1 1  Capabilities: Scalable algebraic solvers for PDEs Freely available and supported research code Usable from C, C++, Fortran 77/90, Python, MATLAB Uses MPI; encapsulates communication details within higher-level objects Tracks the largest DOE but commonly used on moderately sized systems (i.e., machines 1/10th to 1/100th the size of the largest system) 1,100 unique downloads per 300 petsc-maint/petsc-users s per 80 petsc-dev s per week Developed as a platform for experimentation Polymorphism: Single user interface for given functionality; multiple implementations  IS, Vec, Mat, KSP, PC, SNES, TS, etc. No optimality without interplay among physics, algorithmics, and architectures  Download and further info: Public questions: archived Private questions: not archived PETSc: Portable, Extensible Toolkit for Scientific computing

2 2 PETSc: Application highlights  Applications include: acoustics, aerodynamics, air pollution, arterial flow, bone fractures, brain surgery, cancer surgery, cancer treatment, carbon sequestration, cardiology, cells, CFD, combustion, concrete, corrosion, data mining, dentistry, earthquakes, economics, fission, fusion, glaciers, ground water flow, linguistics, mantel convection, magnetic films, materials science, medical imaging, ocean dynamics, oil recovery, page rank, polymer injection molding, polymeric membranes, quantum computing, seismology, semiconductors, rockets, relativity, surface water flow  UNIC (PROTEUS-SN): Neutron transport Uses preconditioned Krylov methods, finalist in 2009 Gordon Bell competition, runs with over 500 billion unknowns on 222,912 cores of Cray XT5 & 294,912 cores of BG/P  PFLOTRAN: Subsurface flow and reactive transport Uses preconditioned Newton-Krylov methods, runs with up 2 billion unknowns on 224,000 cores of Cray XT6

3 3  Algorithms, (parallel) debugging aids, low-overhead profiling  Composability Try new algorithms by choosing from product space and composing existing algorithms (multilevel, domain decomposition, splitting)  Experimentation It is not possible to pick the solver a priori. What will deliver best/competitive performance for a given physics, discretization, architecture, and problem size? PETSc’s response: Expose an algebra of composition so new solvers can be created at runtime; users can develop custom application-specific approaches Important to keep solvers decoupled from physics and discretization because we also experiment with those  Philosophy: Everything has a plugin architecture Vectors, matrices, coloring/ordering/partitioning algorithms Preconditioners, Krylov accelerators Nonlinear solvers, time integrators Spatial discretizations/topology PETSc: Overview of approach