Related papers: A boundary integral equation method for the comple…
The presented paper concentrates on the boundary element method (BEM) for the heat equation in three spatial dimensions. In particular, we deal with tensor product space-time meshes allowing for quadrature schemes analytic in time and…
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…
The electron and photon transport processes in spectroscopy techniques described by the invariant embedding theory is here revisited. We report a convergence method to obtain closed analytical solutions to the 3D integro-differential…
Electrical impedance tomography (EIT) plays a crucial role in non-invasive imaging, with both medical and industrial applications. In this paper, we present three data-driven reconstruction methods for EIT imaging. These three approaches…
Reconstructing complex 3D interfaces from indirect measurements remains a grand challenge in scientific computing, particularly for ill-posed inverse problems like Electrical Impedance Tomography (EIT). Traditional shape optimization…
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…
This work presents a generalized boundary integral method for elliptic equations on surfaces, encompassing both boundary value and interface problems. The method is kernel-free, implying that the explicit analytical expression of the kernel…
We present several versions of Regularized Combined Field Integral Equation (CFIER) formulations for the solution of three dimensional frequency domain electromagnetic scattering problems with Perfectly Electric Conducting (PEC) boundary…
The previously reported neBEM solver has been used to solve electrostatic problems having three-dimensional edges and corners in the physical domain. Both rectangular and triangular elements have been used to discretize the geometries under…
Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
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…
We apply the hp-version of the boundary element method (BEM) for the numerical solution of the electric field integral equation (EFIE) on a Lipschitz polyhedral surface G. The underlying meshes are supposed to be quasi-uniform…
This paper proposes a fast time-domain boundary element method (TDBEM) to solve three-dimensional transient electromagnetic scattering problems regarding perfectly electric conductors in the classical marching-on-in-time manner. The…
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second…
This paper devotes to developing novel boundary integral equation (BIE) solvers for the problem of thermoelastic scattering by open-arcs with four different boundary conditions in two dimensions. The proposed methodology is inspired by the…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
Theoretically, the electric field becomes infinite at corners of two and three dimensions and edges of three dimensions. Conventional finite-element and boundary element methods do not yield satisfactory results at close proximity to these…