arXiv subjects

Davit Aslanyan

Publications and source records attributed to Davit Aslanyan.

4 recordsLinked to original sources

arXiv2026

Fully Automated Adaptive Parameter Selection for 3-D High-order Nyström Boundary Integral Equation Methods

We present an adaptive Chebyshev-based Boundary Integral Equation (CBIE) solver for electromagnetic scattering from smooth perfect electric conductor (PEC) objects. The proposed approach eliminates manual parameter tuning by introducing (i) a unified adaptive quadrature strategy for automatic selection of the near-singular interaction distance and (ii) an adaptive computation of all self- and near-singular precomputation integrals to a prescribed accuracy using Gauss-Kronrod (h-adaptive) or Clenshaw-Curtis (p-adaptive) rules and singularity-resolving changes of variables. Both h-adaptive and p-adaptive schemes are explored within this framework, ensuring high-order accuracy and robustness across a broad range of geometries without loss of efficiency. Numerical results for canonical and complex CAD geometries demonstrate that the adaptive solver achieves accuracy and convergence rates comparable to optimally tuned fixed-grid CBIE implementations, while offering automation and scalability to electrically large, geometrically complex problems.

math.NA↗

arXiv2025

Automated Supervised Identification of Thunderstorm Ground Enhancements (TGEs)

Thunderstorm Ground Enhancements (TGEs) are bursts of high-energy particle fluxes detected at Earth's surface, linked to the Relativistic Runaway Electron Avalanche (RREA) mechanism within thunderclouds. Accurate detection of TGEs is vital for advancing atmospheric physics and radiation safety, but event selection methods heavily rely on expert-defined thresholds. In this study, we use an automated supervised classification approach on a newly curated dataset of 2024 events from the Aragats Space Environment Center (ASEC). By combining a Tabular Prior-data Fitted Network (TabPFN) with SHAP-based interpretability, we attain 94.79% classification accuracy with 96% precision for TGEs. The analysis reveals data-driven thresholds for particle flux increases and environmental parameters that closely match the empirically established criteria used over the last 15 years. Our results demonstrate that modest but concurrent increases across multiple particle detectors, along with strong near-surface electric fields, are reliable indicators of TGEs. The framework we propose offers a scalable method for automated, interpretable TGE detection, with potential uses in real-time radiation hazard monitoring and multi-site atmospheric research.

physics.ins-det↗

arXiv2025

High order-accurate solution of scattering integral equations with unbounded solutions at corners

Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth geometries--owing to field enhancement and singularities that arise at sharp edges and corners which, if left untreated, give rise to significant accuracy losses. The problem is particularly challenging in cases in which the "density" (i.e., the solution of the integral equation) tends to infinity at corners and edges--a difficulty that can be bypassed for 2D configurations, but which is unavoidable in 3D Maxwell integral formulations, wherein the component tangential to an edge of the electrical-current integral density vector tends to infinity at the edge. In order to tackle the problem this paper restricts attention to the simplest context in which the unbounded-density difficulty arises, namely, integral formulations in 2D space whose integral density blows up at corners; the strategies proposed, however, generalize directly to the 3D context. The novel methodologies presented in this paper yield high-order convergence for such challenging equations and achieve highly accurate solutions (even near edges and corners) without requiring a priori analysis of the geometry or use of singular bases.

math.NA↗

arXiv2012

On disjoint matchings in cubic graphs: maximum 2- and 3-edge-colorable subgraphs

We show that any $2-$factor of a cubic graph can be extended to a maximum $3-$edge-colorable subgraph. We also show that the sum of sizes of maximum $2-$ and $3-$edge-colorable subgraphs of a cubic graph is at least twice of its number of vertices. Finally, for a cubic graph $G$, consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let $H$ be the largest matching among such pairs. Let $M$ be a maximum matching of $G$. We show that 9/8 is a tight upper bound for $|M|/|H|$.

cs.DM↗