Tootfinder

🤔 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.

Generic infinite generation, fixed-point-poor representations and compact-element abundance in disconnected Lie groups
Alexandru Chirvasitu
https://arxiv.org/abs/2507.04065

Generic infinite generation, fixed-point-poor representations and compact-element abundance in disconnected Lie groups
The semidirect product $\mathbb{G}=\mathbb{L}\rtimes \mathbb{K}$ attached to a compact-group action on a connected, simply-connected solvable Lie group has a dense set of compact elements precisely when the $s\in \mathbb{K}$ operating on $\mathbb{L}$ fixed-point-freely constitute a dense set. This (along with a number of alternative equivalent characterizations) extends the Wu's analogous result for connected Lie $\mathbb{K}$, and also provides ample supplies of examples of almost-connected Lie…

Accelerating multijet-merged event generation with neural network matrix element surrogates
Tim Herrmann, Timo Jan{\ss}en, Mathis Schenker, Steffen Schumann, Frank Siegert
https://arxiv.org/abs/2506.06203

Accelerating multijet-merged event generation with neural network matrix element surrogates
The efficient simulation of multijet final states presents a serious computational task for analyses of LHC data and will be even more so at the HL-LHC. We here discuss means to accelerate the generation of unweighted events based on a two-stage rejection-sampling algorithm that employs neural-network surrogates for unweighting the hard-process matrix elements. To this end, we generalise the previously proposed algorithm based on factorisation-aware neural networks to the case of multijet mergi…

Wie beeinflusst der #Klimawandel die CO2-Speicherung in den Ozeanen? Die sogenannte #Kohlenstoffpumpe ist ein kritisches Element im globalen #Klimasystem und rettet bisher unser Überleb…

Die Kohlenstoffpumpe der Ozeane: Welche Auswirkungen hat der Klimawandel auf die CO2-Speicherung?
Die Ozeane sind ein wichtiger Kohlendioxidspeicher. Wie funktioniert die Kohlenstoffpumpe der Ozeane und welche Auswirkungen hat der Klimawandel darauf?

One more #squirrel from our visit to the #Nürnberg #zoo (for those who didn't want to visit the blog post 😉)
The blog post:

Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes
Jens Keim, Anna Schwarz, Patrick Kopper, Marcel Blind, Christian Rohde, Andrea Beck
https://arxiv.org/abs/2507.04334

Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes
Hyperbolic-parabolic partial differential equations are widely used for the modeling of complex, multiscale problems. High-order methods such as the discontinuous Galerkin (DG) scheme are attractive candidates for their numerical approximation. However, high-order methods are prone to instabilities in the presence of underresolved flow features. A popular counter measure to stabilize DG methods is the use of entropy-stable formulations based on summation-by-parts (SBP) operators. The present pa…

Ai-fixing jobs are well-paid, but they have a huge AI-education element in them.
The BBC writes about several stories of AI firefighting.
https://www.bbc.com/news/articles/cyvm1dyp9v2o

'I'm being paid to fix issues caused by AI'
Businesses that rush to use AI to write content or computer code, often have to pay humans to fix it.

Higher-Order Harmonics Reduction in Reset-Based Control Systems: Application to Precision Positioning Systems
S. Ali Hosseini, Nima Karbasizadeh, S. Hassan HosseiniNia
https://arxiv.org/abs/2507.04707

Higher-Order Harmonics Reduction in Reset-Based Control Systems: Application to Precision Positioning Systems
To address the limitations imposed by Bode's gain-phase relationship in linear controllers, a reset-based filter called the Constant in gain- Lead in phase (CgLp) filter has been introduced. This filter consists of a reset element and a linear lead filter. However, the sequencing of these two components has been a topic of debate. Positioning the lead filter before the reset element in the loop leads to noise amplification in the reset signal, whereas placing the lead filter after the reset ele…

Just finished "To a Darker Shore" by Leanne Schwartz. It's a blend of fantasy (a genre I enjoyed a lot when younger but which I now feel is hit-or-miss depending on the politics of the author) and romance (a genre I'm currently a bit obsessed with) and I enjoyed it very much. The element of an #OwnVoices autistic perspective was interesting, and the mythology was pretty cool. Even though I felt as though monstrousness could have been explored from an even better angle, the complexity in this book was comfortable, and it to my mind successfully-enough avoided the veneer of racism that runs through the mainstream fantasy tradition.
#AmReading

@… yeah, you’re right — the numbers are aria-hidden. I could modify the component to have the line content embedded in the `<ul>` (but not visible) and hide the primary element from screen readers — that would be better for `<pre>` maybe but not textarea!

The overflow in the Katona Theorem
Peter Frankl, Jian Wang
https://arxiv.org/abs/2506.05704 https://arxiv.org/pdf/2506.05704

The overflow in the Katona Theorem
Let $n>2r>0$ be integers. We consider families $\mathcal{F}$ of subsets of an $n$-element set, in which the union of any two members has size at most $2r$. One of our results states that for $n\geq 6r$ the number of members of size exceeding $r$ in $\mathcal{F}$ is at most $\binom{n-2}{r-1}$. Another result shows that for $n>3.5r$ the number of sets of size at least $r$ is at most $\binom{n}{r}$. Both bounds are best possible and the latter sharpens the classical Katona Theorem. Similar results…

Communication Round and Computation Efficient Exclusive Prefix-Sums Algorithms (for MPI_Exscan)
Jesper Larsson Tr\"aff
https://arxiv.org/abs/2507.04785

