As the demand for transportation through waterways continues to rise, the number of vessels plying the waters has correspondingly increased. This has resulted in a greater number of accidents and collisions between ships, some of which lead to significant loss of life and financial losses. Research has shown that human error is a major factor responsible for such incidents. The maritime industry is constantly exploring newer approaches to autonomy to mitigate this issue. This study presents the use of novel Artificial Potential Fields (APFs) to perform obstacle and collision avoidance in marine environments. This study highlights the advantage of harmonic functions over traditional functions in modeling potential fields. With a modification, the method is extended to effectively avoid dynamic obstacles while adhering to COLREGs. Improved performance is observed as compared to the traditional potential fields and also against the popular velocity obstacle approach. A comprehensive statistical analysis is also performed through Monte Carlo simulations in different congested environments that emulate real traffic conditions to demonstrate robustness of the approach.