Related papers: A boundary integral equation method for the comple…
The electron cyclotron emission (ECE) diagnostics suite at ITER utilizes a front-end quasi-optical (QO) system whose design is fundamentally constrained by a field-stop concept. The field-stop defines the Gaussian beam variation throughout…
In electrical impedance tomography, we aim to solve the conductivity within a target body through electrical measurements made on the surface of the target. This inverse conductivity problem is severely ill-posed, especially in real…
Let $(\Omega,g)$ be a smooth compact two-dimensional Riemannian manifold with boundary, $\Lambda_g: f\mapsto \partial_\nu u|_{\partial\Omega}$ its DN map, where $u$ obeys $\Delta_g u=0$ in $\Omega$ and $u|_{\partial \Omega}=f$. The Electric…
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
In this paper we develop an analytical framework for the study of electrochemical impedance of mixed ionic and electronic conductors (MIEC). The framework is based on first-principles and it features the coupling of electrochemical…
To solve boundary integral equations for potential problems using collocation Boundary Element Method (BEM) on smooth curved 3D geometries, an analytical singularity extraction technique is employed. By adopting the isoparametric approach,…
Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its severe ill-posedness renders direct operator learning with…
This paper proposes a single-domain dual-reciprocity inclusion-based boundary element method (DR-iBEM) for a three-dimensional fully bonded bi-layered composite embedded with ellipsoidal inhomogeneities under transient/harmonic thermal…
This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the…
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
In this work, the inverse problem of quantitative thermoacoustic tomography is studied. In quantitative thermoacoustic tomography, dielectric parameters of an imaged target are estimated from an absorbed energy density induced by an…
We study the complete electrode model boundary condition for second order elliptic PDE. A specific case of this is the PDE describing the electrostatic potential for a conductive body into which current is injected through electrodes that…
We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary integral equation method is developed for efficient numerical determination of…
We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the…
The dynamics of the electrons for a molecule in solution is coupled to the dynamics of its polarizable environment, i.e., the solvent. To theoretically investigate such electronic dynamics, we have recently developed equations of motion…