Related papers: Automatic 3D modeling by combining SBFEM and trans…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
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…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
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…
A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined…
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…
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…
In this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general nonlinear boundary conditions. For such a system we propose…
We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness…
In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of…
The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The…
We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…
Electrical machines commonly consist of moving and stationary parts. The field simulation of such devices can be very demanding if the underlying numerical scheme is solely based on a domain discretization, such as in case of the Finite…
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…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the…