INTRODUCTION OF HUYGENS ABSORBING BOUNDARY CONDITIONS INTO LOD METHOD FOR FDTD

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Abstract

The finite dierence time domain (FDTD) method is based on Yee algorithmwhich employs a very simple way to discretize maxwell equations. Any structureof interest is decomposed into cubic unit cells called voxels and the size of thearea that can be simulated is limited by computer resources.LOD method is an alternative method for the application of the FDTDmethod and it is by design implicit in nature. Implicit methods were introducedto overcome the time step limation inherent in the conventional explicit methods.This implies that a larger time step can be used for the computational domainwhen compared to the normal explicit FDTD method. This results in the speedup of the overall simulation time, highly desirable when electromagnetic fieldsare to be determined for a large computational space or whenever objects havingvery fine details are to be modeled.However during simulation as the wave propagates outward, it will eventuallycome to the edge of the allowable space, which is dictated by how the arrayshave been dimensioned in the program. If nothing were done to address this,unpredictable reflections would be generated that will go back inward. Thus,there would be no way to determine which is the real wave and which is thereflected noise.This is the reason that Absorbing Boundary Conditions (ABCs) have beenan issue for as long as FDTD has been used. In using these absorbing boundaryconditions the objective is to achieve an ideal ABC which absorbs all the outgoingwaves and produces no reflection, along with catering for all incident angles of thewaves propagating towards it. The idea is to simulate the open space in such away that the waves appear to propagate indefinitely. Huygens Absorbing boundaryconditions (HABC) are proactive in both in its design and implementation. Theyincorporate the idea of a hypothetical "Huygens surface" separating the two connectingfield regions such that any field propagating towards the HABC can becanceled by generating a counter field that is equal in magnitude and opposite indirection to its original counterpart.

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Keyword(s)

FDTD, LOD-FDTD, HABC

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