We develop a new high order accurate time-discretisation technique for initial value problems. We focus on problems that originate from a space discretisation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new timediscretisation method is global and together with the approximation in space, i...

We prove that the smooth solutions to the Cauchy problem for the three-dimensional compressible barotropic magnetohydrodynamic equations with conserved total mass and finite total energy lose the initial smoothness within a finite time. Further, we show that the same result holds for the solution to the Cauchy problem for the multidimensional compressible NavierStokes system. Moreover, for the ...

We prove a polynomial energy decay for the Maxwell’s equations with Ohm’s law in partially cubic domains with trapped rays. We extend the results of polynomial decay for the scalar damped wave equation in partially rectangular or cubic domain. Our approach have some similitude with the construction of re‡ected gaussian beams. Keywords .Maxwell’s equations; decay estimates; trapped ray. 1 Introd...

The latency insertion method (LIM) is a transient simulation technique for circuits and is based on a finite-difference formulation, like the well-known finite-difference time-domain (FDTD) method for solving Maxwells equations. The LIM, like the FDTD method, is only conditionally stable resulting in an upper bound for the time step of the transient simulation. This bound on the time step is a ...

To reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static Maxwells equations in the frequency domain. We assume a coarse mesh nested into a fine mesh, which accurately discretizes the setting. For each coarse cell, we independ...