Related papers: openCFS: Open Source Finite Element Software for C…
Structured Finite Element Methods (FEMs) based on low-rank approximation in the form of the so-called Quantized Tensor Train (QTT) decomposition (QTT-FEM) have been proposed and extensively studied in the case of elliptic equations. In this…
We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…
This manuscript is a collection of problems and solutions related to modeling the cryosphere using the finite element software FEniCS. Included is an introduction to the finite element method; solutions to a variety of problems in one, two,…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
The frequency-domain approach (FDA) to transient analysis of the boundary element method, although is appealing for engineering applications, is computationally expensive. This paper proposes a novel adaptive frequency sampling (AFS)…
This paper studies finite element approximations of the stochastic Allen-Cahn equation with gradient-type multiplicative noises that are white in time and correlated in space. The sharp interface limit as the parameter $\epsilon \rightarrow…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…
We introduce an enriched immersed finite element method for addressing interface problems characterized by general non-homogeneous jump conditions. Unlike many existing unfitted mesh methods, our approach incorporates a homogenization…
Simulation is a foundational tool for the analysis and testing of cyber-physical systems (CPS), underpinning activities such as algorithm development, runtime monitoring, and system verification. As CPS grow in complexity and scale,…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
Computational fluid dynamics (CFD) in combination with patient-specific medical images has been used to correlate flow phenotypes with disease initiation, progression and outcome, in search of a prospective clinical tool. A large number of…
This study evaluates four widely used fracture simulation methods, comparing their computational expenses and implementation complexities within the Finite Element (FE) framework when employed on heterogeneous solids. Fracture methods…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for 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…
Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number of surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in the analysis…