Communication Round and Computation Efficient Exclusive Prefix-Sums Algorithms (for MPI_Exscan)
Parallel scan primitives compute element-wise inclusive or exclusive prefix sums of input vectors contributed by $p$ consecutively ranked processors under an associative, binary operator $\oplus$. In message-passing systems with bounded, one-ported communication capabilities, at least $\lceil\log_2 p\rceil$ or $\lceil\log_2 (p-1)\rceil$ communication rounds are required to perform the scans. While there are well-known, simple algorithms for the inclusive scan that solve the problem in $\lceil\l…

Measuring how changes in code readability attributes affect code quality evaluation by Large Language Models
Igor Regis da Silva Simoes, Elaine Venson
https://arxiv.org/abs/2507.05289

Measuring how changes in code readability attributes affect code quality evaluation by Large Language Models
Code readability is one of the main aspects of code quality, influenced by various properties like identifier names, comments, code structure, and adherence to standards. However, measuring this attribute poses challenges in both industry and academia. While static analysis tools assess attributes such as code smells and comment percentage, code reviews introduce an element of subjectivity. This paper explores using Large Language Models (LLMs) to evaluate code quality attributes related to its…

Urban Solitude III 🈳
城市孤独 III 🈳
📷 Pentax MX
🎞️Fujifilm Neopan SS, expired 1995
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

Yiding Cao Geld mit PayPal.Me senden
Folgen Sie dem Link PayPal.Me/dingsterdingster und geben Sie den Betrag ein. Es ist bequem und sicher. Sie haben noch kein PayPal-Konto? Kein Problem.

Positive Varieties of Lattice Languages
Yusuke Inoue, Yuji Komatsu
https://arxiv.org/abs/2506.05824 https://arxiv.org/pdf/2506.05824

Positive Varieties of Lattice Languages
While a language assigns a value of either `yes' or `no' to each word, a lattice language assigns an element of a given lattice to each word. An advantage of lattice languages is that joins and meets of languages can be defined as generalizations of unions and intersections. This fact also allows for the definition of positive varieties -- classes closed under joins, meets, quotients, and inverse homomorphisms -- of lattice languages. In this paper, we extend Pin's positive variety theorem, pro…

First-eigenvalue maximization and inflation of maps
Shin Nayatani
https://arxiv.org/abs/2506.05681 https://arxiv.org/pdf/2506.05681…

First-eigenvalue maximization and inflation of maps
Given a compact manifold equipped with a volume element and a Riemannian metric, we formulate and study a dual pair of optimization problems: one concerning smooth maps from the manifold into the Hilbert space $l^2$ and the other concerning the smallest positive eigenvalue of the Bakry-Emery Laplacian. We present examples of manifolds for which these problems can be solved explicitly. We also prove a Nadirashvili-type theorem.

Pre-Lie algebras up to homotopy with divided powers and homotopy of operadic mapping spaces
Marvin Verstraete
https://arxiv.org/abs/2507.03632 https://

Pre-Lie algebras up to homotopy with divided powers and homotopy of operadic mapping spaces
The purpose of this memoir is to study pre-Lie algebras up to homotopy with divided powers, and to use this algebraic structure for the study of mapping spaces in the category of operads. We define a new notion of algebra called $ΓΛ\mathcal{PL}_\infty$-algebra which characterizes the notion of $Γ(\mathcal{P}re\mathcal{L}ie_\infty,-)$-algebra. We also define a notion of a Maurer-Cartan element in complete $ΓΛ\mathcal{PL}_\infty$-algebras which generalizes the classical definition in Lie alg…

Fast-VGAN: Lightweight Voice Conversion with Explicit Control of F0 and Duration Parameters
Mathilde Abrassart, Nicolas Obin, Axel Roebel
https://arxiv.org/abs/2507.04817

Fast-VGAN: Lightweight Voice Conversion with Explicit Control of F0 and Duration Parameters
Precise control over speech characteristics, such as pitch, duration, and speech rate, remains a significant challenge in the field of voice conversion. The ability to manipulate parameters like pitch and syllable rate is an important element for effective identity conversion, but can also be used independently for voice transformation, achieving goals that were historically addressed by vocoder-based methods. In this work, we explore a convolutional neural network-based approach that aims to…

Mechanics Simulation with Implicit Neural Representations of Complex Geometries
Samundra Karki, Ming-Chen Hsu, Adarsh Krishnamurthy, Baskar Ganapathysubramanian
https://arxiv.org/abs/2507.03087

Mechanics Simulation with Implicit Neural Representations of Complex Geometries
Implicit Neural Representations (INRs), characterized by neural network-encoded signed distance fields, provide a powerful means to represent complex geometries continuously and efficiently. While successful in computer vision and generative modeling, integrating INRs into computational analysis workflows, such as finite element simulations, remains underdeveloped. In this work, we propose a computational framework that seamlessly combines INRs with the Shifted Boundary Method (SBM) for high-fi…

A systematic study of binary neutron star merger rate density history using simulated gravitational wave and short gamma-ray burst observations
Yun-Fei Du, Emre Seyit Yorgancioglu, Shu-Xu Yi, Tian-Yong Cao, Shuang-Nan Zhang
https://arxiv.org/abs/2507.04019

