Related papers: A fast multigrid-based electromagnetic eigensolver…
A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a…
This paper describes a trapezoidal quadrature method for the discretization of singular and hypersingular boundary integral operators (BIOs) that arise in solving boundary value problems for elliptic partial differential equations. The…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
Effective magnetic penetration depth and microwave surface impedance are derived for anisotropic layered superconductors in the shape of spheres and long cylinders, where the external magnetic field is applied in the plane of the highly…
Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…
This study concentrates on advancing mathematical and computational methodology for radar tomography imaging in which the unknown volumetric velocity distribution of a wave within a bounded domain is to be reconstructed. Our goal is to…
We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using…
We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…
Fault tolerant algorithms for the numerical approximation of elliptic partial differential equations on modern supercomputers play a more and more important role in the future design of exa-scale enabled iterative solvers. Here, we combine…
Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…
We propose a new a posteriori error estimator for mixed finite element discretizations of the curl-curl problem. This estimator relies on a Prager--Synge inequality, and therefore leads to fully guaranteed constant-free upper bounds on the…
We present methods for analyzing and designing cylindrical electromagnetic metasurfaces with non-circular cross sections based on conformal transformations. It can be difficult to treat surfaces with non-canonical geometries since they…
For time integration of transient eddy current problems commonly implicit time integration methods are used, where in every time step one or several nonlinear systems of equations have to be linearized with the Newton-Raphson method due to…
We study conformal deformation problems on manifolds with boundary which include prescribing $\sigma_k\equiv0$ in the interior. In particular, we prove a Dirichlet principle when the induced metric on the boundary is fixed and an Obata-type…
The miniaturization of optics through the use of two-dimensional metalenses has enabled novel applications in imaging. To date, single-lens imaging remains the most common configuration, in part due to the limited focusing efficiency of…
We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…
We propose EasyControlEdge, adapting an image-generation foundation model to edge detection. In real-world edge detection (e.g., floor-plan walls, satellite roads/buildings, and medical organ boundaries), crispness and data efficiency are…
We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincar\'e-Steklov method. The method takes as input an unstructured, high-order quadrilateral mesh of…
Based on the Riemannian manifold model, we study the asymptotic behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We…
In this work, a novel Eig-PIELM framework is proposed that extends physics-informed extreme learning machine for an efficient and accurate solution of linear eigenvalue problems. The method reformulates the governing differential equations…