The epitaxial layer structures for blue InGaN light emitting diodes have been optimized for high brightness applications with the output power levels exceeding 1000 $W/cm^2$ by using a self-consistent finite element method. The light-current-voltage relationship has been directly estimated from the multiband Hamiltonian for wurtzite crystals. To analyze the efficiency droop at high injection levels, the major nonradiative recombination processes and carrier spillover have also been taken into account. The wall-plug efficiency at high injection levels up to several thousand $A/cm^2$ has been successfully evaluated for various epilayer structures facilitating optimization of the epitaxial structures for desired output power levels.