A systematic study of binary neutron star merger rate density history using simulated gravitational wave and short gamma-ray burst observations
Measuring the merger rate density history of binary neutron stars (BNS) can greatly aid in understanding the history of heavy element formation in the Universe. Currently, second-generation Gravitational Wave (GW) detectors can only measure the BNS merger rate density history at low redshifts ($z$ $\sim$ 0.1). Short gamma-ray bursts (sGRBs) may trace the BNS merger to higher redshifts ($z$ $\sim$ 3). However, not all BNS mergers result in sGRBs, and it is not certain that all sGRBs originate fr…

Nitrogen-related short-range order in Fe-Ni-Cr austenitic stainless steels: first principles and cluster expansion study
Tianyu Su, Brian J. Blankenau, Namhoon Kim, Jessica A. Krogstad, Elif Ertekin
https://arxiv.org/abs/2507.04580

Nitrogen-related short-range order in Fe-Ni-Cr austenitic stainless steels: first principles and cluster expansion study
Nitrogen (N) is a key alloying element that enhances the performance of Fe-Ni-Cr austenitic stainless steels, improving austenite stability, corrosion resistance, and yield strength. However, the role of N in modifying chemical ordering, particularly short-range order (SRO) and long-range order (LRO), is complex due to the multi-sublattice nature and magnetic interactions in these alloys. In this work, we combine first-principles calculations with the spin cluster expansion (spin CE) method to …

An old friend of mine is a Hasher. Shout-out to Pollywaffle from Canberra. https://sudomakecake.com/@woollypigs/114640950327552671

Transient segregation of bi-disperse granular mixtures in a periodic chute flow
Soniya Kumawat, Vishnu Kumar Sahu, Anurag Tripathi
https://arxiv.org/abs/2507.04025

Transient segregation of bi-disperse granular mixtures in a periodic chute flow
Transient size segregation of a bi-disperse granular mixture flowing over a periodic chute is studied using the Discrete Element Method and continuum simulations. A recently developed particle force-based size segregation model is used to predict the time-dependent flow properties of binary mixtures starting from rest. A two-way coupled continuum model that solves the momentum balance and convection-diffusion equations by incorporating the mixture segregation model along with the generalized in…

Hyperspectral Dual-Comb Compressive Imaging for Minimally-Invasive Video-Rate Endomicroscopy
Myoung-Gyun Suh (Howard), David Dang (Howard), Maodong Gao (Howard), Yucheng Jin (Howard), Byoung Jun Park (Howard), Beyonce Hu (Howard), Wilton J. M. Kort-Kamp (Howard), Ho Wai (Howard), Lee
https://arxiv.org/abs/2507.04157

Hyperspectral Dual-Comb Compressive Imaging for Minimally-Invasive Video-Rate Endomicroscopy
Endoscopic imaging is essential for real-time visualization of internal organs, yet conventional systems remain bulky, complex, and expensive due to their reliance on large, multi-element optical components. This limits their accessibility to delicate or constrained anatomical regions. Achieving real-time, high-resolution endomicroscopy using compact, low-cost hardware at the hundred-micron scale remains an unsolved challenge. Optical fibers offer a promising route toward miniaturization by pro…

Multiuser Beamformig for Pinching-Antenna Systems: An Element-wise Optimization Framework
Mingjun Sun, Chongjun Ouyang, Shaochuan Wu, Yuanwei Liu
https://arxiv.org/abs/2506.03770 …

Multiuser Beamformig for Pinching-Antenna Systems: An Element-wise Optimization Framework
The pinching-antenna system (PASS) reconstructs wireless channels through pinching beamforming, i.e., optimizing the activated locations of pinching antennas (PAs) along the waveguide. The aim of this article is to investigate the joint design of baseband beamforming and pinching beamforming. A low-complexity element-wise sequential optimization framework is proposed to address the sum-rate maximization problem in PASS-enabled downlink and uplink channels. i) For the downlink scenario, maximum …

Scale Dilation Dynamics in Flexible Bandwidth Needlet Constructions
Claudio Durastanti
https://arxiv.org/abs/2507.05075 https://arxiv…

Scale Dilation Dynamics in Flexible Bandwidth Needlet Constructions
Flexible bandwidth needlets offer a versatile multiscale framework for analyzing functions on the sphere. A key element in their construction is the dilation sequence, which controls how the multipole consecutive scales are spaced and overlapped. At any resolution level, this sequence determines the center positions of the needlet weight functions and influences their localization in the spatial domain and spectral concentration properties by means of the relative bandwidth ratio. In this paper…

»How to build a copy-to-clipboard HTML«
– by @…
With JavaScript set HTML to easy use web GUI's.
📃 https://gomakethings.com/how-…

How to build a copy-to-clipboard HTML Web Component
Yesterday, we looked at how to copy items to a user’s clipboard with JavaScriprt. Today, we’re going to turn that into an HTML Web Component. Let’s dig in! The Custom Element For this Web Component, let’s use a element. With the HTML Web Component approach, we start with HTML and enhance it rather than rendering all the things with JavaScript. Let’s add a with our desired text inside the custom element.

