static fracture in strain-limiting solids
Ram Manohar, S. M. Mallikarjunaiah
https://arxiv.org/abs/2507.00376

Adaptive finite element convergence analysis of AT1 phase-field model for quasi-static fracture in strain-limiting solids
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1) phase-field model within the framework of elasticity theories, particularly for material models characterized by an algebraically nonlinear stress-strain relationship. Two distinct and novel adaptive mesh refinement algorithms, underpinned by robust local error ind…

Decision Procedure for A Theory of String Sequences
Denghang Hu, Taolue Chen, Philipp R\"ummer, Fu Song, Zhilin Wu
https://arxiv.org/abs/2509.00948 https://

Decision Procedure for A Theory of String Sequences
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation, forming sub-sequences and updating elements. Strings and sequences are intimately related; many operations, e.g., matching a string according to a regular expression, splitting strings, or joining strings in a sequence, are frequently used in string-manipulat…

High-precision polarization measurements with Lumped Element Kinetic Inductance Detectors
Sofia Savorgnano, Andrea Catalano, Juan-Francisco Mac\'ias Perez, Julien Bounmy, Olivier Bourrion, Martino Calvo, Olivier Choulet, Gregory Garde, Anne Gerardin, Mile Kusulja, Alessandro Monfardini, Nicolas Ponthieu, Damien Tourres, Francis Vezzu
https://

High-precision polarization measurements with Lumped Element Kinetic Inductance Detectors
This work aims to demonstrate that two arrays of Lumped Element Kinetic Inductance Detectors (LEKIDs), when employed in filled array configuration and separated by an external linear polarizer oriented at 45 degrees, can achieve the precision required by next-generation cosmological experiments. The focus here is on validating their ability to meet stringent uncertainty requirements, in particular for polarization angle reconstruction. To achieve this, the uncertainties in the reconstruction of…

Just found out that many chat apps (#Threema, #Signal, #Element, ...) (sometimes??) ignore trailing dashes as not part of the url, breaking the link 😑 Manually replacing that dash with - fixes this.

An Efficient Intrusion Detection System for Safeguarding Radiation Detection Systems
Nathanael Coolidge, Jaime Gonz\'alez Sanz, Li Yang, Khalil El Khatib, Glenn Harvel, Nelson Agbemava, I Putu Susila, Mehmet Yavuz Yagci
https://arxiv.org/abs/2509.01599

An Efficient Intrusion Detection System for Safeguarding Radiation Detection Systems
Radiation Detection Systems (RDSs) are used to measure and detect abnormal levels of radioactive material in the environment. These systems are used in many applications to mitigate threats posed by high levels of radioactive material. However, these systems lack protection against malicious external attacks to modify the data. The novelty of applying Intrusion Detection Systems (IDS) in RDSs is a crucial element in safeguarding these critical infrastructures. While IDSs are widely used in netw…

Impact of Passive Element Technological Limits on CMOS Low-Noise Amplifier Design
J. L. Gonz\'alez, R. L. Moreno, D. V\'azquez
https://arxiv.org/abs/2509.01770 https://

Impact of Passive Element Technological Limits on CMOS Low-Noise Amplifier Design
This paper investigates the impact of technological constraints on passive elements in the design of inductively degenerated CMOS low-noise amplifiers (LNAs). A theoretical analysis is combined with circuit simulations in a 130-nm CMOS process at 2.45~GHz to explore how the available inductance and capacitance values limit key design objectives such as maximum gain, minimum power consumption, and transistor sizing. Results show that these limits significantly restrict the achievable design spac…

A coupled multiscale model of the human cornea accounting for the collagenous microstructure and the extracellular matrix
Christopher Miller, Maria Laura De Bellis, Anna Pandolfi
https://arxiv.org/abs/2507.00668

A coupled multiscale model of the human cornea accounting for the collagenous microstructure and the extracellular matrix
We present a micro-structurally based finite element model of the human cornea, where we explicitly describe the collagen-crosslink architecture in terms of a trusswork of non-linear struts, and the extracellular proteoglycan matrix in terms of continuum solid elements. We regard the cornea as a composite material with strongly non-linear properties within a finite kinematics framework. This innovative approach is based on two previously developed models, each of which has some drawbacks in des…

Hmm - as a frequent advocate for #Matrix and #Element, this is food for thought: https://マリウス.com/giving-up-on-element-

Deep Complex-valued Neural-Network Modeling and Optimization of Stacked Intelligent Surfaces
Abdullah Zayat, Omran Abbas, Loic Markley, Anas Chaaban
https://arxiv.org/abs/2509.00340

Deep Complex-valued Neural-Network Modeling and Optimization of Stacked Intelligent Surfaces
We propose a complex-valued neural-network (CV-NN) framework to optimally configure stacked intelligent surfaces (SIS) in next-generation multi-antenna systems. Unlike conventional solutions that separately tune analog metasurface phases or rely strictly on SVD-based orthogonal decompositions, our method models each SIS element as a unit-modulus complex-velued neuron in an end-to-end differentiable pipeline. This approach avoids enforcing channel orthogonality and instead allows for richer wave…

A mixed Petrov--Galerkin Cosserat rod finite element formulation
Marco Herrmann, Domenico Castello, Jonas Breuling, Idoia Cortes Garcia, Leopoldo Greco, Simon R. Eugster
https://arxiv.org/abs/2507.01552

A mixed Petrov--Galerkin Cosserat rod finite element formulation
This paper presents a total Lagrangian mixed Petrov--Galerkin finite element formulation that provides a computationally efficient approach for analyzing Cosserat rods that is free of singularities and locking. To achieve a singularity-free orientation parametrization of the rod, the nodal kinematical unknowns are defined as the nodal centerline positions and unit quaternions. We apply Lagrangian interpolation to all nodal kinematic coordinates, and in combination with a projection of non-unit …

An AGB star as the source of the abundance pattern of hyper-metal-poor star HE 1327-2326
P. Gil-Pons, S. W. Campbell, C. L. Doherty, M. Lugaro
https://arxiv.org/abs/2509.01302 h…

An AGB star as the source of the abundance pattern of hyper-metal-poor star HE 1327-2326
Abridged. HE 1327-2326 (HE 1327), with [Fe/H]=-5.2, is one of the most metal-poor stars detected and a candidate to be the offspring of the first stars. Numerous efforts have been made to match its abundance pattern. However, no model satisfactorily explains its entire surface chemical composition. The high CNO pattern with [N/Fe]>[C/Fe]>[O/Fe], the light element 'slide' (between Na and Si), and the presence of Sr and Ba in HE 1327 is reminiscent of those asymptotic giant branch (AGB) stars tha…

Toward Sustainable Rare Earth Element Production: Key Challenges in Techno-Economic, Life Cycle, and Social Impact Assessment
Adam Smerigan, Rui Shi
https://arxiv.org/abs/2506.22569

