PVFMM is a scalable FMM library for computing solutions to constant coefficient elliptic PDEs (Poisson, Stokes, Helmholtz) on cubic domain with free-space and periodic boundary conditions. In this talk, we discuss performance optimizations including distributed and shared memory parallelism, integration with co-processors, vectorization and cache optimization.
We also integrate our method with GMRES in PETSc to compute solutions to variable coefficient Stokes problems and demonstrate scalability to thousands of compute nodes on TACC’s Stampede supercomputer.