An Improved Finite Element Modeling Method for Triply Periodic Minimal Surface Structures Based on Element Size and Minimum Jacobian
Siqi Wang, Chuangyu Jiang, Xiaodong Zhang, Yilong Zhang, Baoqiang Zhang, Huageng Luo
https://arxiv.org/abs/2506.04028

An Improved Finite Element Modeling Method for Triply Periodic Minimal Surface Structures Based on Element Size and Minimum Jacobian
Triply periodic minimal surface (TPMS) structures, a type of lattice structure, have garnered significant attention due to their lightweight nature, controllability, and excellent mechanical properties. Voxel-based modeling is a widely used method for investigating the mechanical behavior of such lattice structures through finite element simulations. This study proposes a two-parameter voxel method that incorporates joint control of element size and minimum Jacobian (MJ). Numerical results indi…

Predicting Flow-Induced Vibration in Isolated and Tandem Cylinders Using Hypergraph Neural Networks
Shayan Heydari, Rui Gao, Rajeev K Jaiman
https://arxiv.org/abs/2507.02242

Predicting Flow-Induced Vibration in Isolated and Tandem Cylinders Using Hypergraph Neural Networks
We present a finite element-inspired hypergraph neural network framework for predicting flow-induced vibrations in freely oscillating cylinders. The surrogate architecture transforms unstructured computational meshes into node-element hypergraphs that encode higher-order spatial relationships through element-based connectivity, preserving the geometric and topological structure of the underlying finite-element discretization. The temporal evolution of the fluid-structure interaction is modeled …

Three Hot Jupiters transiting K-dwarfs with a significant heavy element mass
Y. G. C. Frensch, F. Bouchy, G. Lo Curto, S. Ulmer-Moll, S. G. Sousa, N. C. Santos, K. G. Stassun, C. N. Watkins, H. Chakraborty, K. Barkaoui, M. Battley, W. Ceva, K. A. Collins, T. Daylan, P. Evans, J. P. Faria, C. Farret Jentink, E. Fontanet, E. Frid\'en, G. Furesz, M. Gillon, N. Grieves, C. Hellier, E. Jehin, J. M. Jenkins, L. K. W. Kwok, D. W. Latham, B. Lavie, N. Law, A. W. Mann, F. Murgas, E. Palle, …

Three Hot Jupiters transiting K-dwarfs with a significant heavy element mass
Albeit at a lower frequency than around hotter stars, short-period gas giants around low-mass stars ($T_\mathrm{eff} < 4965$ K) do exist, despite predictions from planetary population synthesis models that such systems should be exceedingly rare. By combining data from TESS and ground-based follow-up observations, we seek to confirm and characterize giant planets transiting K dwarfs, particularly mid/late K dwarfs. Photometric data were obtained from the TESS mission, supplemented by ground-bas…

A combined Machine Learning and Finite Element Modelling tool for the surgical planning of craniosynostosis correction
Itxasne Ant\'unez S\'aenz, Ane Alberdi Aramendi, David Dunaway, Juling Ong, Lara Deli\`ege, Amparo S\'aenz, Anita Ahmadi Birjandi, Noor UI Owase Jeelani, Silvia Schievano, Alessandro Borghi
https://a…

A combined Machine Learning and Finite Element Modelling tool for the surgical planning of craniosynostosis correction
Craniosynostosis is a medical condition that affects the growth of babies' heads, caused by an early fusion of cranial sutures. In recent decades, surgical treatments for craniosynostosis have significantly improved, leading to reduced invasiveness, faster recovery, and less blood loss. At Great Ormond Street Hospital (GOSH), the main surgical treatment for patients diagnosed with sagittal craniosynostosis (SC) is spring assisted cranioplasty (SAC). This procedure involves a 15x15 mm2 osteotomy…

#Clojure map-interval
Like `map` -- apply function `f` to each element in `col` in turn and return the values returned in sequence, but in a single thread and pausing between each invocation of `f`.

Useful for example in circumstances where you're querying a rate-limited service.

Map, but with a delay
Map, but with a delay. GitHub Gist: instantly share code, notes, and snippets.

Novel 1-bit Hybrid Reconfigurable Intelligent Surface
Sajedeh Keshmiri, Suren Jayasuriya, Mohammadreza F. Imani
https://arxiv.org/abs/2507.04675 https://…

Novel 1-bit Hybrid Reconfigurable Intelligent Surface
This paper proposes a novel 1-bit hybrid reconfigurable intelligent surface (HRIS) designed to sense the incident signal's angle of arrival (AoA) and redirect it toward desired directions. This device consists of independently tunable resonant patch elements loaded with PIN diodes. To introduce sensing capabilities, a portion of the signal incident on each element is coupled to a parallel plate waveguide (PPWG) through small rectangular slots. Two coaxial connectors are then used to collect the…

A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problems
Soheil Firooz, B. Daya Reddy, Paul Steinmann
https://arxiv.org/abs/2506.01873

A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problems
We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the coupled-field approach is established, together with an error estimate. Through a set of 1D and 2D numerical examples the high accuracy and enhanced stability of the approach in approximating solutions associated with complex problems is demonstrated, for situations …

The Bayesian Finite Element Method in Inverse Problems: a Critical Comparison between Probabilistic Models for Discretization Error
Anne Poot, Iuri Rocha, Pierre Kerfriden, Frans van der Meeer
https://arxiv.org/abs/2506.02815

The Bayesian Finite Element Method in Inverse Problems: a Critical Comparison between Probabilistic Models for Discretization Error
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the epistemic uncertainty due to discretization error. In this work, we apply BFEM to various inverse problems, and compare its performance to the random mesh finite element method (RM-FEM) and the statistical finite element method (statFEM), which serve as a fr…

It's been 7 months since the D-party lost the easiest-to-win election the US has ever had. And it's been 4 months since FFOTUS took office and became a modern Caligula.
And what has the D-party done?
Nada. Nada. Nada. The old faction is spinning in useless circles defending Biden's inexcusable decision to continue to run until too late. The younger element still shows no sign of engaging in the voting part of politics. Our middle-age element still looks first at t…

Midea provides heat pump technology to other big brands, like Bosch, Carrier, and Toshiba, so I wasn't scared by what some would consider a no-name. They have only been producing gas furnaces for 5 years so there's an element of faith involved backed by a 10-year warranty. I might regret making the choice but likely a decade in the future.

