This work presents a computational framework for large-scale nonlinear dynamic analysis by integrating the scaled boundary finite element method (SBFEM) with an octree-based pattern precomputation strategy. The proposed method adopts a pattern‑based precomputation strategy that fully exploits the limited number of unique octree patterns arising from the geometric transformations of octree elements. The stiffness component matrices, strain–displacement matrices, and diagonal lumped mass matrices of these master patterns are precomputed and stored in the hardware cache, thereby eliminating redundant runtime numerical integration and eigenvalue decomposition for repeated element shapes. For nonlinear elastic materials governed by a hypoelastic constitutive model, the tangent stiffness matrix is decomposed into a linear combination of constant basis matrices, enabling the element-level internal force vectors to be reconstructed dynamically through simple matrix–vector multiplications during the time-stepping procedure. A batch processing strategy is further developed to simultaneously compute the internal force contributions for all elements sharing the same master pattern. The framework is implemented with parallel computing capabilities based on domain decomposition, achieving efficient load balancing and minimal communication overhead. The accuracy and efficiency of the proposed method are validated through four numerical examples, including an octree patch test, a concrete cube under uniaxial tension, a slender bar subjected to impulsive loading, and a large-scale arch dam under seismic excitation. The results demonstrate that the proposed approach not only accurately captures the nonlinear material response but also achieves a significant reduction in computational cost compared with conventional methods on single or multiple processors.
Density functional perturbation theory (DFPT) provides a systematic framework to compute higher-order material behavior based on a ground-state Kohn-Sham density functional theory solution. In this study, Kohn-Sham DFPT is formulated for the first time within the real-space variational framework of the finite element method towards interatomic force constants. The formulation is carried out in a pseudopotential setting for non-periodic systems with the generalized-gradient approximation for the exchange-correlation functional, including nonlinear core correction. The validation process is conducted through comparisons with conventional codes and finite difference schemes applied to perturbed ground-state calculations. For the interatomic force constants, it is demonstrated that one obtains convergence rates which parallel the optimal rates for energy and the observed rates for force.
We propose an overlapping Schwarz space-time refinement framework for the material point method (OS-MPM) to improve computational efficiency in problems with strongly localized deformation, contact, and large geometric nonlinearity. The method decomposes the domain into overlapping coarse and fine subdomains with heterogeneous spatial and temporal resolutions, while retaining standard MPM discretizations within each subdomain. Coarse-fine coupling is achieved through an MPM-specific Schwarz iteration combining mass-weighted spatial transmission and temporal interpolation for sub-cycling. In contrast to refinement strategies based on modified basis functions, transition kernels, or strongly enforced interface constraints, the proposed approach preserves the modular structure of standard MPM and shifts the coupling complexity to nonmatching-grid interface operators within the Schwarz alternating procedure. Three numerical benchmarks, namely a gravity-driven cantilever beam, Hertzian contact, and an elastic inclusion problem, show that the method reproduces analytical or fine-resolution reference solutions with good accuracy in the tested cases. In the inclusion benchmark, the proposed framework achieves center-strip stress error comparable to single-domain fine simulations at the finest tested resolutions; timings show 4.3–9.1-fold speedups over uniform fine-grid MPM at the finest tested resolution. A three-dimensional folding example further demonstrates the generality of the framework. These results indicate that the proposed method provides an accurate, modular, and efficient route for local space-time refinement in MPM.
Data-driven computational mechanics offers an alternative solution methodology to conventional methods by replacing constitutive models with data spaces defining admissible material states. Originally proposed for linear elasticity, its application to plasticity remains challenging. Purely data-driven plasticity schemes are usually restricted to one-dimensional problems due to the excessively large data space required as a result of path dependence. Hybrid frameworks combining constitutive assumptions with data have shown promise but are often limited by their underlying assumptions such as isotropic hardening or their inability to capture strain-path changes. In this work, a new hybrid model–data plasticity framework is proposed that incorporates kinematic and isotropic hardening via data spaces derived from discrete datasets, while adopting Prager’s law for back stress evolution without explicitly defining its functional form. The approach preserves the standard computational plasticity algorithmic procedures, while an implicit return-mapping procedure and a search direction calculation akin to the elastoplastic tangent are performed through the data spaces. Numerical examples in one and three-dimensional problems demonstrate the effectiveness of the proposed framework in more general plasticity problems.
The statistics of the frequency response of an uncertain structure are most demanding to compute near lightly damped resonances. As the parameters vary, the resonant frequencies migrate, so at a fixed frequency the response depends sharply on the parameters, and a polynomial surrogate converges slowly there. We propose to work on its partial-fraction representation characterized by poles and residues. The surrogate is an encoder–decoder with a physical bottleneck, in which an encoder maps the random parameters into the spectral data and a fixed analytic pole–residue layer decodes them into the response. We introduce two encoders of the spectral data, a direct polynomial-chaos map, PR-PCE, and a neural-network encoder that takes the chaos basis as its feature map, PR-PCNN. We develop the construction for a random vector indexed by the frequency. A complementary route learns the same spectral code from sampled responses alone, independently of the system matrices. The framework is verified on two systems, a three-degree-of-freedom structure and a clamped–free beam whose flexural rigidity is a random field. On both, the linear PR-PCE map is the most accurate, the neural encoders follow it, and a frequency-wise chaos expansion trails them. The representation is also benchmarked against a stochastic frequency transformation and a per-realisation vector fit. For these smooth spectral data the linear map stays the more accurate, and the value of the neural encoder lies in its flexibility, since it also learns the code end-to-end and from sampled responses alone.
