Fluid-structure interaction occurs when moving fluids act on structures and the resulting structural motion or deformation changes the fluid flow. It plays a central role when blood flows through heart valves, organisms swim or fly, bio-inspired vehicles move through water or air, energy devices convert flow into power, aircraft and turbine components respond to aerodynamic loads, and medical devices interact with the body. Immersed boundary methods are mathematical and computational tools for simulating systems in which fluids and structures influence each other. These simulations can support scientific discovery, engineering design, and medical innovation, but current methods can sometimes fail to preserve volume, produce unrealistic fluid motion near pressurized surfaces, or give inaccurate estimates of local forces. This project will create more reliable simulation methods for fluid-structure interaction. By improving general-purpose tools that can impact cardiovascular modeling, medical device design, energy technology, aircraft and turbine analysis, and other engineered systems, the work will help advance national health, economic competitiveness, public welfare, and national defense. The project will also strengthen open-source software used by scientists and engineers, train students in computational mathematics and scientific computing, and support areas of Federal strategic interest, including biotechnology, advanced manufacturing, medical device design, energy tech