An open-source finite element toolbox for anisotropic creep and irradiation growth: Application to tube and spacer grid assembly
Fabrizio E. Aguzzi, Santiago M. Rabazzi, Mart\'in S. Armoa, C\'esar I. Pairetti, Alejandro E. Albanesi
https://arxiv.org/abs/2506.02807

An open-source finite element toolbox for anisotropic creep and irradiation growth: Application to tube and spacer grid assembly
This work presents an open-source interface that couples the viscoplastic self-consistent (VPSC) model capable of simulating anisotropic creep and irradiation growth in polycrystalline materials with the finite element solver Code_Aster. The interface enables the simulation of the micromechanical response of irradiated zirconium alloy components by integrating grain-level constitutive behavior into a structural FEM framework. A key feature is the automated rotation of stress and strain tensors …

Nanoparticles and Quantum Dots as Emerging Optical Sensing Platforms for $\mathrm{Ni}^{2 }$ Detection: Recent Approaches and Perspectives
Sudhanshu Naithani, Heena, Pooja Sharma, Samar Layek, Franck Thetiot, Tapas Goswami, Sushil Kumar
https://arxiv.org/abs/2507.04944

Nanoparticles and Quantum Dots as Emerging Optical Sensing Platforms for $\mathrm{Ni}^{2+}$ Detection: Recent Approaches and Perspectives
Over the preceding years, nickel (Ni) and its compounds have been increasingly employed in various aspects of human social life, metallurgical/industrial manufactures, healthcare, and chemical processes. Although Ni is considered an essential trace element in biological systems, excessive intake or metabolic deficiency of \(\mathrm{Ni}^{2+}\) ions may cause detrimental health effects to living organisms. Therefore, a facile and accurate detection of \(\mathrm{Ni}^{2+}\), especially in environme…

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 $C = \fracβ{\varepsilon^2}$ …

Crushing, Comminution and Fracture: Extreme Particle Deformation in Three-Dimensional Granular Aggregates
Debdeep Bhattacharya, Davood Damircheli, Robert P. Lipton
https://arxiv.org/abs/2506.05362

Crushing, Comminution and Fracture: Extreme Particle Deformation in Three-Dimensional Granular Aggregates
We present a high-fidelity three dimensional computational framework for simulating the bulk mechanical behavior of granular aggregates composed of deformable brittle grains. Departing from classical discrete element methods (DEM), our approach captures both inter-particle and intra-particle deformation using a nonlocal continuum formulation based on peridynamics. Each grain is individually meshed from level-set representations, enabling accurate modeling of elastic response and autonomous frac…

Rams' Davante Adams giving Puka Nacua confidence boost in OTAs, already making 'positive impact' on offense

https://www.cbssports.com/…

"Autoformalization of mathematical theorems? No shit!"
"what mathematicians need is ... not elementary statements of math olympiad problems, but the most advanced mathematical concepts that the human mind is capable to grasp despite the fact that they involve extremely intricate and sometimes combinatorically involved constructions.
"I am not sure that we fully know what it means to understand these concepts, but I am certain that it doesn't reduce to being…

Urban Solitude II 🈳
城市孤独 II 🈳
📷 Pentax MX
🎞️Fujifilm Neopan SS, expired 1995
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

Yiding Cao Geld mit PayPal.Me senden
Folgen Sie dem Link PayPal.Me/dingsterdingster und geben Sie den Betrag ein. Es ist bequem und sicher. Sie haben noch kein PayPal-Konto? Kein Problem.

This https://arxiv.org/abs/2505.19028 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

InfoChartQA: A Benchmark for Multimodal Question Answering on Infographic Charts
Understanding infographic charts with design-driven visual elements (e.g., pictograms, icons) requires both visual recognition and reasoning, posing challenges for multimodal large language models (MLLMs). However, existing visual-question answering benchmarks fall short in evaluating these capabilities of MLLMs due to the lack of paired plain charts and visual-element-based questions. To bridge this gap, we introduce InfoChartQA, a benchmark for evaluating MLLMs on infographic chart understand…

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…

This https://arxiv.org/abs/2405.04406 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Rényi divergence guarantees for hashing with linear codes
We consider the problem of distilling uniform random bits from an unknown source with a given $p$-entropy using linear hashing. As our main result, we estimate the expected $p$-divergence from the uniform distribution over the ensemble of random linear codes for all integer $p\ge 2$. The proof relies on analyzing how additive noise, determined by a random element of the code from the ensemble, acts on the source distribution. This action leads to the transformation of the source distribution in…

Simultaneous Six-way Observations from the Navy Precision Optical Interferometer
Ellyn K. Baines, Solvay Blomquist, James H. Clark III, Jim Gorney, Erin Maier, Jason Sanborn, Henrique R. Schmitt, Jordan M. Stone, Gerard T. van Belle, Kaspar von Braun
https://arxiv.org/abs/2506.01720

Simultaneous Six-way Observations from the Navy Precision Optical Interferometer
We measured the angular diameters of six stars using the 6-element observing mode of the Navy Precision Optical Interferometer (NPOI) for the first time since the early 2000s. Four of the diameters ranged from 1.2 mas to 1.9 mas, while the two others were much smaller at approximately 0.5 mas to 0.7 mas, which are the two smallest angular diameters measured to date with the NPOI. There is a larger spread in the measurements than data obtained with 3- or 4- or 5-element modes, which can be attri…

wow I don't even know `<data>` HTML tag exists #HTML

: The Data element - HTML: HyperText Markup Language | MDN
The HTML element links a given piece of content with a machine-readable translation. If the content is time- or date-related, the element must be used.

Recognition by the set of exponents in the prime factorization of the product of element orders
Morteza Baniasad Azad, Mostafa Arabtash
https://arxiv.org/abs/2507.02594

Recognition by the set of exponents in the prime factorization of the product of element orders
Let $G$ be a finite group. Let $ρ(G) = \prod_{g \in G} o(g)={p_1}^{α_1} {p_2}^{α_2} \cdots {p_k}^{α_k}$, where $p_1, p_2, \cdots, p_k$ are distinct prime numbers and $o(g)$ denotes the order of $g \in G$. The set of exponents in the prime factorization of the product of element orders is denoted by $ {\operatorname{Exp}}_ρ(G)$, i.e., $ {\operatorname{Exp}}_ρ(G)=\{α_1,α_2, \cdots,α_k\}$. In this paper, we give a new characterization for some groups by $ {\operatorname{Exp}}_ρ(G)$. We p…

A $\mathcal{CR}$-rotated $Q_1$ nonconforming finite element method for Stokes interface problems on local anisotropic fitted mixed meshes
Geng Chenchen, Hua Wang, Fengren Zou
https://arxiv.org/abs/2507.02741

A $\mathcal{CR}$-rotated $Q_1$ nonconforming finite element method for Stokes interface problems on local anisotropic fitted mixed meshes
We propose a new nonconforming finite element method for solving Stokes interface problems. The method is constructed on local anisotropic mixed meshes, which are generated by fitting the interface through simple connection of intersection points on an interface-unfitted background mesh, as introduced in \cite{Hu2021optimal}. For triangular elements, we employ the standard $\mathcal{CR}$ element; for quadrilateral elements, a new rotated $Q_1$-type element is used. We prove that this rotated $Q…

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…

This https://arxiv.org/abs/2404.09319 has been replaced.
initial toot: https://mastoxiv.page/@arXi…

Impact of curved elements for flows over orography with a Discontinuous Galerkin scheme
We present a quantitative assessment of the impact of high-order mappings on the simulation of flows over complex orography. Curved boundaries were not used in early numerical methods, whereas they are employed to an increasing extent in state of the art computational fluid dynamics codes, in combination with high-order methods, such as the Finite Element Method and the Spectral Element Method. Here we consider a specific Discontinuous Galerkin (DG) method implemented in the framework of the de…

It's about time: a thermodynamic information criterion (TIC)
Brendan Lucas, Google Gemini 2. 5 Pro Preview 05-06
https://arxiv.org/abs/2506.04519 https…

It's about time: a thermodynamic information criterion (TIC)
Useful chemical processes often involve a desired steady state probability distribution, equilibrium or not, from which product is extracted. Given many different ways to attain the same steady state, which candidate "loses" the least in terms of time and energy? A scalar thermodynamic information criterion (TIC), inspired by AIC, assigns lower values to chemical processes with less estimated "loss" to generate the same desired steady state. As an element of thermodynamic machine learning, TIC …

Sign Language: Towards Sign Understanding for Robot Autonomy
Ayush Agrawal, Joel Loo, Nicky Zimmerman, David Hsu
https://arxiv.org/abs/2506.02556 https://

Sign Language: Towards Sign Understanding for Robot Autonomy
Signage is an ubiquitous element of human environments, playing a critical role in both scene understanding and navigation. For autonomous systems to fully interpret human environments, effectively parsing and understanding signs is essential. We introduce the task of navigational sign understanding, aimed at extracting navigational cues from signs that convey symbolic spatial information about the scene. Specifically, we focus on signs capturing directional cues that point toward distant locat…

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 …

Discrete Element Parameter Calibration of Livestock Salt Based on Particle Scaling
Lulu Nie, Baoqin Wen, Jingbin Li, Shufeng Li, Yali Li, Zhaokun Zhang, Zhiyuan Wang, Zhihao Fan
https://arxiv.org/abs/2506.03786

Discrete Element Parameter Calibration of Livestock Salt Based on Particle Scaling
In order to obtain accurate contact parameters for the discrete element simulation of salt particles used in animal husbandry, the principle of particle contact scaling and dimensional analysis were used for particle scaling. Firstly, the Plackett Burman experiment was used to screen the parameters that significantly affect the angle of repose: salt salt rolling friction coefficient, salt salt recovery coefficient, and salt steel rolling friction coefficient. Considering the influence of other …

Mixed FEM for coupled unsteady fluid flow problems with $p$-type Brinkman-Forchheimer framework and its application for reverse-osmosis desalination
Zeinab Gharibi, Mostafa Abbaszadeh, Mehdi Dehghan
https://arxiv.org/abs/2507.03974

Mixed FEM for coupled unsteady fluid flow problems with $p$-type Brinkman-Forchheimer framework and its application for reverse-osmosis desalination
This work analyzes a fully discrete mixed finite element method in a Banach space framework for solving nonstationary coupled fluid flow problems modeled by the Brinkman-Forchheimer equations, with applications to reverse osmosis. The model couples unsteady $p$-type convective Brinkman-Forchheimer and transport equations with nonlinear boundary conditions across a semi-permeable membrane. A mixed formulation is used for the fluid equation (pseudostress-velocity) and for the transport equation (…

wow I don't even know `<data>` HTML tag exists #HTML

: The Data element - HTML: HyperText Markup Language | MDN
The HTML element links a given piece of content with a machine-readable translation. If the content is time- or date-related, the element must be used.

