FEM
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Related Articles from SNS
Uniform-in-time Strong Error Estimates of Tamed-FEM to Superlinear SPDEs driven by Multiplicative Noise
arXiv:2606.09173v1 Announce Type: new Abstract: We establish sharp, uniform-in-time strong error estimates for a nonlinearity-explicit tamed finite element method (FEM) applied to a class of superlinear stochastic partial differential equations (SPDEs) driven by multiplicative noise, including the stochastic Allen--Cahn equation with a moderately thick interface. This tamed-FEM was first introduced in [Z. Liu and J. Shen, arXiv:2502.19117] to ensure long-time unconditional stability and to...
FEM-Bench: A Structured Scientific Reasoning Benchmark for Evaluating Code-Generating LLMs
arXiv:2512.20732v2 Announce Type: replace Abstract: As LLMs advance their reasoning capabilities about the physical world, the absence of rigorous benchmarks for evaluating their ability to generate scientifically valid physical models has become a critical gap. Computational mechanics, which develops and applies mathematical models and numerical methods to predict the behavior of physical systems under forces, deformation, and constraints, provides an ideal foundation for structured...
Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative
Announce Type: new Abstract: Automatic-differentiation-based inverse analysis methods, including physics-informed neural networks (PINNs) and differentiable programming, have recently shown great promise due to their ability to compute accurate gradients and convergence efficiency. However, their applicability to falling weight deflectometer (FWD) backcalculation remains unexplored. This study critically evaluates PINN-based inverse analysis for a multilayer pavement system and investigates...
A Second-order Structure-preserving Parametric FEM for Surface Evolution
arXiv:2606.08293v1 Announce Type: new Abstract: In this paper, we propose a second-order-in-time, structure-preserving, and mesh-robust parametric finite element method for surface diffusion and volume-preserving mean curvature flow. We first reformulate the original evolution equations into new systems in which the tangential motion is governed by a harmonic map heat flow. This heat flow maps a fixed reference surface onto the unknown evolving surface and drives points on the evolving...
Numerical analysis of the second-order time-dependent saddle point Maxwell system via a parameter-free discontinuous Galerkin method: The first optimal ${\bf L}^{2}$-norm error estimates
Announce Type: new Abstract: We present a novel parameter-free discontinuous Galerkin (dG) finite element method (FEM) for the time-dependent Maxwell system formulated as a saddle point problem. We establish the stability of the proposed semi-discrete problem and derive optimal error estimates in energy and \( {\bf L}^{2} \) norms for the electric field variable, as well as in \( L^{2} \) norm for the potential function. To the best of our knowledge, this work provides the first optimal \(...
PINNOCHIO: Physics-Informed Neural Network for Coupled Hyperelastic Interface-Volume Simulation in Orthognathic Surgery
Announce Type: cross Abstract: Predicting patient-specific facial soft-tissue deformation is critical for iterative orthognathic surgery planning. However, current computational methods face a strict accuracy-efficiency trade-off: high-fidelity Finite Element Methods (FEM) are computationally prohibitive, whereas pure deep learning models often produce biomechanically inconsistent results. While Physics-Informed Neural Networks (PINNs) offer a promising avenue, learning the complex...
Design of an efficient Tunable Dual narrow-band MEMS Mid and Far IR emitter with Me-NTA for Industrial and Biomedical applications
arXiv:2606.05838v1 Announce Type: new Abstract: Spectrally selective infrared (IR) thermal emitters are gaining much attention now-a-days for sensing, spectroscopy and biomedical applications. In this research, two metasurface incorporated IR emitters are proposed and numerically analyzed using finite element method (FEM).
PDE-Agents: An LLM-Orchestrated Multi-Agent Framework for Automated Finite Element Simulations with Knowledge Graph-Augmented Reasoning
Announce Type: new Abstract: We present PDE-Agents, a multi-agent ecosystem that automates the full lifecycle of partial differential equation (PDE) / finite element method (FEM) simulations through natural-language interaction. Three specialist large language model (LLM) agents (Simulation, Analytics, Database) are orchestrated via a LangGraph supervisor, with a local open-source LLM stack (Qwen3-Coder-Next, Llama 4 Scout) on dual NVIDIA RTX PRO 6000 GPUs. The architecture is...
Physics-Informed Neural Networks for Radial Consolidation of Combined Electroosmotic, Vacuum and Surcharge Preloading Considering Smear Effects
arXiv:2606.00056v1 Announce Type: cross Abstract: This study develops a dimensionless multi-domain physics-informed neural network (PINN) framework for electro-osmotic radial consolidation considering smear effects and combined vacuum and surcharge loading. Three PINN-based models are investigated: a standard soft-constrained PINN (Std-PINN), a modified gated PINN (Mod-PINN), and a modified gated PINN with hard-constraint boundary encoding (Mod-HC-PINN). The models are evaluated against FEM...
Solver-in-the-Loop joint operator learning: fractional Laplace-Beltrami features for interface reconstruction
arXiv:2411.05341v2 Announce Type: replace Abstract: In this work, we propose a joint operator learning method for reconstructing images of conductivity coefficients from boundary data. Inspired by the idea of employing partial differential equation (PDE) solvers as preconditioners for this inverse problem, we investigate a ``solver-in-the-loop'' training mechanism. It allows the interaction of learnable parameters integrated in a PDE solver module and those in neural networks for...