arXiv subjects

David Lee

Publications and source records attributed to David Lee.

At least 19 recordsLinked to original sources

arXiv2026

An intrinsic finite element framework for scalar- and vector-valued partial differential equations on general manifolds

We present an intrinsic finite element framework for the numerical approximation of scalar- and vector-valued partial differential equations on general manifolds described by atlases of charts. Weak formulations and their discretisation are expressed exclusively in the flat parametric space of the manifold, where the exact geometry enters only through the metric tensor that is evaluated at quadrature points. Conforming finite element spaces of arbitrary order for the whole de Rham complex are obtained on multi-chart atlases through purely topological inter-chart gluing. We develop a nodal change of basis construction for vector-valued spaces on multi-chart atlases, where nodal degrees of freedom couple charts with incompatible coordinate systems through transmission maps. Inter-chart continuity holds at the nodes with jumps of the order of the approximation error, and the resulting discrete field is exactly tangent to the manifold. Optimal convergence rates for this method are observed numerically for the surface Stokes problem; no a priori error analysis is provided. Numerical experiments on the cubed sphere manifold in two and three dimensions for the Hodge Laplacian problems demonstrate the intrinsic framework is free of the geometric consistency errors for a sufficient quadrature degree, and that intrinsic assembly is substantially cheaper than its extrinsic counterpart. Further considering the rotating shallow water equations that include orography as a perturbation of the geometry demonstrates that mass is conserved exactly, and energy is conserved up to the time discretisation error.

math.NA↗

arXiv2026

GridapGeosciences.jl: A Julia finite element package for partial differential equations on general manifolds

We present GridapGeosciences$.$jl, a new parallel distributed-memory Julia package for the numerical approximation of partial differential equations on general manifolds. Our abstract approach to generating discrete manifold domains relies on mesh refinement in general, and is implemented within the Gridap finite element library, whose high-level interface enables seamless definition of both intrinsic and extrinsic variational formulations. GridapGeosciences$.$jl features the cubed sphere manifold, which is used in this study to showcase the functionality of GridapGeosciences$.$jl in different applications. The first application involves scalar transport where we develop intrinsic formulations of common stabilisation terms, which are shown to be equivalent to well-known extrinsic stabilisation formalisations. Such stabilisation terms are used to develop an intrinsic formulation of the two-dimensional thermal shallow water equations that includes upwinded numerical fluxes. The final application is a linearisation of the Boussinesq equations where we demonstrate the capacity of GridapGeosciences$.$jl to capture both surface and vertical dynamics on a three-dimensional manifold.

math.NA↗

arXiv2026

Design evolution for the Wide-field Spectroscopic Telescope

WST is proposed as the next large ESO project to follow ELT, combining Multi-Object Spectroscopy and Integral Field Spectroscopy. Each mode offers order-of-magnitude gains over current systems, and each also presents unprecedented design challenges, both separately and in combination. For large MOS systems, both science performance and spectrograph costs vary steeply with the delivered image quality, so exceptional delivered image quality is paramount. But the 12m aperture and 2 degree field give WST an etendue larger than Rubin, larger that LAMOST, and larger than all other existing MOS telescopes combined; while the IFS, segmented primary and windy site all add additional constraints. Hence finding designs with good image quality is challenging. Eventually, 3-lens Forward Cassegrain designs with loss-less ADC were developed in variants mostly differentiated by M2 diameter. The lowest technical risk design, with the smallest M2, was selected as the baseline, with wind-shake control a primary driver. However, other designs have better as-designed image quality, and their perceived risks may diminish as the system design and underlying technologies mature. For IFS mode, delivered image quality is just as crucial, but this is achieved through additional optics and NGS GLAO over the 3'x3' field. The challenges come from (a) transferring the F/3.4 Forward Cassegrain focus to a fixed focus under the telescope; (b) a requirement that the 3'x3' field be selectable from a 13' diameter FoV without repointing the telescope; (c) including a suitably conjugated mirror for GLAO correction; (d) doing all this with minimised vignetting and surface count. Various designs were explored; the baseline design has a field-selecting pick-off at telescope focus, combined with large reimaging optics at Nasmyth, giving an F/28.5 fixed IFS focus.