Toward Sustainable Rare Earth Element Production: Key Challenges in Techno-Economic, Life Cycle, and Social Impact Assessment
Rare earth elements (REEs) are 17 critical minerals used in many clean energy technologies like wind turbines and electric vehicles. Conventionally, we produce REEs from mining in few, geopolitically restricted regions. Developing systems that utilize new technologies and unconventional feedstocks provides an opportunity to meet increasing demand while improving sustainability. Techno-economic analysis (TEA), life cycle assessment (LCA), and social LCA (sLCA) are commonly used tools to assess t…

Series B, Episode 03 - Weapon
TRAVIS: What?
SERVALAN: If he's cornered, he might destroy the weapon.
TRAVIS: I should have realized.
SERVALAN: I don't find stupidity amusing, Travis.
TRAVIS: No.
https://blake.torpidity.net/m/203/266 B7B2

Caccioppoli-type inequalities for the Dunkl-$A$-Laplacian and their application to nonexistence result
Athulya P, Sandeep Kumar Verma
https://arxiv.org/abs/2509.00565 https://…

Caccioppoli-type inequalities for the Dunkl-$A$-Laplacian and their application to nonexistence result
For a suitable function $A:\mathbb{R}^n\to \mathbb{R}^n$, we introduce the $A$-Laplacian in the Dunkl framework as $Δ_{k,A}(u) =\text{div}_k(A(\nabla_ku))$, where $\nabla_k$ is the Dunkl-gradient operator associated with the multiplicity function $k$ and the root system $\mathcal{R}$. We derive the local and global Caccioppoli-type inequality for an element $u$ in the Dunkl-Orlicz-Sobolev space, satisfying the Dunkl-differential inequality $$ -Δ_{k, A}(u) \geq bΦ(u)χ_{\{u>0\}}. $$ Using the…

Scaling particle-size segregation in wide-ranging sheared granular flows
Tianxiong Zhao, Daisuke Noto, Xia Li, Tom\'as Trewhela, Hugo N. Ulloa
https://arxiv.org/abs/2507.01248

Scaling particle-size segregation in wide-ranging sheared granular flows
Scaling relationships have been proposed to describe shear-driven size segregation based on intruder experiments and simulations. While these models have shown agreement with experimental and numerical results under uniform shear rate, their validity across varying shear-rate conditions remains uncertain. Here, we employ Discrete Element Method (DEM) simulations to investigate particle size segregation in sheared granular flows under wide-ranging shear-rate conditions. We find that the scaling …

CAD-Integrated Electrostatic Boundary Element Simulations with Non-Conforming Higher-Order Meshes
Benjamin Marussig, J\"urgen Zechner, Thomas R\"uberg, Lars Kielhorn, Domagoj Bo\v{s}njak, Thomas-Peter Fries
https://arxiv.org/abs/2506.22676

CAD-Integrated Electrostatic Boundary Element Simulations with Non-Conforming Higher-Order Meshes
We present a design through analysis workflow that enables virtual prototyping of electric devices. A CAD plugin establishes the interaction between design and analysis, allowing the preparation of analysis models and the visualization of its results within the design environment. The simulations utilize a fast boundary element method (BEM) that allows for non-conforming and higher-order meshes. Our numerical experiments investigate the accuracy of the approach and its sensitivity to the initia…

Sufficient conditions for strong discrete maximum principles in finite element solutions of linear and semilinear elliptic equations
Andrei Draganescu, L. Ridgway Scott
https://arxiv.org/abs/2509.00932

Sufficient conditions for strong discrete maximum principles in finite element solutions of linear and semilinear elliptic equations
We introduce a novel technique for proving global strong discrete maximum principles for finite element discretizations of linear and semilinear elliptic equations for cases when the common, matrix-based sufficient conditions are not satisfied. The basic argument consists of extending the strong form of discrete maximum principle from macroelements to the entire domain via a connectivity argument. The method is applied to discretizations of elliptic equations with certain pathological meshes, a…

SEAL: Structure and Element Aware Learning to Improve Long Structured Document Retrieval
Xinhao Huang, Zhibo Ren, Yipeng Yu, Ying Zhou, Zulong Chen, Zeyi Wen
https://arxiv.org/abs/2508.20778

SEAL: Structure and Element Aware Learning to Improve Long Structured Document Retrieval
In long structured document retrieval, existing methods typically fine-tune pre-trained language models (PLMs) using contrastive learning on datasets lacking explicit structural information. This practice suffers from two critical issues: 1) current methods fail to leverage structural features and element-level semantics effectively, and 2) the lack of datasets containing structural metadata. To bridge these gaps, we propose \our, a novel contrastive learning framework. It leverages structure-a…

Embodying computation in nonlinear perturbative metamaterials
Sima Zahedi Fard, Paolo Tiso, Parisa Omidvar, Marc Serra-Garcia
https://arxiv.org/abs/2509.01625 https://

Embodying computation in nonlinear perturbative metamaterials
Designing metamaterials that carry out advanced computations poses a significant challenge. A powerful design strategy splits the problem into two steps: First, encoding the desired functionality in a discrete or tight-binding model, and second, identifying a metamaterial geometry that conforms to the model. Applying this approach to information-processing tasks requires accurately mapping nonlinearity -- an essential element for computation -- from discrete models to geometries. Here we formul…

A Model-Based Derivative-Free Optimization Algorithm for Partially Separable Problems
Yichuan Liu, Yingzhou Li
https://arxiv.org/abs/2506.21948 https://

A Model-Based Derivative-Free Optimization Algorithm for Partially Separable Problems
We propose UPOQA, a derivative-free optimization algorithm for partially separable unconstrained problems, leveraging quadratic interpolation and a structured trust-region framework. By decomposing the objective into element functions, UPOQA constructs underdetermined element models and solves subproblems efficiently via a modified projected gradient method. Innovations include an approximate projection operator for structured trust regions, improved management of elemental radii and models, a …

A key element of the administration’s proposal is to redefine what it means for air pollution to cause harm.
If a pollutant causes climate change, it would no longer count as hurting us.
This runs counter to both basic logic and a growing mountain of science documenting direct harms from greenhouse gas

Proposed Rule: Reconsideration of 2009 Endangerment Finding and Greenhouse Gas Vehicle Standards | US EPA
The proposed rule on the reconsideration of the greenhouse gas endangerment finding and motor vehicle rule

Element nucleosynthetic origins from abundance spatial distributions beyond the Milky Way
Zefeng Li, Mark R. Krumholz, Anna F. McLeod, A. Mark Swinbank, Emily Wisnioski, J. Trevor Mendel, Francesco Belfiore, Giovanni Cresci, Giacomo Venturi, Jialai Kang
https://arxiv.org/abs/2506.21365

