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In the field of connectomics, neuroscientists seek to identify cortical connectivity comprehensively. Neuronal boundary detection from the Electron Microscopy (EM) images is often done to assist the automatic reconstruction of neuronal…
The purpose of this work is twofold: (a) To present the theoretical formulation of a 3D acoustic propagation model based on a Boundary Element Method (BEM), which uses a half-space Green function in place of the more conventional free-space…
We present two approximation methods for computing eigenfrequencies and eigenmodes of large-scale nonlinear eigenvalue problems resulting from boundary element method (BEM) solutions of some types of acoustic eigenvalue problems in…
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes with and without shape regularity. For shape-regular meshes,…
Brain extraction is a critical preprocessing step in various neuroimaging studies, particularly enabling accurate separation of brain from non-brain tissue and segmentation of relevant within-brain tissue compartments and structures using…
We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations…
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…
This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with…
Accurately monitoring cognitive load in real time is critical for Brain-Computer Interfaces (BCIs) that adapt to user engagement and support personalized learning. Electroencephalography (EEG) offers a non-invasive, cost-effective modality…
We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method…
A novel 3D micromechanical Finite Element Model (FEM) has been developed to depict the Poynting effect in bi-phasic Representative volume element (RVE) with axons embedded in surrounding extra-cellular matrix (ECM) for simulating the brain…
Many applications like subseismic fault modeling, fractured reservoir modeling and interpretation/validation of fault connectivity involve the solution to an elliptic boundary value problem in a background medium perturbed by the presence…
We present a hybrid numerical-asymptotic (HNA) boundary element method (BEM) for high frequency scattering by two-dimensional screens and apertures, whose computational cost to achieve any prescribed accuracy remains bounded with increasing…
Electroencephalography (EEG) is a non-invasive technique for recording brain activity, widely used in brain-computer interfaces, clinic, and healthcare. Traditional EEG deep models typically focus on specific dataset and task, limiting…
We present a boundary-spheropolygon element method (BSEM), that combines the boundary integral method (BIM) and the spheropolygon-based discrete element method (SEM). The interaction between particles is simulated via the SEM, and the…
Engineering structures are increasingly designed using numerical optimisation. However, traditional optimisation methods can be challenging with multiple objectives and many parameters. In machine learning, stable training of artificial…
This paper presents a novel approach called the boundary integrated neural networks (BINNs) for analyzing acoustic radiation and scattering. The method introduces fundamental solutions of the time-harmonic wave equation to encode the…
The Fisher-KPP partial differential equation has been employed in science to model various biological, chemical, and thermal phenomena. Time fractional extensions of Fisher's equation have also appeared in the literature, aiming to model…
We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution. As the spatial discretization of the resulting time-domain boundary integral…
Electromagnetic (EM) imaging is an important tool for non-invasive sensing with low-cost and portable devices. One emerging application is EM stroke imaging, which enables early diagnosis and continuous monitoring of brain strokes.…