Related papers: Domain Decomposition Framework for Maxwell Finite …
In this article, we present a new unified finite element method (UFEM) for simulation of general Fluid-Structure interaction (FSI) which has the same generality and robustness as monolithic methods but is significantly more computationally…
This article introduces a novel approach for broken-FEEC (Finite Element Exterior Calculus), extending its application to locally refined spline spaces with non-matching interfaces. Traditional broken-FEEC allows for discontinuous…
We propose a boundary element method for the accurate solution of the cell-by-cell bidomain model of electrophysiology. The cell-by-cell model, also called Extracellular-Membrane-Intracellular (EMI) model, is a system of reaction-diffusion…
The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
We present and analyze a new space-time finite element method for the solution of neural field equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
Numerical simulation of nonlinear elastic wave propagation in solids with cracks is indispensable for decoding the complicated mechanisms associated with the nonlinear ultrasonic techniques in Non-Destructive Testing (NDT). Here, we…
A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…
This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…
This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
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 computational efficiency of the Finite-Difference Time-Domain (FDTD) method can be significantly reduced by the presence of complex objects with fine features. Small geometrical details impose a fine mesh and a reduced time step,…
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…
We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\boldsymbol{y}) =…
We survey finite element methods for approximating the time harmonic Maxwell equations. We concentrate on comparing error estimates for problems with spatially varying coefficients. For the conforming edge finite element methods, such…
We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it…
A coupled BEM/FEM formulation for the transient interaction between an acoustic field and a piezoelectric scatterer is proposed. The scattered part of the acoustic wave is represented in terms of retarded layer potentials while the elastic…
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…