Element nucleosynthetic origins from abundance spatial distributions beyond the Milky Way
An element's astrophysical origin should be reflected in the spatial distribution of its abundance, yielding measurably different spatial distributions for elements with different nucleosynthetic sites. However, most extragalactic multi-element analyses of gas-phase abundances to date have been limited to small numbers of sightlines, making statistical characterization of differences in spatial distributions of elements impossible. Here we use integrated field spectroscopic data covering the fu…

Character theoretic techniques for nonabelian partial difference sets
Seth R. Nelson, Eric Swartz
https://arxiv.org/abs/2507.23039 https://arxiv.org/pdf/25…

Character theoretic techniques for nonabelian partial difference sets
A $(v,k,λ, μ)$-partial difference set (PDS) is a subset $D$ of size $k$ of a group $G$ of order $v$ such that every nonidentity element $g$ of $G$ can be expressed in either $λ$ or $μ$ different ways as a product $xy^{-1}$, $x, y \in D$, depending on whether or not $g$ is in $D$. If $D$ is inverse closed and $1 \notin D$, then the Cayley graph ${\rm Cay}(G,D)$ is a $(v,k,λ, μ)$-strongly regular graph (SRG). PDSs have been studied extensively over the years, especially in abelian groups, w…

Global convergence of adaptive least-squares finite element methods for nonlinear PDEs
Philipp Bringmann, Dirk Praetorius
https://arxiv.org/abs/2509.01531 https://

Global convergence of adaptive least-squares finite element methods for nonlinear PDEs
The Zarantonello fixed-point iteration is an established linearization scheme for quasilinear PDEs with strongly monotone and Lipschitz continuous nonlinearity. This paper presents a weighted least-squares minimization for the computation of the update of this scheme. The resulting formulation allows for a conforming finite element discretization of the primal and dual variable of the PDE with arbitrary polynomial degree. The least-squares functional provides a built-in a posteriori discretizat…

I have vague memories of reading years ago about a weapon called a "photic driver" consisting of an LED or strobe or laser array flashing in patterns deliberately crafted to induce photosensitive seizures and disorientation (not just a conventional dazzler intended primarily to interfere with the target's vision).
I have no idea if it was a failed CIA project, a sci-fi plot element, something some military or police department actually fielded, etc.
Anybody ever hea…

Variational PINNs with tree-based integration and boundary element data in the modeling of multi-phase architected materials
Dimitrios C. Rodopoulos, Panos Pantidis, Nikolaos Karathanasopoulos
https://arxiv.org/abs/2506.23357

Variational PINNs with tree-based integration and boundary element data in the modeling of multi-phase architected materials
The current contribution develops a Variational Physics-Informed Neural Network (VPINN)-based framework for the analysis and design of multiphase architected solids. The elaborated VPINN methodology is based on the Petrov-Galerkin approach, with a deep neural network acting as trial function and local polynomials as test functions. For the analysis, a Galerkin Boundary Element Method (GBEM) scheme is developed to generate the mechanical field data, employing solely domain boundary information. …

Multi-fidelity Bayesian Data-Driven Design of Energy Absorbing Spinodoid Cellular Structures
Leo Guo, Hirak Kansara, Siamak F. Khosroshahi, GuoQi Zhang, Wei Tan
https://arxiv.org/abs/2507.22079

Multi-fidelity Bayesian Data-Driven Design of Energy Absorbing Spinodoid Cellular Structures
Finite element (FE) simulations of structures and materials are getting increasingly more accurate, but also more computationally expensive as a collateral result. This development happens in parallel with a growing demand of data-driven design. To reconcile the two, a robust and data-efficient optimization method called Bayesian optimization (BO) has been previously established as a technique to optimize expensive objective functions. In parallel, the mesh width of an FE model can be exploited…

$ L_\infty $-spectral sequences for Hochschild cohomology
Jasper van de Kreeke
https://arxiv.org/abs/2508.21716 https://arxiv.org/pdf/2508.21716

$ L_\infty $-spectral sequences for Hochschild cohomology
Spectral sequences are a common tool to compute cohomology spaces, but higher structure is often lost on the way. In this article we exhibit a strategy to retain the higher structure on the cohomology, which works in case the chain complex with higher structure is presented as the twisting of a simpler chain complex by a Maurer-Cartan element. This works particularly well in case of the Hochschild complex of a minimal $ A_\infty $-category, where the Hochschild complex can be seen as the twisti…

🤔 This seems to be getting pretty close to @… 's work on emoji-picker-element (https://github.com/nolanlawson/emoji-picker-element):

GitHub - nolanlawson/emoji-picker-element: A lightweight emoji picker for the modern web
A lightweight emoji picker for the modern web. Contribute to nolanlawson/emoji-picker-element development by creating an account on GitHub.

Exploiting Movable Elements of Intelligent Reflecting Surface for Enhancement of Integrated Sensing and Communication
Xingyu Peng, Qin Tao, Yong Liang Guan, Xiaoming Chen
https://arxiv.org/abs/2507.23296

Exploiting Movable Elements of Intelligent Reflecting Surface for Enhancement of Integrated Sensing and Communication
In this paper, we propose to exploit movable elements of intelligent reflecting surface (IRS) to enhance the overall performance of integrated sensing and communication (ISAC) systems. Firstly, focusing on a single-user scenario, we reveal the function of movable elements by performance analysis, and then design a joint beamforming and element position optimization scheme. Further, we extend it to a general multi-user scenario, and also propose an element position optimization scheme according …

A Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) Framework for Non-linear Finite Element/Meshfree Analysis
Yingjian Liu, Monish Yadav Pabbala, Jiachen Guo, Chanwook Park, Gino Domel, Wing Kam Liu, Dong Qian
https://arxiv.org/abs/2509.02435

A Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) Framework for Non-linear Finite Element/Meshfree Analysis
We present a framework for the Convolutional Hierarchical Deep Neural Network (C-HiDeNN) tailored for nonlinear finite element and meshfree analysis. Building upon the structured foundation of HiDeNN, which includes the evaluation of shape function derivatives, adaptivity, and material derivatives, C-HiDeNN introduces a convolution operator to enhance the HiDeNN approximation. A distinctive feature of C-HiDeNN is its expanded set of optimization parameters, such as the polynomial order 'p,' dil…

Hybrid Codebook Design for Localization Using Electromagnetically Reconfigurable Fluid Antenna System
Alireza Fadakar, Yuchen Zhang, Hui Chen, Musa Furkan Keskin, Henk Wymeersch, Andreas F. Molisch
https://arxiv.org/abs/2508.21351

Hybrid Codebook Design for Localization Using Electromagnetically Reconfigurable Fluid Antenna System
Electromagnetically reconfigurable fluid antenna systems (ER-FAS) introduce additional degrees of freedom in the electromagnetic (EM) domain by dynamically steering per-antenna radiation patterns, thereby enhancing power efficiency in wireless links. Unlike prior works on spatially reconfigurable FAS, which adjust element positions, ER-FAS provides direct control over each element's EM characteristics to realize on-demand beam-pattern shaping. While existing studies have exploited ER-FAS to boo…

