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This paper presents techniques that can be used with the Haar MRTD method for time and space adaptive gridding. For the first time, absolute and relative thresholds for wavelet functions are used to change the resolution as a function of time and space. This technique is applied to the composite cell Haar MRTD scheme, which is capable of representing multiple conductors (and other subcell elements) per cell. Using this technique, complex structures can be represented more efficiently than with fixed grid techniques. Included is a comparison of the Haar method with FDTD, as well as the advantages of the Haar time-space adaptive method (10-40% economy in memory and execution time) with fixed grid FDTD and MRTD techniques. A dual patch antenna structure suitable for RF front ends in modern multilayer substrates is presented; the final version will also include an LC CPW structure suitable for metamaterial applications.