Time Domain Scheme Based on Positive Sampling Basis Associated with Coifman Scaling Function

In order to simplify the Coifman scaling function based S-MRTD scheme for electromagnetic field problems, we develop the update formulations based on the positive sampling basis. We show the approximate interpolation property of the positive sampling basis associated with Coifman scaling function exactly. That makes the implementation of boundary condition, inhomogeneous media interface, and the total field computation simple. Actually the time domain scheme introduced in this paper has the merits of Coifman scaling function based S-MRTD and is simpler to formulate than S-MRTD. The some numerical results are provided to validate this work. The numerical results also validate the sampling property of Coifman scaling function.