Towards higher accuracy gravitational waveforms from large mass ratio and eccentric binaries*

Gravitational wave detection requires waveform libraries from highly accurate numerical simulations in full general relativity.  Current libraries are largely sufficient for today's detectors, but future detectors such as the space based LISA mission will be sensitive to new wavebands, higher signal-to-noise ratios, a larger variety of sources and will require yet higher accuracy waveforms.  There will be a growing need to be able to better model challenging systems including binary black holes with large mass ratios, high spins and very eccentric orbits.  We describe progress in the development of the numerical code, Dendro-GR, as applied to some of these complications as well to binary systems in alternative gravity theories.