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The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
The boundary element method (BEM) enables the efficient electromagnetic modelling of lossy conductors with a surface-based discretization. Existing BEM techniques for conductor modelling require either expensive dual basis functions or the…
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…
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
Physics has played a fundamental role in medicine sciences, specially in imaging diagnostic. Currently, image reconstruction techniques are already taught in Physics courses and there is a growing interest in new potential applications. The…
Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what appears to be the first application of the boundary element method (BEM) where each BEM basis…
Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and important conductive features such as anisotropic…
Source analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction…
Electroencephalography (EEG) foundation models hold significant promise for universal Brain-Computer Interfaces (BCIs). However, existing approaches often rely on end-to-end fine-tuning and exhibit limited efficacy under frozen-probing…
In order to simulate elastic wave propagation in a complex structure with inhomogeneous media, we often need to obtain the propagating eigenmodes of an elastic waveguide. As the waveguide is assumed uniform in one direction, the original…
Electrocorticography (ECoG) or intracranial electroencephalography (iEEG) monitors electric potential directly on the surface of the brain and can be used to inform treatment planning for epilepsy surgery when paired with numerical…
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…
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…
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 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…
Electroencephalography (EEG) and Magnetoencephalography (MEG) are pivotal in understanding brain activity but are limited by their poor spatial resolution. EEG/MEG source imaging (ESI) infers the high-resolution electric field distribution…
This paper presents a new fast multipole boundary element method (FM-BEM) for solving the acoustic transmission problems in 2D periodic media. We divide the periodic media into many fundamental blocks, and then construct the boundary…
The finite element method (FEM) and the boundary element method (BEM) can numerically solve the Helmholtz system for acoustic wave propagation. When an object with heterogeneous wave speed or density is embedded in an unbounded exterior…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…