This https://arxiv.org/abs/2401.09280 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Posets arising from decompositions of objects in a monoidal category
Given a symmetric monoidal category $C$ with product $\sqcup$, where the neutral element for the product is an initial object, we consider the poset of $\sqcup$-complemented subobjects of a given object $X$. When this poset has finite height, we define decompositions and partial decompositions of $X$ which are coherent with $\sqcup$, and order them by refinement. From these posets, we define complexes of frames and partial bases, augmented Bergman complexes and related ordered versions. We prop…

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Remarkable upper bounds for the interpolation error constants on the triangles
Kenta Kobayashi
https://arxiv.org/abs/2507.04032 https://

Remarkable upper bounds for the interpolation error constants on the triangles
We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the Finite Element Method. In this study, we proved boundness via the numerical verification method and asymptotic analysis. This study is also essential in that it demonstrates a valuable application of the numerical verification method. The proof process of this s…

Adaptive finite element type decomposition of Gaussian processes
Jaehoan Kim, Anirban Bhattacharya, Debdeep Pati
https://arxiv.org/abs/2505.24066 https://

Adaptive finite element type decomposition of Gaussian processes
In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution. This general class includes a popular approach that uses a finite element approximation of the stochastic partial differential equation (SPDE) associated with Matérn GP. We explored another scalable alternative popularly used in the computer emulation literatu…

PINN-DG: Residual neural network methods trained with Finite Elements
Georgios Grekas, Charalambos G. Makridakis, Tristan Pryer
https://arxiv.org/abs/2507.03521

PINN-DG: Residual neural network methods trained with Finite Elements
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical techniques such as finite elements and finite differences. In this paper, we introduce a new class of Physics-Informed Neural Networks (PINNs) trained using discontinuous Galerkin finite element methods. Unlike standard collocation-based PINNs that rely on pointwise g…

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…

A finite element implementation of a large deformation gradient-damage theory for fracture with Abaqus user material subroutines
Keven Alkhoury, Shawn A. Chester, Vikas Srivastava
https://arxiv.org/abs/2507.02702

A finite element implementation of a large deformation gradient-damage theory for fracture with Abaqus user material subroutines
Recent advancements in computations have enabled the application of various modeling approaches to predict fracture and failure, such as the gradient-damage (phasefield) method. Several existing studies have leveraged the heat equation solver in Abaqus to model gradient-damage, due to its mathematical resemblance to the heat equation. Particular care is required when extending the approach to large deformation scenarios due to differences in the referential and spatial configurations, especiall…

This https://arxiv.org/abs/2504.21059 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A remark on the number of automorphisms of some algebraic structures
In these notes we look at the following question. Given a category $\mathcal C$ of algebraic structure (e.g. the category of groups, monoids, partial groups, ...) and a rational $r\in \mathbb Q$, does there exists an element $x\in \mathcal C$ such that the size of its automorphism group $\text{Aut}_{\mathcal C} (x)$ divided by the size of $x$ (whatever that would means) is equal to $r$\,? To our knowledge, this question was introduced by Tărnăuceanu in the category of groups. Here, we answer …

Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes
Luis Wirth
https://arxiv.org/abs/2506.02429 https://…

Rust Implementation of Finite Element Exterior Calculus on Coordinate-Free Simplicial Complexes
This thesis presents the development of a novel finite element library in Rust based on the principles of Finite Element Exterior Calculus (FEEC). The library solves partial differential equations formulated using differential forms on abstract, coordinate-free simplicial complexes in arbitrary dimensions, employing an intrinsic Riemannian metric derived from edge lengths via Regge Calculus. We focus on solving elliptic Hodge-Laplace eigenvalue and source problems on the nD de Rham complex. We …

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…

This https://arxiv.org/abs/2505.04227 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modeling of thin plate flexural vibrations by Partition of Unity Finite Element Method
This paper presents a conforming thin plate bending element based on the Partition of Unity Finite Element Method (PUFEM), for the simulation of steady-state forced vibration. The issue of ensuring the continuity of displacement and slope between elements is addressed by the use of cubic Hermite-type Partition of Unity (PU) functions. With appropriate PU functions, the PUFEM allows the incorporation of the special enrichment functions into the finite elements to better cope with plate oscillati…

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This https://arxiv.org/abs/2408.16243 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotically Compatible Error Bound of Finite Element Method for Nonlocal Diffusion Model with An Efficient Implementation
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes with and without shape regularity. For shape-regular meshes, the error is bounded by \(O(h^k + δ)\), where \(h\) is the mesh size, \(δ\) is the nonlocal horizon, and \(k\) is the order of the FEM basis. Without shape regularity, the bound becomes \(O(h^{k+1}/δ+ δ)\). In addition, we present an efficient implementati…

