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Source localization based on electroencephalography (EEG) has become a widely used neuroimagining technique. However its precision has been shown to be very dependent on how accurately the brain, head and scalp can be electrically modeled…
The divergence condition is reformulated in the scaled boundary coordinates so as to prevent the spurious solutions in the finite element formulation.
We analyse a numerical method for the coupled system of the eddy current equations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in a bounded domain. The unbounded domain is discretised by means of…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
The aim of this paper is to propose a novel methodology to deal with micro-structural boundary conditions for the analysis of granular materials. The response of the granular assembly is modelled through the discrete element method (DEM),…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
The mixed spectral element method (MSEM) is applied to solve the waveguide problem with Bloch periodic boundary condition (BPBC). Based on the BPBC for the original Helmholtz equation and the periodic boundary condition (PBC) for the…
We derive and analyze a fully computable discrete scheme for fractional partial differential equations posed on the full space $\mathbb{R}^d$ . Based on a reformulation using the well-known Caffarelli-Silvestre extension, we study a…
Phase transformations and crystallographic defects are two essential tools to drive innovations in materials. Bulk materials design via tuning chemical compositions has been systematized using phase diagrams. We show here that the same…
A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…
The electrostatic modeling of conductors is a fundamental challenge in various applications, including the prediction of parasitic effects in electrical interconnects, the design of biasing networks, and the modeling of biological,…
Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field expansion of these long-range fields identifies low-rank…
In experimental physics, it is essential to understand electromagnetic (EM) wave scattering across EM spectrum, from radio waves to X-rays, and is pivotal in driving photonics innovations. Recent advancements have uncovered phenomena like…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
A Novel Scaled boundary finite element method, initially developed in Civil Engineering, is reformulated for solving boundary value problems in computational electromagnetics.
The objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3D configurations involving arbitrary beam-to-beam orientations. It is shown in a…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…