Federal Project Grant Award Summary

The California Institute of Technology received a $450,000 Project Grant from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049) awarded July 1, 2026, with a completion date of June 30, 2029. The award supports development of accurate and efficient mathematical formulations and fast computational algorithms for solving partial differential equations (PDEs) and wave phenomena in geometrically complex, high-frequency regimes. The research focuses on creating new PDE solvers in frequency, time, and hybrid frequency-time domains, with particular emphasis on problems involving geometric singularities such as edges and corners, as well as fractional Laplacian equations.

The project deliverables include foundational computational tools and methodologies designed to improve the speed, reliability, and realism of scientific simulations across multiple disciplines. The resulting capabilities are expected to support high-fidelity predictive models for wave propagation, transport phenomena, and multiscale physical interactions, generating simulation data suitable for training and validating artificial intelligence-based methods. Beyond fundamental computational advancement, the work has direct applications in biomedical imaging and ultrasound technologies, materials science and microelectronics design, quantum device technologies, and manufacturing optimization. The research will enhance efficient utilization of high-performance computing resources while enabling faster innovation in areas of long-term national scientific interest.