Nikita Sakovich¹, Dmitry Aksenov¹, Ekaterina Pleshakova^1,*, Sergey Gataullin^1,2

CMC-Computers, Materials & Continua, Vol.88, No.3, 2026, DOI:10.32604/cmc.2026.081449 - 23 July 2026

Abstract Neural operators provide a data-driven framework for learning mappings between function spaces and have shown strong performance in scientific computing and surrogate modeling. Existing architectures, however, typically rely on a single representation of the input function—either purely pointwise, as in DeepONet, or purely spectral, as in Fourier Neural Operators—which limits their ability to simultaneously capture local variability and global structure. In this work, we propose NOASLRR, a neural operator that integrates three complementary branches within a unified DeepONet-style formulation: a pointwise MLP embedding, a spectral branch based on Chebyshev polynomial coefficients, and a low-rank linear… More >

Miklós Molnár^*

CMC-Computers, Materials & Continua, Vol.88, No.1, 2026, DOI:10.32604/cmc.2026.077825 - 08 May 2026

Abstract This article presents a particular tree covering technique. To cover a set of nodes belonging to an unknown tree, a set of connected small Steiner trees is proposed. These Steiner trees can be represented as hyperedges, and a chain or tree of hyperedges provides the cover. The model allows the calculation of approximate (partial) spanning trees in graphs. The idea of covering a set of nodes by hyperedges can be used directly in Steiner heuristics. The NP-hard Steiner problem in graphs is one of the most studied graph-related problems. Several heuristics are known to give More >

S. N. Garibova^1,2, M. E. Aliyev³, U. I. Ashurova⁴, L. C. Suleymanova⁴, A. M. Kerimova¹, S. A. Rzayeva¹, S. O. Guseynova¹, H. I. Novruzova¹, R. Z. Amirov¹, F. Sarcan⁵

Chalcogenide Letters, Vol.22, No.12, pp. 999-1008, 2025, DOI:10.15251/CL.2025.2212.999 - 03 December 2025

Abstract In this work, the electronic behavior of the chalcogenide semiconductor Ge₂Sb₂Te₅ was examined using a first-principles computational approach. The study was carried out within the density functional theory framework, where the spin-polarized generalized gradient approximation was applied through the Atomistix ToolKit software. A double-zeta polarized basis set formed the foundation of the calculations, while exchange–correlation interactions were treated using the Perdew–Burke–Ernzerhof functional. Sampling of the Brillouin zone was performed according to the Monkhorst–Pack method with a 2 × 2 × 2 k-point grid, ensuring accuracy through special-point integration. Atomic configuration optimization, also conducted in Atomistix ToolKit,… More >

S. N. Garibova^a,b,*, А. I. Isayev^a, S. A. Rzayeva^a, F. N. Mammadov^c

Chalcogenide Letters, Vol.22, No.1, pp. 1-9, 2025, DOI:10.15251/CL.2025.221.1

Abstract The structure particulars of amorphous Ge2Sb2Te5 thermally evaporated on glass substrates, as well as films annealed at temperatures of 500 and 700 K have been studied by the considering of experimentally established facts obtained from X-ray analysis and Raman spectroscopy measurements. The Debye-Scherrer and Williams-Hall methods were applied to the X-ray diffraction data for estimate the size of crystallites, interatomic distances, dislocation density and structure distortion degree. The features of heat treatment effect on numerical values of the above quantities at a given temperatures have been established. The analysis of the spectral distribution of Raman… More >

Junseo Lee¹, Bongsoo Jang¹, Umer Saeed^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 2165-2189, 2025, DOI:10.32604/cmes.2025.069023 - 31 August 2025

Abstract In recent years, variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability to model complex physical phenomena with memory and spatial heterogeneity. However, existing numerical methods often struggle with the computational challenges posed by such equations, especially in nonlinear, multi-term formulations. This study introduces two hybrid numerical methods—the Linear-Sine and Cosine (L1-CAS) and fast-CAS schemes—for solving linear and nonlinear multi-term Caputo variable-order (CVO) fractional partial differential equations. These methods combine CAS wavelet-based spatial discretization with L1 and fast algorithms in the time domain. A key feature of the approach is More >

