Related papers: Boundary element methods for the magnetic field in…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
The Landau--Lifshitz--Baryakhtar (LLBar) and the Landau--Lifshitz--Bloch (LLBloch) equations are nonlinear vector-valued PDEs which arise in the theory of micromagnetics to describe the dynamics of magnetic spin field in a ferromagnet at…
This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region,…
In recent years there have been tremendous advances in the theoretical understanding of boundary integral equations for Maxwell problems. In particular, stable dual pairing of discretisation spaces have been developed that allow robust…
We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are…
Implicit-solvent models are widely used to study the electrostatics in dissolved biomolecules, which are parameterized using force fields. Standard force fields treat the charge distribution with point charges, however, other force fields…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
The Fokker-Planck equation derived by Brown for the probability density function of the orientation of the magnetic moment of single domain particles is one of the basic equations in the theory of superparamagnetism. Usually this equation…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
This article concerns the weak Galerkin mixed finite element method (WG-MFEM) for second order elliptic equations on 2D domains with curved boundary. The Neumann boundary condition is considered since it becomes the essential boundary…
A novel boundary element formulation for solving problems involving eddy currents in the thin skin depth approximation is developed. It is assumed that the time-harmonic magnetic field outside the scatterers can be described using the…
The aim of this work is to present the details of the finite element approach we developed for solving the Landau-Lifschitz-Gilbert equations in order to be able to treat problems involving complex geometries. There are several…
This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic poroelasticity in two dimensions. The main contribution of this work consists of two aspescts: the…
We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…
We consider three common mathematical models for time-harmonic high frequency scattering: the Helmholtz equation in two and three spatial dimensions, a transverse magnetic problem in two dimensions, and Maxwell's equation in three…