A semi-analytical approach to characterize high-frequency three-dimensional wave propagation through clamp-on flowmeters
Sabiju Valiya Valappil, Alejandro M. Aragon, Johannes F. L. Goosen
https://arxiv.org/abs/2509.00020

A semi-analytical approach to characterize high-frequency three-dimensional wave propagation through clamp-on flowmeters
Wave propagation analysis at high frequencies is essential for applications involving ultrasound waves, such as clamp-on ultrasonic flowmeters. However, it is extremely challenging to perform a 3D transient analysis of a clamp-on flowmeter using standard tools such as finite element analysis (FEA) due to the enormous associated computational cost. In this study, we separate the clamp-on flowmeter into different domains and analyze them separately. Wave propagation in the fluid domain is analyze…

Energy non-equipartition in vibrofluidized particles
Alok Tiwari, Manaswita Bose, V. Kumaran
https://arxiv.org/abs/2509.00474 https://arxiv.org/pdf/2509.00…

Energy non-equipartition in vibrofluidized particles
The aim of the present work is to investigate the influence of the realistic model parameters on the equipartition of energy in a vibrofluidized system. To achieve this, a three-dimensional vertically vibrated granular system consisting of spherical particles is simulated using the discrete element method (DEM) using the open-source software LAMMPS. Interparticle and wall-particle interactions are determined using the linear-spring dashpot model. Simulations are performed for nearly perfectly s…

Content-Aware Foveated Camera for Multi-Target Tracking
Zihan Zang, Do Young Kim, Yifeng Zeng, Liang Gao
https://arxiv.org/abs/2509.01165 https://arxiv.org…

Content-Aware Foveated Camera for Multi-Target Tracking
Modern image sensors deliver substantial space-time bandwidth, yet indiscriminate acquisition often overwhelms memory, computation, and downstream perception. We present a content-aware, multi-foveated camera that dynamically reallocates sensing and magnification to multiple regions of interest (ROIs). A phase-only spatial light modulator (SLM) serves as a solid-state, inertia-free beam-steering and lens element, enabling per-frame field-of-view (FOV) reconfiguration and content-aware target tr…

An entropy-stable and kinetic energy-preserving macro-element HDG method for compressible flows
Vahid Badrkhani, Marco F. P. ten Eikelder, Dominik Schillinger
https://arxiv.org/abs/2507.22195

An entropy-stable and kinetic energy-preserving macro-element HDG method for compressible flows
This paper introduces a high order numerical framework for efficient and robust simulation of compressible flows. To address the inefficiencies of standard hybridized discontinuous Galerkin (HDG) methods in large scale settings, we develop a macro element HDG method that reduces global and local degrees of freedom by embedding continuous Galerkin structure within macro-elements. This formulation supports matrix free implementations and enables highly parallel local solves, leading to substantia…

Frequency Domain Design of a Reset-Based Filter: An Add-On Nonlinear Filter for Industrial Motion Control
S. Ali Hosseini, Fabian R. Quinten, Luke F. van Eijk, Dragan Kostic, S. Hassan HosseinNia
https://arxiv.org/abs/2507.01491

Frequency Domain Design of a Reset-Based Filter: An Add-On Nonlinear Filter for Industrial Motion Control
This study introduces a modified version of the Constant-in-Gain, Lead-in-Phase (CgLp) filter, which incorporates a feedthrough term in the First-Order Reset Element (FORE) to reduce the undesirable nonlinearities and achieve an almost constant gain across all frequencies. A backward calculation approach is proposed to derive the additional parameter introduced by the feedthrough term, enabling designers to easily tune the filter to generate the required phase. The paper also presents an add-on…

A surface finite element scheme for a stochastic PDE on an evolving curve
Paola Pozzi, Bj\"orn Stinner
https://arxiv.org/abs/2507.01527 https://

A surface finite element scheme for a stochastic PDE on an evolving curve
In this paper we consider an ESFEM method for the advection and diffusion of a scalar quantity on a moving closed curve. The diffusion process is controlled by a forcing term that may include a rough term (specifically a stochastic noise) which in particular destroys the classical time differentiability properties of the solution. We provide a suitable variational solution concept and a fully discrete FEM discretization. Our error analysis appropriately generalizes classical estimates to this w…

Recent advances in arrow relations and traces of sets
Mingze Li, Jie Ma, Mingyuan Rong
https://arxiv.org/abs/2507.23375 https://arxiv.org/pdf/2507.23375

Recent advances in arrow relations and traces of sets
The arrow relation, a central concept in extremal set theory, captures quantitative relationships between families of sets and their traces. Formally, the arrow relation $(n, m) \rightarrow (a, b)$ signifies that for any family $\mathcal{F} \subseteq 2^{[n]}$ with $|\mathcal{F}| \geqslant m$, there exists an $a$-element subset $T \subseteq [n]$ such that the trace $\mathcal{F}_{|T} = \{ F \cap T : F \in \mathcal{F} \}$ contains at least $b$ distinct sets. This survey highlights r…

An energy-stable parametric finite element method for Willmore flow with normal-tangential velocity splitting
Harald Garcke, Robert N\"urnberg, Quan Zhao
https://arxiv.org/abs/2507.00193

An energy-stable parametric finite element method for Willmore flow with normal-tangential velocity splitting
We propose and analyze an energy-stable fully discrete parametric approximation for Willmore flow of hypersurfaces in two and three space dimensions. We allow for the presence of spontaneous curvature effects and for open surfaces with boundary. The presented scheme is based on a new geometric partial differential equation (PDE) that combines an evolution equation for the mean curvature with a separate equation that prescribes the tangential velocity. The mean curvature is used to determine the…

Modelling and simulation of electro-mechanically coupled dielectric elastomers and myocardial tissue using smoothed finite element methods
Tan Tran, Denisa Martonova, Sigrid Leyendecker
https://arxiv.org/abs/2507.22838

Modelling and simulation of electro-mechanically coupled dielectric elastomers and myocardial tissue using smoothed finite element methods
Computational modelling offers a cost-effective and time-efficient alternative to experimental studies in biomedical engineering. In cardiac electro-mechanics, finite element method (FEM)-based simulations provide valuable insights into diseased tissue behaviour and the development of assistive systems such as di-electric elastomer actuators. However, the use of automatically generated tetrahedral meshes, commonly applied due to geometric complexity, often leads to numerical issues including ov…

Simulation of Speckle Interferometric Results for Enhanced Measurement and Automated Defect Detection
Jessica Plassmann, Michael Schuth, Georg von Freymann
https://arxiv.org/abs/2507.00732

Simulation of Speckle Interferometric Results for Enhanced Measurement and Automated Defect Detection
Techniques like speckle holography and shearography are rarely applied due to the complexity of instrument setup and lack of automated result analysis, despite their potential. By simulating speckle interferometric outcomes, we seek to address these challenges, enabling more efficient measurement processes and paving the way for automated defect recognition. This research focuses on developing a simulation code for speckle interferometric results derived from finite element analyses. The aim is…

Hypergraph Splitting-Off via Element-Connectivity Preserving Reductions
Karthekeyan Chandrasekaran, Chandra Chekuri, Shubhang Kulkarni
https://arxiv.org/abs/2508.18637 https://

Hypergraph Splitting-Off via Element-Connectivity Preserving Reductions
Bérczi, Chandrasekaran, Király, and Kulkarni (ICALP 2024) recently described a splitting-off procedure in hypergraphs that preserves local-connectivity and outlined some applications. In this note we give an alternative proof via element-connectivity preserving reduction operations in graphs.