astro-ph.IM↗

arXiv2026

WST, the Wide-field Spectroscopic Telescope: dispersing elements

The Wide-field Spectroscopic Telescope (WST) is a proposed 12-m class facility entirely dedicated to spectroscopic surveys, combining a high-multiplex multi-object spectrograph operating at low (MOS-LR) and high (MOS-HR) spectral resolution with a giant panoramic integral-field spectrograph (IFS), all three operating in parallel. Diffraction gratings are the key dispersing elements of all three instruments and, given the very large number and size of the units required, drive critical trade-offs in throughput, feasibility and production cost. This paper reviews the two grating technologies under consideration for WST, Volume Phase Holographic Gratings (VPHG) and binary (lithographic, surface-relief) gratings, summarizing their working principles and the parameters that control their diffraction efficiency. We then present the current baseline grating parameters and vendor results for each instrument: low-dispersion, VPHGs for the IFS; a four-arm GRISM layout for MOS-LR; and two competing high-resolution disperser architectures (8M16D and 16M4D) for MOS-HR, where binary gratings show a promising path to diffraction efficiencies beyond what is achievable with VPHGs. We conclude with the main open challenges, chiefly the mass production of hundreds of grating units within cost and schedule and the next steps foreseen to consolidate the disperser baseline for WST.

astro-ph.IM↗

arXiv2026

The Wide-field Spectroscopic Telescope (WST): design trade-offs for the low-resolution multi-object spectrograph instrument

astro-ph.IM↗

arXiv2026

ANDES, the high-resolution spectrograph for the ELT: design and performance analysis of the YJH spectrograph

The ArmazoNes high Dispersion Echelle Spectrograph (ANDES) is a powerful second-generation high-resolution spectroscopic instrument for the Extremely Large Telescope (ELT). The UBV, RIZ, and YJH modules comprise fibre-fed spectrographs of the ANDES baseline design and will offer continuous wavelength coverage of 0.35-1.8 $\mu$m, with the addition of a K-band channel providing coverage up to 2.4 $\mu$m. Coupled with a spectral resolution of $\sim$100,000, ANDES must deliver the required wavelength calibration stability of 1 m/s over 24 hours, with a goal of 0.02 m/s across 10 years. These requirements establish the framework for the infrared module of ANDES, the YJH Spectrograph, leading to what will likely be the largest cryogenic, ultra-stable, high-resolution spectrograph ever built, and will offer the unique ability to observe in both seeing- and diffraction-limited modes interchangeably. We present the current design and performance analysis of the ANDES YJH Spectrograph, outlining the engineering challenges encountered alongside the corresponding strategies adopted to navigate them. In particular, we detail the technology development of the primary dispersing element, an echelle grating mosaic that will span over a metre in length.

astro-ph.IM↗

arXiv2026

Data driven non-equilibrium moist phase exchanges for atmospheric convection within a discontinuous Galerkin model of the compressible Euler equations

A discrete formulation of the multiphase moist compressible Euler equations is presented for which the energy and tracer variance conserving dynamics is coupled to the non-equilibrium moist phase exchanges in a thermodynamically consistent manner. A neural network is then trained to learn the mass exchanges between vapour, liquid and ice phases in atmospheric convection. The network is trained on convection resolving output from a regional configuration of the LFRic model with a multi-moment microphysics parameterisation (CASIM). The loss function for learning these phase exchanges is formulated under the assumptions of thermal and mechanical equilibrium (same temperature and pressure for all phases), and chemical dis-equilibrium (different Gibbs free energies for all phases). The network outputs determine the exchanges of vapour, liquid and ice so as to conserve mass, and the resulting change in entropy is determined from the network outputs so as to conserve energy. The neural network is implemented in a thermodynamically consistent manner within the discontinuous Galerkin moist compressible Euler model in order to simulate the formation of three-phase clouds for convection at sub-km resolution. The results are compared to those from a physics based representation of three-phase moist processes at thermodynamic equilibrium, as well as to an idealised configuration of LFRic model.

