This special issue, dedicated to the inaugural edition of the ECCOMAS-IACM conference series Math 2 Product (M2P), contains eleven articles on frontier topics in Computational Science and Engineering, with a specific focus on next-generation methodologies for industrial problems and sustainability.
We propose a new reduced-order modeling (ROM) strategy for tackling parametrized Darcy-flow systems in which the constraint is given by mass conservation. Our approach employs classical neural-network architectures and supervised learning, but it is constructed in such a way that the resulting ROM is guaranteed to satisfy the linear constraints exactly. The procedure is based on a splitting of the solution into a particular solution satisfying the constraint and a homogenous solution. The homogeneous solution is approximated by mapping a suitable potential function, generated by a neural-network model, onto the kernel of the constraint operator. For the particular solution, instead, we propose an efficient spanning-tree algorithm. Starting from this paradigm, we present three approaches that follow this methodology, obtained by exploring different choices of the potential spaces: derived either via proper orthogonal decomposition (POD) or using the properties of a differential complex. To demonstrate the effectiveness of the proposed strategies and to emphasize their advantages over neural-network regression approaches, we present a series of numerical experiments, ranging from mixed-dimensional problems to nonlinear systems.
Fast and efficient simulation strategies are a basic requirement of technologies such as digital twins. Particularly for roadway infrastructure, recent developments have demonstrated that the arbitrary Lagrangian Eulerian (ALE) formulation can be utilized to improve computational efficiency, when simulating the response of such pavement structures subjected to moving loads. It is also well-established in literature, that model order reduction (MOR) techniques significantly enhance calculation speed. This contribution details the combination of both these tools into a novel model order reduced arbitrary Lagrangian Eulerian (MORALE) formulation. Both hyperelastic and viscoelastic material models are considered in this work. Transient simulations of pavement structures subjected to moving loads are then carried out with the developed framework, and these show a significant enhancement in computational speed and efficiency over conventional simulation techniques. Also in this work, a comprehensive breakdown of the computational costs involved in using the MORALE formulation is provided and analysed. Such an efficient and fast simulation framework is of vital importance in technologies such as digital twins of roadway infrastructure (like pavements), as it enables engineers to quickly run what-if analyses and make informed decisions about the management of the structure under consideration.
This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. We compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.
Multiscale modelling methods are important for accurately predicting the behaviour of complex, heterogeneous materials. First-order homogenisation (1OH) has been widely used in this context but shows limitations in cases where the microstructural length scale becomes comparable to the macrostructural length scale, such as in the case of woven composites. To address these limitations, second-order homogenisation (2OH) methods have been developed which incorporate higher-order deformation gradients into the formulation of the RVE boundary value problem. However, the computational cost and memory requirements of 2OH, particularly in large-scale simulations, pose significant challenges due to dense constraint matrices and non-scalable operations. This paper presents computational solutions aimed at overcoming these bottlenecks, enabling the efficient application of 2OH to large-scale RVE models. We introduce a predictor–corrector scheme that replaces the conventional direct displacement method in the downscaling process, significantly reducing runtime and memory usage. For upscaling, we identify memory bottlenecks during the evaluation of constitutive tangents, where we highlight limitations of conventional approaches and evaluate alternatives to provide recommendations for large-scale RVE models. The methods are implemented on a 3D woven composite RVE, and the results demonstrate a significant reduction in computational time and memory requirements.
Eigenvalue and eigenvector sensitivities with respect to design parameters are crucial for advancing design, optimization, and uncertainty quantification in structural systems. This paper introduces a novel, efficient, and general numerical method for computing arbitrary-order sensitivities of eigenpairs in self-adjoint undamped and underdamped systems. The proposed approach integrates Hypercomplex Automatic Differentiation (HYPAD) with a residual-based formulation to compute sensitivities with machine precision. Sensitivities are calculated in ascending order by solving a sequence of linear systems that share a common coefficient matrix. The method preserves the sparsity of the mass and stiffness matrices, allowing for efficient factorization and compatibility with current sparse direct solvers. The methodology is demonstrated through a numerical example under both undamped and underdamped conditions. Up to tenth-order sensitivities are computed with respect to multiple material and geometric parameters, showing excellent agreement with analytical solutions. Runtime analysis confirms that the computational cost per derivative remains constant, regardless of the order, underscoring the method's efficiency. Overall, the proposed approach offers a scalable and accurate framework for sensitivity analysis in large-scale eigenvalue problems.
