A demo using PETSc - UC Denvermath.ucdenver.edu/~mmccourt/talks/kernel-petsc-aug10.pdf ·...
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Transcript of A demo using PETSc - UC Denvermath.ucdenver.edu/~mmccourt/talks/kernel-petsc-aug10.pdf ·...
Distributed Kernel Finite DifferenceA demo using PETSc
Michael McCourt
OVERVIEW
A brief demonstration of the core
PETSc tools and how localized kernel
approximations can be executed in a
distributed setting.
WHAT IS PETSc?
A freely available and supported research code for
the parallel solution of nonlinear algebraic
equations: http://www.mcs.anl.gov/petsc
Support via email: [email protected]
Usable from C, C++, Fortran 77/90, Matlab, Julia,
and Python
WHAT DOES PETSc DO?
PETSc has run implicit problems with over 500 billion unknowns
● UNIC on BG/P and XT5
● PFLOTRAN for flow in porous media
PETSc has run on over 1,500,000 cores efficiently
● Gordon Bell Prize Mantle Convection on IBM BG/Q Sequoia
PETSc applications have run at 23% of peak (600 Teraflops)
● Jed Brown on NERSC Edison
WHAT DOES PETSc DO?
● Eliminate the MPI from MPI programming!
● Provide wrappers to other useful libraries.
● Provide high level access to GPU computing.
PETSc is not a black-box PDE solver. Examples are
provided but you have to build your own solution.
WHAT DOES PETSc PROVIDE?
● Many (parallel) vector/array operations
● Numerous (parallel) matrix formats and operations
● Numerous linear solvers
● Nonlinear solvers
● Limited ODE integrators
● Limited parallel grid/data management
● Common interface for most DOE solver software ...
WHAT DOES PETSc PROVIDE?
WHAT DOES PETSc PROVIDE?
WHAT DOES PETSc PROVIDE?
PETSc STRUCTURE
PETSc PROGRAMMING IDEALS
● Distributed memory, “shared-nothing” ○ Requires only a standard compiler○ Access to data on remote machines through
MPI● Hide within objects the details of the communication● User orchestrates communication at a higher
abstract level than direct MPI calls
PETSc PDE FLOW
PETSc NUMERICAL COMPONENTS
PETSc LINEAR SOLVE STRUCTURE
BUILDING A DISTRIBUTED VECTOR
LOADING A DISTRIBUTED VECTOR
COMMUNICATING VECTOR ENTRIES
PREPARING THE DIFFERENTIATION MATRIX
Match data distribution between matrix and vector
Preallocate memoryCompressed Sparse Row
POPULATING THE DIFFERENTIATION MATRIX
INTERPOLATION MATRIX ENTRIES
FORMING THE DIFFERENTIATION MATRIX
COMPUTING THE DERIVATIVE
Confirm It Is Accurate
