The National Science Foundation (NSF) has awarded a $100,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to Michigan Technological University. The grant will fund the development of novel finite element methods for solving nonlinear eigenvalue problems, which have important applications in science and engineering. The project focuses on recasting these problems as eigenvalue problems of holomorphic Fredholm operator functions, and developing effective numerical methods to compute the eigenvalues and eigenvectors. Two key model problems will be studied: band structure calculations for dispersive photonic crystals and transmission eigenvalue problems for anisotropic media. The project aims to advance finite element theory and enable scientists and engineers to more effectively compute nonlinear eigenvalue problems. Both graduate and undergraduate students are expected to receive training in analysis, modeling, and programming through this award, which runs from September 1, 2023 to August 31, 2026.
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