Benjamin Wacker¹, Jan Christian Schlüter^2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 2191-2229, 2025, DOI:10.32604/cmes.2025.067397 - 31 August 2025

Abstract In this work, we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution. As our first contribution, we establish non-negativity, boundedness of some solution components, existence globally in time, and uniqueness on a time interval for an arbitrary for the time-continuous problem which extends known results of Kirschner’s model in the literature. As our second analytical result, we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question. Our More >

N. A. Ismayilova^a,b,*, S. G. Asadullayeva^a,c,d, E. K. Kasumova^e, Kh. A. Hidiyev^a, N. N. Hashimova^c, J. A. Guliyev^a

Chalcogenide Letters, Vol.21, No.7, pp. 493-498, 2024, DOI:10.15251/CL.2024.217.493

Abstract DFT calculation is used to investigate the structural, electronic, optical, and elastic properties of AgCuSe and AgCuS. The calculations are performed using the ATK with generalized gradient approximation (GGA) in combination with Hubbard U correction parameters for both structures. The calculated band gap energies and partial density of state reveal that AgCuS has semiconductor properties unlike this AgCuSe has a metallic nature. The optical properties, real and imaginary parts of dielectric function are obtained for the energy range of 0 to 5 eV. Elastic stiffness coefficients (Cij), bulk modulus (B), shear modulus (G), and Young modulus (E) More >

Pugazhenthi Sivasankar^1,*, Austin B. Probe², Tarek A. Elgohary¹

Digital Engineering and Digital Twin, Vol.2, pp. 169-205, 2024, DOI:10.32604/dedt.2024.052805 - 31 December 2024

Abstract In Space Situational Awareness (SSA), accurate and efficient uncertainty quantification and propagation are essential for various applications, such as conjunction analysis, track correlation, and orbit prediction. The propagation of the probability density function (PDF) in nonlinear systems results in non-Gaussian distributions, which are difficult to approximate. Furthermore, the computational cost of approximating the PDF increases exponentially with the number of random variables, a phenomenon known as the curse of dimensionality. To address these challenges, the Orthogonal Probability Approximation (OPA) method is presented for high-fidelity uncertainty propagation and PDF approximation in nonlinear dynamical systems. The method… More >

Yuxiang Peng^1,*, Pengnan Sun¹, Niannian Liu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.31, No.3, pp. 1-1, 2024, DOI:10.32604/icces.2024.011902

Abstract Immersed boundary method (IBM) has been widely applied in the simulation of fluid-structure interaction problems. The traditional direct force model is less accurate, and the sharp-interface approaches involve complex topological operations which are not conducive to dealing with complex structures. The boundary data immersion method (BDIM) is a new fluid-structure coupling scheme that does not need to cut the mesh and can be extended to reach second-order accuracy. However, the traditional boundary data immersion method needs special treatment to deal with the sharp corners of the structure. In the present work, the volume fraction of More >

Sara Salem Alzaid¹, Badr Saad T. Alkahtani^1,*, Kumar Chandan², Ravikumar Shashikala Varun Kumar³

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.3, pp. 2555-2574, 2024, DOI:10.32604/cmes.2024.055312 - 31 October 2024

Abstract Heat transport has been significantly enhanced by the widespread usage of extended surfaces in various engineering domains. Gas turbine blade cooling, refrigeration, and electronic equipment cooling are a few prevalent applications. Thus, the thermal analysis of extended surfaces has been the subject of a significant assessment by researchers. Motivated by this, the present study describes the unsteady thermal dispersal phenomena in a wavy fin with the presence of convection heat transmission. This analysis also emphasizes a novel mathematical model in accordance with transient thermal change in a wavy profiled fin resulting from convection using the… More >