Light trapping via plasmonic nanostructures has emerged as a novel method for guiding and confining light in nanoscale photovoltaics. In our design, the metal nanostructures are built directly into the back contact of an a-Si:H device, such that the large scattering cross section of the plasmonic particles couples incident sunlight into localized and guided modes overlapping with the a-Si:H layer. This enables the use of ultrathin absorbing layers, which are attractive for cost and stability as well as higher open circuit voltages. Here we show that electromagnetic simulation can be used to accurately simulate nanopatterned solar cells, including for randomly textured and non-periodic patterns. We also show that non-periodic arrangements of plasmonic nanostructures are promising for enhancing photocurrent in ultrathin film a-Si:H solar cells.