Related papers: Space-Time Spectral Collocation Tensor-Network App…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of…
We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces for the spatial and velocity domains, respectively, to…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…
We prove that the Maxwell-Schr\"odinger system in $\R^{3+1}$ is globally well-posed in the energy space. The key element of the proof is to obtain a short time wave packet parametrix for the magnetic Schr\"odinger equation, which leads to…
We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and…
We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…
A discrete analysis of the phase and dissipation errors of an explicit, semi-Lagrangian spectral element method is performed. The semi-Lagrangian method advects the Lagrange interpolant according the Lagrangian form of the transport…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
In this paper we explicitly demonstrate separability of the Maxwell equations in a wide class of higher-dimensional metrics which include the Kerr-NUT-(A)dS solution as a special case. Namely, we prove such separability for the most general…
We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with…
We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $\Omega\subset\mathbb{R}^2$, possibly occupied by piecewise homogeneous media with different propagation speeds.…
This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder.…
Electromagnetic particle-in-cell (PIC) codes are widely used to perform computer simulations of a variety of physical systems, including fusion plasmas, astrophysical plasmas, plasma wakefield particle accelerators, and secondary photon…
In this paper we solve $m$-parameter eigenvalue problems ($m$EPs), with $m$ any natural number by representing the problem using Tensor-Trains (TT) and designing a method based on this format. $m$EPs typically arise when separation of…
The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary…
This paper presents an approach for obtaining approximate solutions to quasi-variational inequalities in a real Hilbert space by modifying Tseng's scheme, which was originally designed for variational inequalities. The study explores the…
A framework for Chebyshev spectral collocation methods for the numerical solution of functional and delay differential equations (FDEs and DDEs) is described. The framework combines interpolation via the barycentric resampling matrix with a…
We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…