Finite Element Analysis
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Related Articles from SNS
Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries
arXiv:2606.08287v1 Announce Type: new Abstract: Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios. Machine learning surrogate models offer a promising alternative, yet most approaches struggle with a critical limitation: generalizing across varying geometries. This work presents a mesh graph network (MGN) for predicting von Mises stress fields in 2D structural...
Sparse FEONet: A Low-Cost, Memory-Efficient Operator Network via Finite-Element Local Sparsity for Parametric PDEs
Announce Type: replace Abstract: In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, Finite Element Operator Network for Solving Elliptic-Type Parametric PDEs, SIAM J. Sci. Comput., 47(2), C501-C528, 2025. FEONet realizes the parameter-to-solution map on a finite element space and admits a training procedure that does not require training data, while exhibiting high...
Hessian-recovery-based C0 finite element methods for non-divergence form elliptic equations
arXiv:2606.03276v1 Announce Type: new Abstract: A Hessian-recovery-based C0 finite element framework is proposed for second-order elliptic equations in non-divergence form. The construction is based on a direct approximation of the strong non-divergence operator: the Hessian D2u is replaced by a recovered Hessian Hhuh, so that A : D2u is approximated by A : Hhuh. The resulting discretizations include a nodal formulation and a Galerkin-type formulation for general Lagrange finite element...
A decoupled energy-stable mixed finite element method for Poisson-Nernst-Planck-Navier-Stokes equations
arXiv:2606.04941v1 Announce Type: new Abstract: We propose a novel linearized mixed finite element method for the Poisson-Nernst-Planck-Navier-Stokes (PNPNS) system. Specifically, the method combines a staggered time discretization that eliminates the need for expensive nonlinear solvers by carefully treating nonlinear terms in a time-staggered manner, with a mimetic spatial discretization that preserves the exact structure of the discrete de Rham complex. Both semi-discrete scheme and its...
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...
The Immersed Discontinuous Galerkin Method for Elliptic Interface Problems
arXiv:2606.01814v1 Announce Type: new Abstract: This paper is devoted to construction and convergence analysis of the linear explicit immersed finite element (IFE) function. For the interface elements, the proposed IFE functions precisely satisfy the interface conditions on the actual interface. The IFE functions are constructed in an explicit form and can be obtained directly without solving any auxiliary problems or local linear systems.
Numerical Analysis on Backward Stochastic Differential Equations by Finite Transposition Method
arXiv:2606.08731v1 Announce Type: cross Abstract: In this paper, we propose a finite transposition method to solve backward stochastic differential equations (BSDEs, for short). Based on the transposition solution theory for BSDEs, our method offers a promising way of efficiently computing solutions, which can be regarded as an analogous method for BSDEs as the classical finite element method for partial differential equations. Our method has the advantage of easily computable conditional...
MidSurfNet: Learnable Face Pairing and Interference Implicit Fields for Generalized Mid-surface Abstraction
arXiv:2606.01891v1 Announce Type: new Abstract: Mid-surface abstraction is essential for finite element analysis of thin-walled CAD models. Existing face pairing-based methods rely on handcrafted geometric heuristics, yet real-world industrial models frequently exhibit multi-wall-thickness regions, self-matching face configurations, and demand for non-center offset surfaces--scenarios where rule-based approaches consistently fail. We present MidSurfNet, a learning-augmented framework that...
Trace-Preserving hp Interpolation and Polynomial Liftings on Conforming Hexahedral Meshes
Announce Type: new Abstract: Trace-compatible polynomial extensions are a recurring local ingredient in high-order finite element analysis on conforming hexahedral meshes. They are needed whenever prescribed edge and face traces must be preserved while a polynomial is extended into a neighboring cell or boundary patch. The main contribution of this paper is the construction of p-robust polynomial liftings on nonsingular conforming hexahedral boundary patches, with stable control of both the...
Constrained Extreme Gradient Boosting for Adapting Reduced-Order Models
arXiv:2605.04130v2 Announce Type: replace Abstract: High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization, and real-time control. Projection-based reduced-order models (ROMs) alleviate this cost by projecting the governing dynamics onto low-dimensional subspaces. However, their performance can deteriorate...