Related papers: Simplex space-time meshes in engineering applicati…
Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition…
Spatial Galerkin projection transfers fields between different meshes. In the area of finite element analysis of electromagnetic fields, it provides great convenience for remeshing, multi-physics, domain decomposition methods, etc. In this…
A unified construction of $H(\textrm{div})$-conforming finite element tensors, including vector element, symmetric matrix element, traceless matrix element, and, in general, tensors with linear constraints, is developed in this work. It is…
We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we…
We develop a space-time mortar mixed finite element method for parabolic problems. The domain is decomposed into a union of subdomains discretized with non-matching spatial grids and asynchronous time steps. The method is based on a…
For linear parabolic initial-boundary value problems with self-adjoint, time-homogeneous elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and for incompatible, time-analytic forcing term in…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
Delamination is a critical mode of failure that occurs between plies in a composite laminate. The cohesive element, developed based on the cohesive zone model, is widely used for modeling delamination. However, standard cohesive elements…
One of the main approaches for modeling fracture and crack propagation in solid materials is adaptive insertion of cohesive elements, in which line-like (2D) or surface-like (3D) elements are inserted into the finite element mesh to model…
Localized deformation patterns are a common motif in morphogenesis and are increasingly finding widespread applications in materials science, for instance as memory devices. Here we describe the emergence of spatially localized deformations…
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…
Four-dimensional twisted group lattices are used as models for space-time structure. Compared to other attempts at space-time deformation, they have two main advantages: They have a physical interpretation and there is no difficulty in…
We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual…
In this work we develop new finite element discretisations of the shear-deformable Reissner--Mindlin plate problem based on the Hellinger-Reissner principle of symmetric stresses. Specifically, we use conforming Hu-Zhang elements to…
We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces.…
A new framework is proposed for analyzing staggered-grid finite difference finite volume methods on unstructured meshes. The new framework employs the concept of external approximation of function spaces, and gauge convergence of numerical…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…