AFSI: Automated Fluid-Structure Interaction Solver Development for Nonlinear Solid Mechanics
Pengfei Ma, Li Cai, Xuan Wang, Hao Gao
https://arxiv.org/abs/2509.00014 https://

AFSI: Automated Fluid-Structure Interaction Solver Development for Nonlinear Solid Mechanics
AFSI is a novel, open-source fluid-structure interaction (FSI) solver that extends the capabilities of the FEniCS finite element library through an immersed boundary (IB) framework. Designed to simulate large deformations in hyperelastic materials (such as cardiac tissue), AFSI avoids the need for expensive remeshing by coupling a Lagrangian representation of the solid with an Eulerian description of the surrounding fluid. This approach retains the full expressiveness of FEniCS's variatio…

Higher Order Unfitted Space-Time Methods for Transport Problems
Erik Burman, Fabian Heimann
https://arxiv.org/abs/2509.02253 https://arxiv.org/pdf/2509.022…

Higher Order Unfitted Space-Time Methods for Transport Problems
In this article, we present an Unfitted Space-Time Finite Element method for the scalar transport equation posed on moving domains. We consider the case of the domain boundary being transported by the same velocity field as the scalar concentration inside the physical domain. A standard continuous Galerkin Finite element space is considered on a fixed background mesh, as well as tensor product Space-Time elements, which can be discontinuous along time slice boundaries. For the computational geo…

Revisit of Two-dimensional CEM on Crack Branching: from Single Crack-tip Tracking to Multiple Crack-tips Tracking
Yuxi Xie, Hongyou Cao, Miao Su, Zhipeng Lai, Xiaolong He
https://arxiv.org/abs/2509.01827

Revisit of Two-dimensional CEM on Crack Branching: from Single Crack-tip Tracking to Multiple Crack-tips Tracking
In this work, a Multiple Crack-tips Tracking algorithm in two-dimensional Crack Element Model (MCT-2D-CEM) is developed, aiming at modeling and predicting advanced and complicated crack patterns in two-dimensional dynamic fracturing problems, such as crack branching and fragmentation. Based on the developed fracture energy release rate formulation of split elementary topology, the Multiple Crack-tips Tracking algorithm is proposed and a series of benchmark examples are provided to validate effe…

Stabilization techniques for immersogeometric analysis of plate and shell problems in explicit dynamics
Giuliano Guarino, Yannis Voet, Pablo Antolin, Annalisa Buffa
https://arxiv.org/abs/2509.00522

Stabilization techniques for immersogeometric analysis of plate and shell problems in explicit dynamics
Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the underlying partial differential equations and the slenderness of the structures all impose a stringent constraint on the critical time step in explicit dynamics. Unfortunately, badly cut elements in immersed finite element discretizations further aggravate the …

Autoencoder-based non-intrusive model order reduction in continuum mechanics
Jannick Kehls, Ellen Kuhl, Tim Brepols, Kevin Linka, Hagen Holthusen
https://arxiv.org/abs/2509.02237

Autoencoder-based non-intrusive model order reduction in continuum mechanics
We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a compact latent space, (ii) a supervised regression network maps problem parameters to latent codes, and (iii) an end-to-end surrogate reconstructs full-field solutions directly from input parameters. To overcome limitations of existing approaches, we propose two…

Finding one excellent element in case of one lie
Aanchal Gupta, Gyula O. H. Katona
https://arxiv.org/abs/2507.13948 https://arxiv.org…

Finding one excellent element in case of one lie
An n-element set contains an unknown number of excellent elements, and our goal is to identify at least one of these elements. The members of a family of subsets can be asked if they contain at least one excellent element or not. At most one of the answers can be wrong. We find the smallest family that finds one excellent element or claims that there is none.

Design and Experimental Validation of UAV Swarm-Based Phased Arrays with MagSafe- and LEGO-Inspired RF Connectors
Bidya Debnath, Mst Mostary Begum, Prashant Neupant, Brooke E. Molen, Junming Diao
https://arxiv.org/abs/2507.22295

Design and Experimental Validation of UAV Swarm-Based Phased Arrays with MagSafe- and LEGO-Inspired RF Connectors
This paper presents a novel UAV swarm-based phased array antenna system that leverages MagSafe- and LEGO-inspired radio frequency (RF) connectors to address key challenges in distributed phased arrays, including inter-element oscillator synchronization, localization, phase coherence, and positional accuracy. The proposed non-threaded, hands-free connectors enable precise inter-element spacing and establish a continuous, low-loss RF signal propagation path during mid-flight docking. A multi-stag…

I-FENN with DeepONets: accelerating simulations in coupled multiphysics problems
Fouad M. Amin, Diab W. Abueidda, Panos Pantidis, Mostafa E. Mobasher
https://arxiv.org/abs/2509.00604

I-FENN with DeepONets: accelerating simulations in coupled multiphysics problems
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the Finite Element Method (FEM) to address coupled thermoelasticity and poroelasticity problems. This integration occurs within the context of I-FENN, a framework where neural networks are directly employed as PDE solvers within FEM, resulting in a hybrid staggere…

Long-time error estimate and decay of finite element method to a generalized viscoelastic flow
Yingwen Guo, Yinnian He, Wenlin Qiu, Xiangcheng Zheng
https://arxiv.org/abs/2506.22782

Long-time error estimate and decay of finite element method to a generalized viscoelastic flow
This work analyzes the finite element approximation to a viscoelastic flow model, which generalizes the Navier-Stokes equation and Oldroyd's model by introducing the tempered power-law memory kernel. We prove regularity and long-time exponential decay of the solutions, as well as a long-time convolution-type Grönwall inequality to support numerical analysis. A Volterra-Stokes projection is developed and analyzed to facilitate the parabolic-type duality argument, leading to the long-time error …

$hp$-adaptive finite element simulation of a static anti-plane shear crack in a nonlinear strain-limiting elastic solid
S. M. Mallikarjunaiah, Pavithra Venkatachalapthy
https://arxiv.org/abs/2507.23195

