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We have extended the Multiscale Hybrid-Mixed finite element method (MHM for short) for dealing with the system of time-domain Maxwell equations modeling electromagnetic wave propagation in heterogeneous media. The MHM method arises from the decomposition of the exact electric and magnetic fields in terms of the solutions of locally independent Maxwell problems tied together through an one-field formulation on top of a coarse mesh skeleton. The multiscale basis functions, which are responsible for upscaling, are driven by local Maxwell problems with tangential component of the magnetic field prescribed on the faces. A high order Discontinuous Galerkin method in space combined with a second order explicit Leap-Frog scheme in time discretizes the local problems. This makes the MHM method effective and yields a staggered algorithm within a divide and conquer framework. The MHM has been formulated for the system of time-domain Maxwell equations in the three-dimensional case. Preliminary numerical results have been obtained in the two-dimensional case.

A MHM formulation has also been proposed and studied for the system of time-domain elastodynamic equations in mixed (velocity-stress) form. Preliminary numerical results have been obtained in the two-dimensional case.

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MHM for the system of time-domain elastodynamic equations

A MHM formulation has also been proposed and studied for the system of time-domain elastodynamic equations in mixed (velocity-stress) form. Preliminary numerical results have been obtained in the two-dimensional case.

For more details: slides of Diego Paredes presentation at WONAPDE 2016

For more details: slides of Diego Paredes presentation at Wonapde 2016

For more details: [http://www-sop.inria.fr/nachos/slides/Wonapde_2016-DParedes.pdf | slides of Diego Paredes presentation at Wonapde 2016]

Nanowaveguide problem: coarse quandrangular meshes

DGTD method with 589,824 DoF (left) and 4,608 DoF (right)

MHM-DGTD method with 9,216 DoF

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MHM for the system of time-domain Maxwell equations

This work extends the Multiscale Hybrid-Mixed finite element method (MHM for short) for the two- and three-dimensional Maxwell equations in time-domain with heterogeneous media. The MHM method arises from the decomposition of the exact electric and magnetic fields in terms of the solutions of locally independent Maxwell problems tied together through an one-field formulation on top of a coarse mesh skeleton. The multiscale basis functions, which are responsible for upscaling, are driven by local Maxwell problems with tangential component of the magnetic field prescribed on the faces. A high order Discontinuous Galerkin method in space combined with a second order explicit Leap-Frog scheme in time discretizes the local problems. This makes the MHM method effective and yields a staggered algorithm within a divide and conquer framework.

MHM for teh system of time-domain Maxwell equations

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