1. A method of operating a Linear Complementarity Problem (LCP) solver comprising a plurality of Island Processing Engines (IPEs) arranged in parallel, wherein each one of the plurality of IPEs further comprises a plurality of execution units arranged in parallel, the method comprising: defining a plurality island data sets from an initial data set defining a physics-based problem, wherein each one of the plurality of island data set defines at least one corresponding LCP; transferring each one of the plurality of island data sets to a corresponding one of the plurality of IPEs; and, within each IPE, defining a plurality of data portions from the island data set; transferring each one of the plurality of data portions to a corresponding one of the plurality of execution units; and resolving the plurality of data portions in parallel.