$hp$-adaptive finite element simulation of a static anti-plane shear crack in a nonlinear strain-limiting elastic solid
An $hp$-adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law relating stress and strain that is algebraically nonlinear. In this investigation, the constitutive relation utilized is \textit{uniformly bounded}, \textit{monotone}, \textit{coercive}, and \textit{Lipschitz continuous}, ensuring the well-posedness of the mat…

A new definition of peridynamic damage for thermo-mechanical fracture modeling
Sitong Tao, Fei Han
https://arxiv.org/abs/2509.01079 https://arxiv.org/pdf/2…

A new definition of peridynamic damage for thermo-mechanical fracture modeling
A thermo-mechanical fracture modeling is proposed to address thermal failure issues, where the temperature field is calculated by a heat conduction model based on classical continuum mechanics (CCM), while the deformation field with discontinuities is calculated by the peridynamic (PD) model. The model is calculated by a CCM/PD alternating solution based on the finite element discretization, which ensures the calculation accuracy and facilitates engineering applications. The original PD model d…

On Generalized Rickart $*$-rings
Anil Khairnar, Sanjay More
https://arxiv.org/abs/2508.20842 https://arxiv.org/pdf/2508.20842

On Generalized Rickart $*$-rings
A ring $R$ with an involution $*$ is a generalized Rickart $*$-ring if for all $x\in R$ the right annihilator of $x^n$ is generated by a projection for some positive integer $n$ depending on $x$. In this work, we introduce generalized right projection of an element in a $*$-ring and prove that every element in a generalized Rickart $*$-ring has generalized right projection. Various characterizations of generalized Rickart $*$-rings are obtained. We introduce the concept of generalized weakly Ri…

Error analysis for a Finite Element Discretization of a radially symmetric harmonic map heat flow problem
Nam Anh Nguyen, Arnold Reusken
https://arxiv.org/abs/2506.23748

Error analysis for a Finite Element Discretization of a radially symmetric harmonic map heat flow problem
We consider the harmonic map heat flow problem for a radially symmetric case. For discretization of this problem we apply a $H^1$-conforming finite element method in space combined with a semi-implicit Euler time stepping. The semi-implicit Euler method results in a linear problem in each time step. We restrict to the regime of smooth solutions of the continuous problem and present an error analysis of this discretization method. This results in optimal order discretization error bounds. Key in…

Efficient Numerical Integration for Finite Element Trunk Spaces in 2D and 3D using Machine Learning: A new Optimisation Paradigm to Construct Application-Specific Quadrature Rules
Tomas Teijeiro, Pouria Behnoudfar, Jamie M. Taylor, David Pardo, Victor M. Calo
https://arxiv.org/abs/2506.23741…

Efficient Numerical Integration for Finite Element Trunk Spaces in 2D and 3D using Machine Learning: A new Optimisation Paradigm to Construct Application-Specific Quadrature Rules
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than necessary, especially as the polynomial degree $p$ or the spatial dimension increases, leading to considerable computational overhead. This work starts from the hypothesis that reducing the dimensionality of the polynomial space can lead to quadrature rules wi…

A new family of a posteriori error estimates for non-conforming finite element methods leading to stabilization-free error bounds
T. Chaumont-Frelet
https://arxiv.org/abs/2506.23381

A new family of a posteriori error estimates for non-conforming finite element methods leading to stabilization-free error bounds
We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulations of the standard Prager-Synge identity, and enable to prove efficiency estimates without extra stabilization terms in the error measure for a large class of discretization schemes. We propose a residual-based estimator for which the efficiency constant scales optimally in polynomial degree, as well as two equilibr…

A Chimera domain decomposition method with weak Dirichlet-Robin coupling for finite element simulation of particulate flows
Raphael M\"unster, Otto Mierka, Dmitri Kuzmin, Stefan Turek
https://arxiv.org/abs/2506.22831

A Chimera domain decomposition method with weak Dirichlet-Robin coupling for finite element simulation of particulate flows
We introduce a new multimesh finite element method for direct numerical simulation of incompressible particulate flows. The proposed approach falls into the category of overlapping domain decomposition / Chimera / overset grid meshes. In addition to calculating the velocity and pressure of the fictitious fluid on a fixed background mesh, we solve the incompressible Navier-Stokes equations on body-fitted submeshes that are attached to moving particles. The submesh velocity and pressure are used …

Rectangular $C^1$-$Q_k$ Bell finite elements in two and three dimensions
Hongling Hu, Shangyou Zhang
https://arxiv.org/abs/2506.23702 https://

Rectangular $C^1$-$Q_k$ Bell finite elements in two and three dimensions
Both the function and its normal derivative on the element boundary are $Q_k$ polynomials for the Bogner-Fox-Schmit $C^1$-$Q_k$ finite element functions. Mathematically, to keep the optimal order of approximation, their spaces are required to include $P_k$ and $P_{k-1}$ polynomials respectively. We construct a Bell type $C^1$-$Q_k$ finite element on rectangular meshes in 2D and 3D, which has its normal derivative as a $Q_{k-1}$ polynomial on each face, for $k\ge 4$. We show, with a big re…

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators
Weihang Ouyang, Yeonjong Shin, Si-Wei Liu, Lu Lu
https://arxiv.org/abs/2506.18427

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale simulations. Emerging machine learning-based methods (e.g., neural operators) provide data-driven solutions to PDEs, yet they present challenges, including high training cost and low model reusability. Here, we propose the neural-operator element method (NOEM) by s…

Do locking-free finite element schemes lock for holey Reissner-Mindlin plates with mixed boundary conditions?
Mark Ainsworth, Charles Parker
https://arxiv.org/abs/2506.21999

Do locking-free finite element schemes lock for holey Reissner-Mindlin plates with mixed boundary conditions?
We revisit finite element discretizations of the Reissner-Mindlin plate in the case of non-simply connected (holey) domains with mixed boundary conditions. Guided by the de Rham complex, we develop conditions under which schemes deliver locking-free, optimal rates of convergence. We naturally recover the typical assumptions arising for clamped, simply supported plates. More importantly, we also see new conditions arise naturally from the presence of holes in the domain or in the case of mixed b…

Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Models
Natalia L. Rubio, Eric F. Darve, Alison L. Marsden
https://arxiv.org/abs/2508.21165 h…

Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Models
Three-dimensional (3D) finite-element simulations of cardiovascular flows provide high-fidelity predictions to support cardiovascular medicine, but their high computational cost limits clinical practicality. Reduced-order models (ROMs) offer computationally efficient alternatives but suffer reduced accuracy, particularly at vessel bifurcations where complex flow physics are inadequately captured by standard Poiseuille flow assumptions. We present an enhanced numerical framework that integrates …

Computational Insights into Orthotropic Fracture: Crack-Tip Fields in Strain-Limiting Materials under Non-Uniform Loads
Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah
https://arxiv.org/abs/2507.01150