math.NA↗

arXiv2026

The Wide-field Spectroscopic Telescope: optical designs for the low-resolution multi-object spectrographs

In MOS Low-Resolution mode, WST has a 'spectral etendue' per fiber (etendue x spectral resolution elements) twice as large as any existing MOS instrument, and a total spectral etendue ~20 times larger. Combined, these present enormous challenges for the spectrograph design. Initial designs were based on (a) a novel F/0.775 Folded Solid Schmidt camera with 6cm detectors, (b) an F/1.15 dioptric camera with 6cm detectors, and (c) an F/1.31 dioptric camera with 9cm detectors, all with YAG field-flatteners. However, the imperative of fast camera speed has greatly diminished, as the projected cost and read-noise of large format CMOS detectors is projected to decrease greatly. The adopted baseline solution has 4 dioptric F/1.64 cameras, each with two doublets, a YAG field lens and 9cm x 9cm detector. Theoretical image quality is 8 microns rms radius. The design seems readily athermalised, potentially allowing passive temperature control. Each spectrograph accepts 500+ fibers. Expected RoM costs (scaled from earlier designs) suggest a total cost <4M Euro per spectrograph.

astro-ph.IM↗

arXiv2026

Current status of the High-Resolution Multi-Object Spectrograph (MOS-HR) for the Wide-field Spectroscopic Telescope

The Wide-field Spectroscopic Telescope (WST) is a planned 12-meter class dedicated spectroscopic facility for massive spectroscopic surveys. This paper presents the current status of Work Package 4.5, the High Resolution Multi-Object Spectrograph (HR-MOS) module. We describe the international team organization and optical design resulting from extensive trade-off studies, presenting its evolution driven by scientific requirements and technical constraints. Design parameters derived from science cases and astronomical community requirements are detailed. Given the critical importance of mass and volume budgets, we present envelope dimensions and mass estimates for HR-MOS. The spectrograph constructive parameters are defined, including optical fiber specifications, multiplex capability, and modular architecture. Finally, we present the structural analysis addressing mechanical stability and performance requirements for this high-resolution multi-object spectrograph.

astro-ph.IM↗

arXiv2026

A generalized Liouville theorem via division

W}e study the equation $P(i\nabla)u=0$ on $\mathbb{R}^d$ for a class of admissible symbols $P$ whose zero set is the unit sphere $S^{d-1}$ and which vanish there to some finite order. Working in the framework of Lizorkin distributions, and hence without any boundedness or decay hypothesis on $u$, we give a complete classification of the solutions: $u$ solves $P(i\nabla)u=0$ if and only if $\hat{u}$ is a multi-layer distribution on $S^{d-1}$ of order at most $N$. Alternatively, $u$ solves $P(i\nabla)u=0$ if and only if $(1+\Delta)^{N+1}u=0$ if $P$ satisfies a flatness condition. The proof recasts the equation as a division problem and combines the order of vanishing of $P$ with the structure theorem for distributions. This unifies and extends known Helmholtz-type rigidity results, which correspond to a simple zero on the sphere, to symbols with zeros of arbitrary finite order.

math.AP↗

arXiv2026

WST, the Wide-field Spectroscopic Telescope: Mechanical Design and FE Analyses for the High Resolution Spectrograph

The Wide-field Spectroscopic Telescope (WST) is a planned 12-meter-class dedicated spectroscopic facility designed to address key scientific challenges through large spectroscopic surveys. This paper presents the current status of Work Package 4.5, which focuses on the High-Resolution Multi-Object Spectrograph (MOS-HR) module for WST. The MOSHR instrument is expected to provide a resolving power of R = 40,000 with a multiplexing capability of about 2,000 targets. The mechanical design activities carried out for the development of the HR spectrograph and for the definition of its optomechanical architecture are described. To account for both the scientific requirements of the spectrograph and the manufacturability constraints associated with such a complex instrument, the mechanical layout has been organized into four larger modules, each containing two sub-modules. Guided by feasibility considerations, such as mechanical performance, available volume, and fabrication and assembly aspects, each sub-module adopts a vertical optical bench configuration with optical elements mounted on both sides. Starting from the baseline optical design, the mechanical configuration has been developed to achieve the required alignment accuracy, structural stability, and environmental robustness. The workflow includes the translation of the optical prescription into a complete mechanical model, the definition of the main mounting and alignment interfaces, and preliminary static, modal, and seismic analyses to evaluate performance under operational and survival loads. As an outcome, the proposed design provides architecture that enables preliminary estimates of mass, volume, cost, and mechanical performance in terms of deformation, stress, and modal behavior of the modules.

