Ayomide Olumide-Attah
MIT Department:
Electrical Engineering and Computer Science
Faculty Mentor:
Justin Solomon
Undergraduate Institution:
Fisk University
Biography
Ayomide Olumide-Attah is a rising junior at Fisk University, double majoring in mathematics and computer science. He is a budding computer scientist and mathematician with formidable competitive problem-solving and programming skills as well as interests spanning data science, AI/ML, and quantum computing. He’s explored these interests through building innovative projects, participating in diverse programs, and competing in hackathons. He also has extensive experience participating in competition-level math contests, which have enabled him to hone formal reasoning, problem-solving, and deduction skills. Beyond his experiences, he’s an extremely curious individual who has always sought to answer questions and solve problems, which has led him to learn more about the world. His goal is to conduct innovative research at the intersection of mathematics and computer science and develop innovative solutions to the world’s hardest problems, one line of code at a time.
A Sparse Multigrid Hierarchy Construction for Linear Systems
Ayomide Olumide-Attah1 and Dr. Justin Solomon2
1Department of Mathematics and Computer Science, Fisk University
2Electrical Engineering and Computer Science, Massachusetts Institute of Technology
Multigrid (MG) methods are widely considered a powerful class for solving large linear systems of equations that arise in many application domains, including the discretization of partial differential equations (PDEs), computing surface parameterizations, fluid simulations, and many others. These methods solve linear systems by restricting them to smaller domains, solving them in these domains, and extending the resulting solution to the larger original space. However, as observed in [Liu et al., 2021], the resulting matrices become much denser than the corresponding Laplacians as one descends the hierarchy, undermining the efficiency of a multigrid implementation. For our project, we propose a multigrid hierarchy construction with improved sparsity properties, and we demonstrate its efficiency by implementing a multigrid solver that implements our construction. Our method builds on the approach proposed by [Wiersma et al., 2023] by employing strategies to improve the sparsity of the level matrices, and we demonstrate that the best results are obtained when the level matrices are modified so that the smallest nonzero entries are removed. We hope our work will lead to more efficient multigrid solvers, which can offer significant speedups in solving linear systems.
