Related papers: I-FENN with DeepONets: accelerating simulations in…

Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs) offer a highly expressive and flexible framework for modeling complex…

The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the…

Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existing approaches are limited in their ability to generalize…

Federated Learning (FL) enables collaborative training without centralizing data, essential for privacy compliance in real-world scenarios involving sensitive visual information. Most FL approaches rely on expensive, iterative deep network…

This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…

Structural optimization is essential for designing safe, efficient, and durable components with minimal material usage. Traditional methods for vibration control often rely on active systems to mitigate unpredictable vibrations, which may…

In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…

This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network based on the DeepONet framework. We consider a 2D square domain with an inclusion of arbitrary boundary…

This paper proposes a methodology to estimate stress in the subsurface by a hybrid method combining finite element modeling and neural networks. This methodology exploits the idea of obtaining a multi-frequency solution in the numerical…

Finite element methods (FEM) are popular approaches for simulation of soft tissues with elastic or viscoelastic behavior. However, their usage in real-time applications, such as in virtual reality surgical training, is limited by…

This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…

The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

This paper introduces BFEMP, a new approach for monolithically coupling the Material Point Method (MPM) with the Finite Element Method (FEM) through barrier energy-based particle-mesh frictional contact using a variational time-stepping…

In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…

Although current deep learning methods have achieved impressive results for semantic segmentation, they incur high computational costs and have a huge number of parameters. For real-time applications, inference speed and memory usage are…

Aircraft design optimization traditionally relies on computationally expensive simulation techniques such as Finite Element Method (FEM) and Finite Volume Method (FVM), which, while accurate, can significantly slow down the design iteration…

A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…

Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often…

We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…