Related papers: Finite element model updating for structural appli…
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…
In the automotive industry, predicting noise during design cycle is a necessary step. Well-known methods exist to answer this issue in low frequency domain. Among these, Finite Element Methods, adapted to closed domains, are quite easy to…
The scaled boundary finite element method is known for its capability in reproducing highly-detailed solution fields. This, however, is only attainable in those cases where analytical solutions exist. Many others invoke the use of numerical…
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…
Sensitivity-based Finite Element Model Updating (FEMU) is one of the widely accepted techniques used for damage identification in structures. FEMU can be formulated as a numerical optimization problem and solved iteratively making automatic…
The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we…
In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical…
Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. Quick generation of high-quality interatomic potentials is of urgent need under present circumstances,…
In this paper, the stabilized finite element method based on local projection is applied to discretize the Stokes eigenvalue problems and the corresponding convergence analysis is given. Furthermore, we also use a method to improve the…
In this paper, finite element method is applied to Leland's model for numerical simulation of option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are formulated in combination with a…
This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation, that is based on a proposed modified version of the mortar method. The…
A local and parallel algorithm based on the multilevel discretization is proposed in this paper to solve the eigenvalue problem by the finite element method. With this new scheme, solving the eigenvalue problem in the finest grid is…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several…