Nonlinear elastodynamic material identification of heterogeneous isogeometric Bernoulli-Euler beams
Bart{\l}omiej {\L}azorczyk, Roger A. Sauer
https://arxiv.org/abs/2506.04960

Nonlinear elastodynamic material identification of heterogeneous isogeometric Bernoulli-Euler beams
This paper presents a Finite Element Model Updating framework for identifying heterogeneous material distributions in planar Bernoulli-Euler beams based on a rotation-free isogeometric formulation. The procedure follows two steps: First, the elastic properties are identified from quasi-static displacements; then, the density is determined from modal data (low frequencies and mode shapes), given the previously obtained elastic properties. The identification relies on three independent discretiza…

Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians
Yohance A. P. Osborne, Iain Smears
https://arxiv.org/abs/2506.03039

Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians
We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In particular, we obtain a rate of convergence in the $H^1$-norm for the value function approximations and in the $L^2$-norm for the approximations of the density. We also establish a rate of convergence for the error between the exact solution of the MFG system…

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 …

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 …

A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
Ben S. Ashby, Abdalaziz Hamdan, Tristan Pryer
https://arxiv.org/abs/2506.01105

A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is a positivity-preserving formulation that guarantees non-negative fluence and dose, even on coarse meshes. This enables reliable computation of clinically relevant quantities for treatment planning. We derive a priori error estimates demonstrating optimal convergence rates and validate the method through numerical ben…

This https://arxiv.org/abs/2403.10282 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-Conforming Structure Preserving Finite Element Method for Doubly Diffusive Flows on Bounded Lipschitz Domains
We study a stationary model of doubly diffusive flows with temperature-dependent viscosity on bounded Lipschitz domains in two and three dimensions. A new well-posedness and regularity analysis of weak solutions under minimal assumptions on domain geometry and data regularity are established. A fully non-conforming finite element method based on Crouzeix-Raviart elements, which ensures locally exactly divergence-free velocity fields is explored. Unlike previously proposed schemes, this discreti…

This https://arxiv.org/abs/2504.03393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Effects of Interpolation Error and Bias on the Random Mesh Finite Element Method for Inverse Problems
Bayesian inverse problems are an important application for probabilistic solvers of partial differential equations: when fully resolving numerical error is computationally infeasible, probabilistic solvers can be used to consistently model the error and propagate it to the posterior. In this work, the performance of the random mesh finite element method (RM-FEM) is investigated in a Bayesian inverse setting. We show how interpolation error negatively affects the RM-FEM posterior, and how these …

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…

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…

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…

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 …

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…

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 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 …

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 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…

This https://arxiv.org/abs/2504.10710 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On an efficient line smoother for the p-multigrid γ-cycle
As part of the development of a Poisson solver for the spectral element discretization used in the GeoFluid Object Workbench (GeoFLOW) code, we propose a solver for the linear system arising from a Gauss-Legendre-Lobatto global spectral method. We precondition using a p-multigrid γ-cycle with highly-vectorizable smoothers, that we refer to as line smoothers. Our smoothers are restrictions of spectral and finite element discretizations to low-order one-dimensional problems along lines, that are…

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…

This https://arxiv.org/abs/2008.12591 has been replaced.
link: https://scholar.google.com/scholar?q=a

Convergence of adaptive stochastic collocation with finite elements
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an adaptive algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.

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…

Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals
Heiko Gimperlein, Ruma R. Maity
https://arxiv.org/abs/2506.04880

Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals
This paper introduces a comprehensive finite element approximation framework for three-dimensional Landau-de Gennes $Q$-tensor energies for nematic liquid crystals, with a particular focus on the anisotropy of the elastic energy and the Ball-Majumdar singular potential. This potential imposes essential physical constraints on the eigenvalues of the $Q$-tensor, ensuring realistic modeling. We address the approximation of regular solutions to nonlinear elliptic partial differential equations with…

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…

An Array Decomposition Method for Finite Arrays with Electrically Connected Elements for fast Toeplitz Solvers
Lucas {\AA}kerstedt, Harald Hultin, B. L. G. Jonsson
https://arxiv.org/abs/2506.04710

An Array Decomposition Method for Finite Arrays with Electrically Connected Elements for fast Toeplitz Solvers
A large part of the geometry of array antennas is often partially defined by finite translational symmetries. Applying the method of moments (MoM) with the RWG-like element on an appropriately structured mesh to these arrays results in an impedance matrix where the main part exhibits a multilevel block Toeplitz structure. This article introduces a memory-efficient construction method that effectively represents and reuses impedance calculations. The proposed method, applicable to electrically c…

Scalable Analysis and Design Using Automatic Differentiation
Julian Andrej, Tzanio Kolev, Boyan Lazarov
https://arxiv.org/abs/2506.00746 https://

Scalable Analysis and Design Using Automatic Differentiation
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to localize the application of AD at the integration point level by combining it with the so-called Finite Element Operator Decomposition. The proposed methods are computationally effective, scalable, automatic, and non-intrusive, making them ideal for existing serial…

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time
Santolo Leveque, Yunhui He, Maxim Olshanskii
https://arxiv.org/abs/2506.04451

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time
We consider a Runge--Kutta method for the numerical time integration of the nonstationary incompressible Navier--Stokes equations. This yields a sequence of nonlinear problems to be solved for the stages of the Runge--Kutta method. The resulting nonlinear system of differential equations is discretized using a finite element method. To compute a numerical approximation of the stages at each time step, we employ Newton's method, which requires the solution of a large and sparse generalized saddl…