1. A computer-implemented 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 computer-implemented method comprising: defining a plurality of island data sets from an initial data set defining a physics based problem, wherein each one of the plurality of island data sets 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, wherein each one of the plurality of data portions comprises data associated with an object or a constraint characterized in the initial data set; transferring each one of the plurality of data portions to a corresponding one of the plurality of execution units; processing each one of the plurality of data portions in parallel to produce output data that solves the at least one corresponding LCP; and transmitting the output data to a processing unit to animate a physics-based interaction of objects.