astro-ph.IM↗

arXiv2026

WST, the wide-field spectroscopic telescope: progress on the design of the instruments

WST, the Wide-field Spectroscopic Telescope is a proposed new facility that will provide a transformational gain in spectroscopic survey capability over existing facilities. The WST is a 12 metre class telescope equipped with instrumentation to provide simultaneous observations in both multiple-object spectroscopy and integral field spectroscopy modes. This paper will describe the status of the instruments being designed for the WST, the fibre positioner module, the low and high-resolution multiple object spectrographs, the integral field spectrograph, disperser technology, sustainable detector and cryostat technology, and the calibration system. An overview of the overall layout of the instruments within the WST facility will be provided.

astro-ph.IM↗

arXiv2026

A perfectly matched layer for damping vertically propagating waves in the compressible Boussinesq equations

This paper introduces a new application of the perfectly matched layer (PML) for mitigating model top wave reflections in geophysical fluid models. Typically, a strong Laplacian or Rayleigh damping sponge layer is used near the upper boundary, but these often need many vertical levels or a high model top to be sufficiently effective. An advantage of the PML is that, at the continuous level, it is free of wave reflection at the onset of the damping layer. This enables the PML to be effective even with a thin damping layer. We derive PMLs for the linear and nonlinear versions of the Boussinesq equations, which are a simplified model for vertical dynamics in the atmosphere. In the nonlinear system, we define a novel PML that damps perturbations from a hydrostatically balanced reference state. We approximate the PML equations using the compatible finite element method for numerical experiments. First, tests with the linear Boussinesq system show that the PML is more effective than a typical sponge layer in absorbing acoustic waves near the model top. Next, tests in the nonlinear system show that i) the PML can damp acoustic waves even when they are under-resolved by the time discretisation, and ii) the PML can avoid the standing wave pattern caused by model top reflection of orographic gravity waves. We propose that the PML is worth further development and investigation as a sponge layer alternative in dynamical cores for atmospheric modelling.

math.NA↗

arXiv2026

WST -- Wide-field Spectroscopic Telescope: The Next Leap in Wide-field Spectroscopy

The Wide-field Spectroscopic Telescope (WST) is a concept for a dedicated 12-m spectroscopic survey facility designed to address some of the most important questions in astrophysics in the 2040s. The WST will provide unprecedented spectroscopic survey capabilities by operating simultaneously over a 2-degree diameter field of view with 54 low-resolution spectrographs fed by 30,000 fibres, 8-16 high-resolution spectrographs fed by 2,000 fibres, and a large panoramic low-resolution integral-field spectrograph. Supported by Horizon Europe, the concept study has refined the science cases, facility architecture, operations model, sustainability strategy, and technology roadmap. The resulting reference design demonstrates that the WST is both scientifically transformative and technically feasible, while identifying the developments required to mitigate the remaining risks. The WST is designed as an ESO flagship facility for the post-ELT construction era and a key spectroscopic complement to the major imaging, time-domain, and multi-messenger facilities of the coming decades.

astro-ph.IM↗

arXiv2026

WST Multi-Object Spectrograph Fiber Positioners:Development of a 32,000-Unit Precision Robotic System

