Related papers: Theoretical Considerations on the Computation of G…
We propose to use a hybridizable discontinuous Galerkin (HDG) method combined with the continuous Galerkin (CG) method to approximate Maxwell's equations. We make two contributions in this paper. First, even though there are many papers…
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…
A new idea for iterative solution of the Helmholtz equation is presented. We show that the iteration which we denote WaveHoltz and which filters the solution to the wave equation with harmonic data evolved over one period, corresponds to a…
We construct a two-parameter family of explicit solutions to the cubic wave equation on $\mathbb{R}^{1+3}$. Depending on the value of the parameters, these solutions either scatter to linear, blow-up in finite time, or exhibit a new type of…
We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…
Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
The minimalist approach in the study of perturbations in fluid dynamics and magnetohydrodynamics involves describing their evolution in the linear regime using a single first-order ordinary differential equation, dubbed principal equation.…
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatio-temporal systems including fluid turbulence is supported by non-chaotic, exactly recurring time-periodic solutions of the…
One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…
We present analytic integral solutions for the second-order induced gravitational waves (GWs). After presenting all the possible second-order source terms, we calculate explicitly the solutions for the GWs induced by the linear scalar and…
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…
We carry out the homogenization of time-harmonic Maxwell's equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. In this setting,…
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
Recently, ParaExp was proposed for the time integration of hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…