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The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the…
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…
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization…
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…
In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. Micro-mechanics studies are commonly performed using the…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's…
Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic…
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…
Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf…
An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lam\'e-Navier equations for…
This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open…
The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…
Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…
The Boundary Element Method (BEM) is implemented using piecewise linear elements to solve the two-dimensional Dirichlet problem for Laplace's equation posed on a disk. A benefit of the BEM as opposed to many other numerical solution…
Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures with cross-sections of the order of microns ($\mu m$) and lengths of the order of tens or hundreds of microns. These structures are often plates or array of…
A coupled boundary spectral element method (BSEM) and spectral element method (SEM) formulation for the propagation of small-amplitude water waves over variable bathymetries is presented in this work. The wave model is based on the…
This work illustrates the possibility to apply the Fast Fourier Transformation to obtain the integrals of the Boundary Element Method (BEM) on arbitrary shapes. The procedure is inspired by the technique used with great success within the…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
We formulate a new atomistic/continuum (a/c) coupling scheme that employs the boundary element method (BEM) to obtain an improved far-field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect…