Real time simulation is a critical supplement to in-water testing for the assessment of naval system performance. Limitations exist on the number of independent runs, on geographical locations in which in-water tests can be performed, and on the amount of control experimenters possess over the test environment. Many systems have critical time-sensitive functionality (e.g., acoustic homing) which constrains the ability to produce realistic time series for injection; but a reduced fidelity solution can still be of use. Graphics hardware (GPU) has become a significant computing platform in its own right. Its application requires a mapping of the propagation algorithm to the GPU computing paradigm and careful tweaking to squeeze out maximum performance. We will look at taking from theory just what we need to hand-tune code for a GPU + CPU computing platform, and the limitations of a high speed, range dependent, eigenray code. We also consider a related approach that uses the resulting eigenrays to initialize an iterative method which updates the eigenray solution as the source and receiver update their relative positions. [Work funded by the Office of the Secretary of Defense, Test Resource Management Center's Resource Enhancement Project element of the Central Test and Evaluation Investment Program.]