First and foremost, I thank my brother, Abhinav, for encouraging me to come to the US for graduate studies. I am grateful to my advisor, Clint Dawson, who believed in me and took me under his guidance in my first semester, without which I would have had to face a lot of financial hardships. I am deeply thankful for his excellent mentorship, considerate nature, continued support, and for funding me throughout the last three years. I thank the Engineering Research and Development Center (ERDC),

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... Army Corps of Engineers, for their generous funding for this project, and Corey Trahan, Lucas Pettey, and Matthew Farthing from ERDC for helping me in critical aspects of the project, without which this work could not have been completed. I am indebted to the many professors and teachers at UT Austin, IIT Kharagpur, M. Prakash Academy, and Bhaskaracharya Pratishthana who have helped me build a strong theoretical foundation. In particular, I thank my mathematics teachers M. Prakash and Leszek Demkowicz for being an inspiration. They imbibed in me, a deep respect for mathematics through their fiercely passionate teaching, and their rigorous proofs have shaped more than just my mathematical thinking. I look up to them as role models for teachers.