Parallelization of Level Set Functions Using Message Passing Interface

Many physical phenomena in the world, such as the burning of a flame, or water moving through a pipe, can be described using partial differential equations (PDEs). In particular, a level set function is a type of PDE that represents the interaction between two interfaces or shapes, such as air and water. However, depending on the complexity of the equations, solving these simulations by hand can be near impossible to accomplish; therefore, we use computers to do these computations for us. While computers can solve these equations, they can still take several weeks to run a simulation. The goal of this project is to reduce the computing time of these simulations by utilizing a parallel solution using message passing interface (MPI) and running that parallel code on a supercomputer with thousands of processors. First we set up a serial code, or a single-core implementation, of our level set simulation in order to use it as a control to compare our parallel code to, or multi-core implementation. Next, we develop a parallel code by building on top of our original serial code and extending its functionality with MPI and then running that code on a supercomputer. We hope that the parallel code will cut down the time of these simulations from several weeks to a few days; however, further optimizations in the code can be done to improve performance. We hope to conclude that a parallel solution will enable more research to be done and reduce the downtime between simulations.