The Wide-field Spectroscopic Telescope Multi-Object Spectrograph requires an unprecedented fiber positioning system comprising 30'000 low-resolution and 2'000 high-resolution positioners across a 3.1 deg squared field of view. Each robotic positioner must achieve 5um RMS positioning accuracy in a densely packed focal plane, representing a more than sixfold scale increase over current instruments like 4MOST and DESI. To mitigate risks associated with industrial-scale production of 32'000 precision mechanisms, WST is pursuing a multi-concept development strategy. Four distinct positioner architectures are being prototyped and tested by an international collaboration (EPFL, AIP, UKATC, AAO) using 6.2 mm pitch triangular modules of 63 units each or a new inline modular concept. Performance metrics including positioning accuracy, repeatability, reconfiguration speed, collision avoidance, and manufacturability are being systematically evaluated. Down-selection to one or two concepts is planned for 2026-2027 during the HORIZON Europe-funded conceptual study phase. Current prototype testing demonstrates feasibility of meeting specifications, supporting WST's path toward first light in the early 2040s as ESO's next major spectroscopic facility.

astro-ph.IM↗

arXiv2026

Consistency analysis for combined homogenization and shallow water limit of water waves

We consider a shallow water model in a homogenization framework. For periodic topographies, Craig, Lannes and Sulem have established a consistency result under some non-resonance conditions. In the present contribution, we significantly relax the periodicity condition and treat general topographies under minimal assumptions.

math.AP↗

arXiv2026

Lossless Prompt Compression via Dictionary-Encoding and In-Context Learning: Enabling Cost-Effective LLM Analysis of Repetitive Data

In-context learning has established itself as an important learning paradigm for Large Language Models (LLMs). In this paper, we demonstrate that LLMs can learn encoding keys in-context and perform analysis directly on encoded representations. This finding enables lossless prompt compression via dictionary encoding without model fine-tuning: frequently occurring subsequences are replaced with compact meta-tokens, and when provided with the compression dictionary in the system prompt, LLMs correctly interpret these meta-tokens during analysis, producing outputs equivalent to those from uncompressed inputs. We present a compression algorithm that identifies repetitive patterns at multiple length scales, incorporating a token-savings optimization criterion that ensures compression reduces costs by preventing dictionary overhead from exceeding savings. The algorithm achieves compression ratios up to 80$\%$ depending on dataset characteristics. To validate that LLM analytical accuracy is preserved under compression, we use decompression as a proxy task with unambiguous ground truth. Evaluation on the LogHub 2.0 benchmark using Claude 3.7 Sonnet demonstrates exact match rates exceeding 0.99 for template-based compression and average Levenshtein similarity scores above 0.91 for algorithmic compression, even at compression ratios of 60$\%$-80$\%$. Additionally, compression ratio explains less than 2$\%$ of variance in similarity metrics, indicating that decompression quality depends on dataset characteristics rather than compression intensity. This training-free approach works with API-based LLMs, directly addressing fundamental deployment constraints -- token limits and API costs -- and enabling cost-effective analysis of large-scale repetitive datasets, even as data patterns evolve over time.

cs.CL↗

arXiv2026

Gradual smoothing: strong hypercontractivity and logarithmic Sobolev inequalities

We study the possibility of a gradual improvement as time progresses of the regularity of solutions to evolution problems of parabolic type driven by L\'evy-type operators, not necessarily translation invariant. In the course of our analysis we study the equivalence between general smoothing effects and a family of logarithmic Sobolev inequalities. This equivalence allows us to identify a new type of regularization, strong hypercontractivity, characterized by the existence of a time at which solutions belong to every $L^p$ space with $p$ finite. It can also be used to prove logarithmic Sobolev inequalities in a context not previously seen in the literature. We then show that any purely nonlocal L\'evy-type operator whose kernel is comparable to that of $\log(I-\Delta)$ is strongly hypercontractive, but fails to be supercontractive and, consequently, also fails to be ultracontractive. Furthermore, in the translation-invariant case, we also prove that solutions get bounded eventually and start improving in differentiability right after doing so. Finally, we show that this behaviour only appears if the kernel defining the operator behaves as $|x-y|^{-N}$ for small interactions ($0^+$-order operators): more singular kernels yield instantaneous smoothing, while less singular ones do not produce any regularization.

math.AP↗