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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…
The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a…
We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
Applying proper orthogonal decomposition to a usual finite element (FE) formulation for space fractional partial differential equation, we get a reduced FE model, which greatly reduces the complexity of computation. Then, the stability…
Standard approaches to domain decomposition methods (DDM) are uncapable of producing block-diagonal system matrices. The derived-vector-space (DVS), approach to DDM, introduced in 2013, overcomes this limitation. However, the DVS approach…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…
We present a domain decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller…
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as…
In the last years, automated segmentation has become a necessary tool for volume electron microscopy (EM) imaging. So far, the best performing techniques have been largely based on fully supervised encoder-decoder CNNs, requiring a…
Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in…
In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique…
An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems…
In this work, we propose the application of the eXtended Finite Element Method (XFEM) in the context of the coupling between three-dimensional and one-dimensional elliptic problems. In particular, we consider the case in which the 3D-1D…
We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.
The optical cross sections of plasmonic nanoparticles are intricately linked to the morphology of the particle. If this connection can be made accurately enough, it would become possible to determine a particles shape solely from its…
The accurate and efficient prediction of crack propagation in dielectric materials is a critical challenge in structural health monitoring and the design of smart systems. This work presents a hybrid modeling framework that combines an…