Discrete Singular Convolution and Symplectic Operators

A nontrivial weakness of the (2, 4) and (4, 4) schemes is the incomplete modeling of PEC structures or dissimilar media configurations, whenever the stencils of the discrete derivatives have to surpass the interface. Typically, such realizations are prone to instabilities, especially in 

Let us first concentrate on the DSC method and assume that T is a distribution and fix) an element of the test-function space. Then, the singular convolution of f jx) is denoted as 

8a (x — x 0 the DSC delta kernel, and 3 the bandwidth of possible points. There is a variety of delta kernels available in mathematical analysis. According to [13], the best choice is the LK kernel due to its optimal bandwidth for a preset level of accuracy, defined by 

The product operator of (6.8) is usually obtained by a recurrence method, like those depicted in [15]. As DSC kernels can be either symmetric or antisymmetric, they need f values that 

The next part of the method refers to temporal integration that is conducted by a sym-plectic integrator approach. To start with, one has to express the lossy version of Maxwell s equations in matrix form as 

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