A mathematical model and computational results are presented for wind driven ocean modeling based on the Spectral Ocean Element Method (SEOM). The method features advanced algorithms, based on h-p type finite element methods, allowing accurate representation of complex coastline and oceanic bathymetry, variable lateral resolution, and high order solution of the three dimensional oceanic equations of motion. SEOM is robust, accurate over a many year simulation, and scales extremely well on a wide variety of parallel computers including traditional supercomputers and clusters. Acceleration techniques will be defined that lead to significant speedups.