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Conventionally, piecewise polynomials have been used in the boundary elements method (BEM) to approximate unknown boundary values. Since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for…
We study a symmetric BEM-FEM coupling scheme for the scattering of transient acoustic waves by bounded inhomogeneous anisotropic obstacles in a homogeneous field. An incident wave in free space interacts with the obstacles and produces a…
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…
We present a novel solution to the problem of localizing magnetoencephalography (MEG) and electroencephalography (EEG) brain signals. The solution is sequential and iterative, and is based on minimizing the least-squares criterion by the…
High-intensity focused ultrasound (HIFU) is a promising treatment modality for the non-invasive ablation of pathogenic tissue in many organs. Optimal treatment planning strategies based on high-performance computing methods are expected to…
Objective: The subtraction approach is known for being a theoretically-rigorous and accurate technique for solving the forward problem in electroencephalography by means of the finite element method. One key aspect of this approach consists…
This study compares the Boundary Element Method (BEM) and Physics-Informed Neural Networks (PINNs) for solving the two-dimensional Helmholtz equation in wave scattering problems. The objective is to evaluate the performance of both methods…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
Data fusion refers to the joint analysis of multiple datasets which provide complementary views of the same task. In this preprint, the problem of jointly analyzing electroencephalography (EEG) and functional Magnetic Resonance Imaging…
The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…
We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, where the boundary condition is given by the complete electrode…
Electroencephalograph (EEG) is a crucial tool for studying brain activity. Recently, self-supervised learning methods leveraging large unlabeled datasets have emerged as a potential solution to the scarcity of widely available annotated EEG…
Invasive intracranial electroencephalography (iEEG) or electrocorticography (ECoG) measures electric potential directly on the surface of the brain and can be used to inform treatment planning for epilepsy surgery. Combined with numerical…
Electroencephalography (EEG) source imaging aims to reconstruct the spatial distribution of neural activity within the brain from non-invasive scalp measurements. This inverse problem is severely ill-posed due to the low spatial resolution…
Electroencephalography (EEG) is a non-invasive technique for recording brain electrical activity, widely used in brain-computer interface (BCI) and healthcare. Recent EEG foundation models trained on large-scale datasets have shown improved…
In this work we investigate the numerical identification of the diffusion coefficient in elliptic and parabolic problems using neural networks. The numerical scheme is based on the standard output least-squares formulation where the…
The spatial covariance matrix has been considered to be significant for beamformers. Standing upon the intersection of traditional beamformers and deep neural networks, we propose a causal neural beamformer paradigm called Embedding and…
The incidence of Alzheimer's disease (AD) and other forms of dementia is increasing in most western countries. For a precise and early diagnosis, several examination modalities exist, among them single-photon emission computed tomography…
A data-driven surrogate framework to accelerate particle-resolved modelling of quasi-dilute suspensions of rigid, non-spherical particles in Stokes flow is introduced. A regularized-Stokeslet boundary element method (BEM) is implemented to…
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…