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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…
We present a generalization of standard Yee approach for Cauchy problem in electrodynamic simulations on unstructured triangulated mesh. In the paper the whole flow from mesh creation to actual simulation is presented. The proposed…
A systematic analysis of defect textures in facetted nanoparticles with polygonal configurations embedded in a nematic matrix is performed using the Landau-de Gennes model, homeotropic strong anchoring in a square domain with uniform…
Continuum structures of three short-range interacting particles in a deformed external one-body field are investigated. We use the equivalent $d$-method employing non-integer dimension, $d$, in a spherical calculation with a…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We consider the nonlinear Neumann problem for fully nonlinear elliptic PDEs on a quadrant. We establish a comparison theorem for viscosity sub and supersolutions of the nonlinear Neumann problem. The crucial argument in the proof of the…
We propose a novel efficient algorithm to solve Poisson equation in irregular two dimensional domains for electrostatics. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
Modeling of kinetic plasmas using electromagnetic particle in cell methods (EM-PIC) is a problem that is well worn, in that methods developed have been used extensively both understanding physics and exploiting them for device design.…
This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…
This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an…
We develop an exact electrostatic formulation for a finite-length conducting cylindrical shell of finite thickness separating two dielectric media with arbitrary permittivity contrast. The boundary-value problem is reduced to a coupled…
The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate…
We study the inverse electrostatic and elasticity problems associated with Poisson and Navier equations. The uniqueness of solutions of these problems is proved for piecewise constant electric charge and internal stress distributions having…
In this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the polynomial space (Lagrangian on equispaced, Lagrangian on quadrature points (Cubature) and…
We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
The inner surfaces of the electrodes encompassing the gas volume of a Resistive Plate Chamber (RPC) have been found to exhibit asperities with, grossly, three kinds of features. The desired uniform electric field within the gas volume of…