Computational Insights into Orthotropic Fracture: Crack-Tip Fields in Strain-Limiting Materials under Non-Uniform Loads
A finite element framework is presented for analyzing crack-tip phenomena in transversely isotropic, strain-limiting elastic materials. Mechanical response is characterized by an algebraically nonlinear constitutive model, relating stress to linearized strain. Non-physical strain singularities at the crack apex are mitigated, ensuring bounded strain magnitudes. This methodology significantly advances boundary value problem (BVP) formulation, especially for first-order approximate theories. For …

Linear, decoupled, positivity preserving, positive-definiteness preserving and energy stable schemes for the diffusive Oldroyd-B coupled with PNP model
Wenxing Zhu, Mingyang Pan, Dongdong He
https://arxiv.org/abs/2509.01278

Linear, decoupled, positivity preserving, positive-definiteness preserving and energy stable schemes for the diffusive Oldroyd-B coupled with PNP model
In this paper, we present a first-order finite element scheme for the viscoelastic electrohydrodynamic model. The model incorporates the Poisson-Nernst-Planck equations to describe the transport of ions and the Oldroyd-B constitutive model to capture the behavior of viscoelastic fluids. To preserve the positive-definiteness of the conformation tensor and the positivity of ion concentrations, we employ both logarithmic transformations. The decoupled scheme is achieved by introducing a nonlocal a…

On discrete Sobolev inequalities for nonconforming finite elements under a semi-regular mesh condition
Hiroki Ishizaka
https://arxiv.org/abs/2509.00505 https://

On discrete Sobolev inequalities for nonconforming finite elements under a semi-regular mesh condition
We derive a discrete $ L^q-L^p$ Sobolev inequality tailored for the Crouzeix--Raviart and discontinuous Crouzeix--Raviart finite element spaces on anisotropic meshes in both two and three dimensions. Subject to a semi-regular mesh condition, this discrete Sobolev inequality is applicable to all pairs $(q,p)$ that align with the local Sobolev embedding, including scenarios where $q \leq p$. Importantly, the constant is influenced solely by the domain and the semi-regular parameter, ensuring robu…

Conservative data-driven finite element formulation
Adriana Kulikov\'a (Glasgow Computational Engineering Centre), Andrei G. Shvarts (Glasgow Computational Engineering Centre), {\L}ukasz Kaczmarczyk (Glasgow Computational Engineering Centre), Chris J. Pearce (Glasgow Computational Engineering Centre)
https://arxiv.org/abs/25…

Conservative data-driven finite element formulation
This paper presents a new data-driven finite element framework derived with mixed finite element formulation. The standard approach to diffusion problems requires the solution of the mathematical equations that describe both the conservation law and the constitutive relations, where the latter is traditionally obtained after fitting experimental data to simplified material models. To exploit all available information and avoid bias in the material model, we follow a data-driven approach. While …

Global Energy Minimization for Simplex Mesh Optimization: A Radius Ratio Approach to Sliver Elimination
Dong Wang, Chunyu Chen, Huayi Wei
https://arxiv.org/abs/2507.01762

Global Energy Minimization for Simplex Mesh Optimization: A Radius Ratio Approach to Sliver Elimination
The quality of simplex mesh is crucial for the stability and accuracy of numerical simulations in finite element analysis and computational geometry. However, the presence of sliver elements in 3D simplex mesh can severely impact the results. This paper presents a novel method based on a radius ratio energy function to optimize the quality of simplex mesh elements. This method can effectively eliminate sliver elements, thereby enhancing mesh quality.The gradient of the proposed energy function …

Linear, decoupled, second-order and structure-preserving scheme for Carreau fluid equations coupled with steric Poisson-Nernst-Planck model
Wenxing Zhu, Mingyang Pan, Dongdong He
https://arxiv.org/abs/2509.01270

Linear, decoupled, second-order and structure-preserving scheme for Carreau fluid equations coupled with steric Poisson-Nernst-Planck model
In this paper, to study ionic steric effects, we present a linear, decoupled, second-order accurate in time and structure-preserving scheme with finite element approximations for Carreau fluid equations coupled with steric Poisson-Nernst-Planck (SPNP) model. The logarithmic transformation for the ion concentration is used to preserve positivity property. To deal with the nonlinear coupling terms in fluid equation, a nonlocal auxiliary variable with respect to the free energy of SPNP equations a…

Fractional differential equations: non-constant coefficients, simulation and model reduction
Ruben Aylwin, G\"oksu Oruc, Karsten Urban
https://arxiv.org/abs/2509.02465 http…

Fractional differential equations: non-constant coefficients, simulation and model reduction
We consider boundary value problems with Riemann-Liouville fractional derivatives of order $s\in (1, 2)$ with non-constant diffusion and reaction coefficients. A variational formulation is derived and analyzed leading to the well-posedness of the continuous problem and its Finite Element discretization. Then, the Reduced Basis Method through a greedy algorithm for parametric diffusion and reaction coefficients is analyzed. Its convergence properties, and in particular the decay of the Kolmogoro…

Isogeometric contact analysis in subsea umbilical and power cables
Tianjiao Dai (School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics, HUST, Wuhan, China), Shuo Yang (Zoomlion Heavy Industry Science and Technology Co., Ltd., China), Xing Jin (China Offshore Engineering and Technology Co., Ltd., China), Svein S{\ae}vik (Department of Marine Technology, Norwegian U…

Isogeometric contact analysis in subsea umbilical and power cables
Subsea umbilical and power cables contain a large number of contact interfaces between different geometries and materials. These complex interactions rise significant challenges for accurately considering contact surface properties by using traditional analytical solutions or finite element methods. These properties have been identified as the most sensitive parameters when performing the numerical simulation for stress analysis. Therefore, it is essential to apply a novel approach for contact …

PDE-Constrained High-Order Mesh Optimization
Tzanio Kolev, Boyan Lazarov, Ketan Mittal, Mathias Schmidt, Vladimir Tomov
https://arxiv.org/abs/2507.01917 ht…

PDE-Constrained High-Order Mesh Optimization
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regula…

DefElement: an encyclopedia of finite element definitions
Matthew W. Scroggs, Pablo D. Brubeck, Joseph P. Dean, J{\o}rgen S. Dokken, India Marsden
https://arxiv.org/abs/2506.20188

DefElement: an encyclopedia of finite element definitions
DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elements defined in the literature easily available in a standard format. There are a number of open-source finite element libraries available, and it can be difficult to check that an implementation of an element in a library matches the element's definition in the literature or implementation in another library, especiall…

Divergence-free Preserving Mix Finite Element Methods for Fourth-order Active Fluid Model
Nan Zheng, Xu Guo, Wenlong Pei, Wenju Zhao
https://arxiv.org/abs/2507.21392 https://

Divergence-free Preserving Mix Finite Element Methods for Fourth-order Active Fluid Model
This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-Δu$, the original fourth problem is transformed into a system of second-order equations, which relaxes the regularity requirements of standard $H^2$-conforming finite spaces. To further enhance the robustness and efficiency of the algorithm, an additional auxiliary variable $ϕ$, treated analogously to the pressu…

