We develop a new high order accurate time-integration technique for initial value problems. We focus on problems that originate from a space approximation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the timedomain. The new time-integration method is global, high order accurate, unconditionally stable and toget...

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equati...

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...

It is explained how FEMLAB / COMSOL Multiphysics can be configured to calculate, the frequencies, electromagneticfield patterns, mode volumes, filling factors, radiation losses ... of the whispering-gallery modes of axisymmetric microresonators. The method exploits COMSOL’s ability to accept the definition of solutions to Maxwells equations in so-called ‘weak form’. As no transverse approximati...

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...

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 ...

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...