Related papers: Neural enrichment finite element method: A hybrid …
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
In this paper, we propose two time-splitting finite element methods to solve the semiclassical nonlinear Schr\"odinger equation (NLSE) with random potentials. We then introduce the multiscale finite element method (MsFEM) to reduce the…
The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce…
We present a method whereby the finite element method is used to train physics-informed neural networks that are suitable for surrogate modeling. The method is based on a custom convolutional operation called stencil convolution which…
State estimation of nonlinear dynamical systems has long aimed to balance accuracy, computational efficiency, robustness, and reliability. The rapid evolution of various industries has amplified the demand for estimation frameworks that…
Software effort estimation is a critical part of software engineering. Although many techniques and algorithmic models have been developed and implemented by practitioners, accurate software effort prediction is still a challenging…
Federated learning (FL) is an emerging paradigm for decentralized training of machine learning models on distributed clients, without revealing the data to the central server. The learning scheme may be horizontal, vertical or hybrid (both…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
The Finite Element Method (FEM) is a widely used technique for simulating crash scenarios with high accuracy and reliability. To reduce the significant computational costs associated with FEM, the Finite Element Method Integrated Networks…
In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…
The Adaptive Stabilized Finite Element method (AS-FEM) developed in Calo et. al. combines the idea of the residual minimization method with the inf-sup stability offered by the discontinuous Galerkin (dG) frameworks. As a result, the…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
We propose an extrinsic, continuous-Galerkin (CG), extended finite element method (XFEM) that generalizes the work of Hansbo and Hansbo to allow multiple Heaviside enrichments within a single element in a hierarchical manner. This approach…
In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…
Computational modelling offers a cost-effective and time-efficient alternative to experimental studies in biomedical engineering. In cardiac electro-mechanics, finite element method (FEM)-based simulations provide valuable insights into…
In recent years, the immersed finite element methods (IFEM) introduced in \cite{Li2003}, \cite{Li2004} to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of…
Recently, federated learning has emerged as a promising approach for training a global model using data from multiple organizations without leaking their raw data. Nevertheless, directly applying federated learning to real-world tasks faces…