Space-time finite element methods for nonlinear wave equations via elliptic regularisation
Lehel Banjai, Emmanuil H. Georgoulis, Brian Hennessy
https://arxiv.org/abs/2507.22757 …

Space-time finite element methods for nonlinear wave equations via elliptic regularisation
We present and analyse a new conforming space-time Galerkin discretisation of a semi-linear wave equation, based on a variational formulation derived from De Giorgi's elliptic regularisation viewpoint of the wave equation in second-order formulation. The method is shown to be well-posed through a minimisation approach, and also unconditionally stable for all choices of conforming discretisation spaces. Further, a priori error bounds are proven for sufficiently smooth solutions. Special attentio…

Low-order finite element complex with application to a fourth-order elliptic singular perturbation problem
Xuewei Cui, Xuehai Huang
https://arxiv.org/abs/2506.20240

Low-order finite element complex with application to a fourth-order elliptic singular perturbation problem
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous $H^1$-nonconforming vector-valued finite element space, the lowest-order Raviart-Thomas space, and piecewise constant functions. While nonconforming for the smooth complex, the discretization conforms to the classical de Rham complex. It is applied to develop a decou…

A Taylor-Hood finite element method for the surface Stokes problem without penalization
Alan Demlow, Michael Neilan
https://arxiv.org/abs/2506.20419 https:…

A Taylor-Hood finite element method for the surface Stokes problem without penalization
Finite element approximation of the velocity-pressure formulation of the surfaces Stokes equations is challenging because it is typically not possible to enforce both tangentiality and $H^1$ conformity of the velocity field. Most previous works concerning finite element methods (FEMs) for these equations thus have weakly enforced one of these two constraints by penalization or a Lagrange multiplier formulation. Recently in [A tangential and penalty-free finite element method for the surface Sto…

A comparative study of finite element methods for a class of harmonic map heat flow problems
Nam Anh Nguyen, Arnold Reusken
https://arxiv.org/abs/2508.20590 https://

A comparative study of finite element methods for a class of harmonic map heat flow problems
In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework. Numerical tests validate the convergence rates in a regime of smooth solutions and are used to compare the methods in terms of computational efficiency. For one of the methods a discrete inf-sup stability result is derived.

Spectral element methods for boundary-value problems of functional differential equations
Alessia and\`o, Jan Sieber
https://arxiv.org/abs/2507.20266 https://

Spectral element methods for boundary-value problems of functional differential equations
We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems (BVP) for functional differential equations with possibly state-dependent delays. If the exact solution of the BVP has an analytic extension then the collocation solution converges geometrically. This means that the accuracy of the approximation is of order $\mathrm{e}^{-ηm}$ for some $η>0$ depending on the size of the mesh, when using polynomials of degree $m…

Automated Runge-Kutta-Nystr\"om time stepping for finite element methods in Irksome
Robert C. Kirby, Scott P. MacLachlan, Pablo D. Brubeck
https://arxiv.org/abs/2508.20255 …

Automated Runge-Kutta-Nyström time stepping for finite element methods in Irksome
Irksome is a library based on the Unified Form Language (UFL) that automates the application of Runge-Kutta time-stepping methods for finite element spatial discretizations of partial differential equations (PDEs). This paper describes recent updates to Irksome that allow users to express semidiscrete forms of PDEs that contain second-order temporal derivatives, whence it generates stage-coupled variational problems to be solved at each time step for Runge-Kutta-Nyström methods. Firedrake then…

Uniform error analysis of a rectangular Morley finite element method on a Shishkin mesh for a 4th-order singularly perturbed boundary value problem
Xiangyun Meng, Martin Stynes
https://arxiv.org/abs/2508.20857

Uniform error analysis of a rectangular Morley finite element method on a Shishkin mesh for a 4th-order singularly perturbed boundary value problem
The singularly perturbed reaction-diffusion problem $\varepsilon^2Δ^2 u - \mathrm{div}\left(c\nabla u\right) = f$ is considered on the unit square $Ω$ in $\mathbb{R}^2$ with homogenous Dirichlet boundary conditions. Its solution typically contains boundary layers on all sides of~$Ω$. It is discretised by a finite element method that uses rectangular Morley elements on a Shishkin mesh. In an associated energy-type norm that is natural for this problem, we prove an $O(\varepsilon^{1/2}N^{-1}+\…

An adaptive finite element discretization based parallel orbital-updating method for eigenvalue problems
Xiaoying Dai, Yan Li, Bin Yang, Aihui Zhou
https://arxiv.org/abs/2508.19832

An adaptive finite element discretization based parallel orbital-updating method for eigenvalue problems
It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating method, which can significantly reduce the computational cost and enhance the parallel scalability, has been shown to be efficient in electronic structure calculations. In this paper, we provide a mathematical justification for the method for clustered eigenvalu…

An energy-stable parametric finite element method for the Willmore flow in three dimensions
Weizhu Bao, Yifei Li, Dongmin Wang
https://arxiv.org/abs/2506.21025

An energy-stable parametric finite element method for the Willmore flow in three dimensions
This work develops novel energy-stable parametric finite element methods (ES-PFEM) for the Willmore flow and curvature-dependent geometric gradient flows of surfaces in three dimensions. The key to achieving the energy stability lies in the use of two novel geometric identities: (i) a reformulated variational form of the normal velocity field, and (ii) incorporation of the temporal evolution of the mean curvature into the governing equations. These identities enable the derivation of a new vari…

A discontinuous in time Streamline Diffusion Virtual Element Method for Darcy-transport problem
R A Caraballo Diaz, F Dassi
https://arxiv.org/abs/2506.21326

A discontinuous in time Streamline Diffusion Virtual Element Method for Darcy-transport problem
We present a first numerical study of transport phenomena involving chemically reactive species, modeled by advection-diffusion-reaction systems with flow fields governed by Darcy's law. Among the various discretisation approaches, we consider the Streamline Diffusion method. Both the velocity field and the species concentrations are computed using the Virtual Element Method using a Discontinuous Galerkin scheme for time. An abstract error estimate has been derived using a special technique tha…

Machine-precision energy conservative quadrature hyperreduction of Lagrangian hydrodynamics
Chris Vales, Siu Wun Cheung, Dylan M. Copeland, Youngsoo Choi
https://arxiv.org/abs/2508.21279

Machine-precision energy conservative quadrature hyperreduction of Lagrangian hydrodynamics
We present an energy conservative, quadrature based model reduction framework for the compressible Euler equations of Lagrangian hydrodynamics. Building on a high order finite element discretization of the governing equations, we develop a projection based reduced model using data driven reduced basis functions and hyperreduction via the empirical quadrature procedure (EQP). We introduce a strongly energy conservative variant of EQP that enforces exact discrete total energy conservation during …