Related papers: A Space-Time Approach for the Time-Domain Simulati…
The work aims effective and low-dimensional systems. Some different contexts involving gravitational and electromagnetic interactions are investigated. The electromagnetic one approaches bosonic and fermionic Effective Quantum Field…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…
High-performance computing trends towards many-core systems are expected to continue over the next decade. As a result, parallel-in-time methods, mathematical formulations which exploit additional degrees of parallelism in the time…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
The Darwin field model addresses an approximation to Maxwell's equations where radiation effects are neglected. It allows to describe general quasistatic electromagnetic field phenomena including inductive, resistive and capacitive effects.…
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discretizations based on Runge-Kutta convolution quadrature are…
We present results of 3D numerical simulations using a finite difference code featuring fixed mesh refinement (FMR), in which a subset of the computational domain is refined in space and time. We apply this code to a series of test cases…
This article introduces a novel approach for broken-FEEC (Finite Element Exterior Calculus), extending its application to locally refined spline spaces with non-matching interfaces. Traditional broken-FEEC allows for discontinuous…
We propose and analyze a mixed finite element method for the spatial approximation of a time-fractional Fokker--Planck equation in a convex polyhedral domain, where the given driving force is a function of space. Taking into account the…
We consider nearly-integrable Hamiltonian systems defined over a non-resonant domain. In the neighborhood of resonances, we use Nekhoroshev-like estimates to provide effective stability bounds for the action variables over long time. The…
With the concept of "discrete space-time" the space-time continuum is resolved into discrete points at the scale of the Planck length. We postulate with the "principle of the fermionic projector" that physical equations must be formulated…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…
Maxwell equations generally explain the propagation of light through an arbitrary medium by using wave mechanics. However, scientific evidence since Newton suggest a discrete interpretation of light more generally explains its nature. This…
This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same…