EEG is widely used as an efficient tool in clinical diagnosis and human cognitive studies due to its high temporal resolution. While EEG provides a wealth of physiological information about the brain, the execution of data analysis algorithms is rather time-consuming due to the massive amount of EEG data and the complexity of the algorithms used in the process. A typical example is Independent Component Analysis (ICA), which is a fundamental tool in EEG data analysis. It is widely used for separating unwanted noise artifacts from neural signals and in cortical source localization. In our lab, executing the Infomax ICA algorithm in MATLAB on an 8-core computer for 21 subjects (three 10-minute measurements per subject with 128-channel EEG at 2048 Hz sampling frequency) took 4.5 days to complete. Graphics Processing Units (GPU) are high-performance compute accelerator devices used in most supercomputers providing orders of magnitude higher performance than CPUs, which seem to be ideal for speeding up the time-consuming EEG processing algorithms. However, creating parallel implementations that can run efficiently on supercomputers requires not only significant code refactoring but also exquisite data-to-architecture hierarchy mapping strategies, which can be challenging. We are committed to developing high-performance parallel EEG processing algorithms for supercomputers to provide increased computational performance and shorter execution times for the EEG research community. In the presentation, we will introduce the EEG processing workflow on the Hungarian Komondor supercomputer, as well as the implementation details and performance of the ICA algorithm optimized for GPU and supercomputer architectures.