The explicit moving particle simulation (EMPS) method, due to its pressure calculation through the equation of state, has high computational efficiency and broad prospects for engineering applications. However, the conventional EMPS method has issues of numerical instability such as high-frequency oscillations and discontinuous distributions of pressure. In this paper, to improve the accuracy and stability of numerical simulations, an enhanced δMPS-EMPS method was proposed, in which a new enhanced equation of state and a diffusion term of particle number density were developed. The new enhanced equation of state includes the terms of the velocity divergence and the particle number density. It describes the relationship between pressure and fluid density through the changes in the velocity field and the particle number density field, resulting in a smooth pressure. It is worth noting that the artificial bulk modulus K in this equation is accurately calibrated using the specified pressure field calculated by the MPS method at the first time step. Additionally, the particle number density is corrected by introducing a diffusion term into the mass conservation equation. This approach can reduce high-frequency pressure oscillations by filtering out non-physical density fluctuations. The proposed method was evaluated and validated through simulations of four benchmark cases, including a hydrostatic pressure tank, the deformation of an elliptical droplet, the Taylor-Green vortex flow, the 2D water dam-break flow, and the evolution of a square patch of fluid. The simulation results proved the effectiveness and robustness of the enhanced δMPS-EMPS method.
Engineers can accomplish customised thermal properties that maximise fluid performance in various operating scenarios by hybridising alloy nanoparticles. The present study provides new insights into the heat and mass transfer of the squeezing flow of hybrid nanofluid between the parallel Riga plates under the impacts of shape effects, non-uniform heat generation/absorption and activation energy. A suitable similarity approach is implemented to transform governing equations into non-linear systems of ordinary differential equations and is solved numerically using the bvp-5c technique. The results show that the velocity profile increases near the lower plate and decreases near the upper plate. In contrast, both the temperature and concentration profiles rise for growing values of the squeezing number. It is found that both temperature and concentration profile rise for augmented values of the Biot number parameters. Also, engineering factors are discussed graphically with specific parameters. Further, properly aligned residual plots and less variance in fitted values reveal the response surface methodology's great accuracy and validity. And from the sensitivity analysis, it is observed that the Skin friction has a positive influence for Hartman and porosity parameters and negative influence for squeezing parameter also the Nusselt number has a negative sensitivity for both squeezing and Biot number and less positive sensitive to the Hartman number.
This study introduces a microstructure-temperature coupled framework to analyze the collapse behavior of non-API high-toughness casings (BG110V/BG140V), addressing a 16%–18% prediction error in conventional API standards through experimental validation, 3D modeling, and a novel multifactor correction formula. Full-scale collapse tests at 50°C and 85°C revealed temperature-dependent elastoplastic behavior. BG140V showed higher-pressure resistance (75.89 MPa at 50°C vs. 59.47 MPa for BG110V), attributed to its finer grain structure (ASTM 10.0 vs. BG110V's 6.5). Thermal softening reduced yield strength by 4.3% (BG110V) and 2.4% (BG140V) at 85°C, correlating with accelerated dislocation mobility (1.5 × 108/cm2 vs. 108/cm2 at 50°C). Finite element simulations (mesh size: 5 mm global/2 mm local) replicated collapse pressures with ≤ 3% error, validated against experimental data. Microstructural analysis identified dual failure mechanisms: axial collapse initiated at stress-concentrated zones (100–150 mm from ends, 30% above average stress), while radial failure originated from surface defects (0.1 mm scratches amplifying strain by 40%). A novel multifactor correction formula integrating API standards with microstructure-aware terms (grain size: n = 0.5 Hall–Petch exponent; defect tolerance: ovality ≤ 2%) reduced collapse pressure prediction errors from 16% to 18% (API) to ≤ 6.7%. The model quantifies temperature effects via Arrhenius-type decay (αT = 0.0032 for BG110V) and inclusion-driven microcrack thresholds (Cinclusion ≤ 1.2 vol%). These findings establish a microstructure-property-performance framework for optimizing casing design in ultra-deep reservoirs, balancing computational efficiency with industrial reliability. Recommendations include expanding validation to cyclic fatigue scenarios and hydrogen embrittlement environments to advance next-generation well integrity protocols.
New triangular elements incorporating an interior node are developed based on barycentric coordinates and implemented in the Element Differential Method. Shape functions for four- and seven-node triangular elements are constructed following a serendipity-inspired approach, with explicit expressions for their first- and second-order derivatives. Numerical validation is performed through steady-state and transient heat conduction, as well as solid mechanics problems involving both regular and complex geometries. Results demonstrate that the seven-node barycentric element (T7B3) achieves second-order convergence, exhibits superior numerical stability, and outperforms its Cartesian counterpart (T7C3) and conventional elements in both accuracy and robustness. Notably, proper placement of the interior node at the centroid markedly enhances performance, whereas deviation leads to numerical oscillations and instability. The proposed T7B3 element demonstrates excellent performance for high-fidelity simulations in complex geometries and offers an effective alternative to traditional triangular and quadrilateral elements.
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