Procedures

Perform N steps of ark on level level_index and set qend appropriately. Assign pointer to appropriate level

Subroutine to call hooks associated with the hook and level

Subroutine to stop a timer

Helper function to return the array part

Helper function to return the array part

Helper function to return the array part

Subroutine to deallocate sweeper

Subroutine to evaluate function value at node m

Subroutine to evaluate the function values at all nodes

Subroutine to initialize matrices and space for sweeper Array of substep sizes

Subroutine to compute Picard integral of function values

deallocate

Evaluate all function values

Make space for rhs

Assign level pointer

Subroutine to compute Residual

Perform nsweep SDC sweeps on level level_index and set qend appropriately. Assign level pointer

Assign level pointer

Assign explicit approximate quadrature rule Make space for temporary variables

Save function values so that difference can be computed

Perform nsweep sweeps on level and set qend appropriately.

Subroutine to update the fine initial condition from coarse increment by spatial interpolation

Subroutine to update the fine terminal condition from coarse increment by spatial interpolation used for adjoint solver

Subroutine to interpolate (in time and space) level_index-1 to level_index Interpolation is done by interpolating increments.
The fine function values are re-evaluated after interpolation. create workspaces set time at coarse and fine nodes interpolate coarse level correction in space only interpolate corrections in time

Compute SDC integral fintSDC = \int_{t_n}^{t_m} fSDC dt

this loop not OMP'd because the deferred procs are OMP'd

Subroutine to evaluate function value at node m

Subroutine to evaluate the function values at all nodes

Array of substep sizes

Evaluate all function values

Array of substep sizes

Assign level pointer

Subroutine to compute Residual

Assign level pointer

Routine to compute the LU decomposition of spectral integration matrix

Subroutine to compute y = a x + y where a is a scalar and x and y are arrays

Subroutine to allocate the array and set the size parameters

Subroutine to copy an array

Subroutine to create an array of arrays

Subroutine to create a single array

Subroutine to destroy array

Subroutine to destroy an array of arrays

Subroutine to destroy an single array

Interfaces to output routines in pf_numpy.c

Subroutine to print the array to the screen (mainly for debugging purposes)

Interfaces to output routines in pf_numpy.c

Subroutine to define the norm of the array (here the max norm)

Subroutine to compute y = a x + y where a is a scalar and x and y are arrays

Subroutine to allocate the array and set the size parameters

Subroutine to copy an array

Subroutine to create an array of arrays

Subroutine to create a single array

Subroutine to destroy array

Subroutine to destroy an array of arrays

Subroutine to destroy an single array

Subroutine to print the array to the screen (mainly for debugging purposes)

Subroutine to define the norm of the array (here the max norm)

Subroutine to pack an array into a flat array for sending

Subroutine to set array to a scalar value.

Subroutine to unpack a flatarray after receiving

Subroutine to pack an array into a flat array for sending

The following are the base subroutines that all encapsulations must provide

Subroutine to unpack a flatarray after receiving

Subroutine to compute y = a x + y where a is a scalar and x and y are arrays

Subroutine to allocate the array and set the size parameters

Subroutine to copy an array

Subroutine to create an array of arrays

Subroutine to create a single array

Subroutine to destroy array (simple)

Subroutine to destroy an array of arrays

Subroutine to destroy an single array

Interfaces to output routines in pf_numpy.c

Subroutine to print the array to the screen (mainly for debugging purposes)

Interfaces to output routines in pf_numpy.c

Subroutine to define the norm of the array (here the max norm)

Subroutine to pack an array into a flat array for sending

The following are the base subroutines that all encapsulations must provide

Subroutine to unpack a flatarray after receiving

Function to decide if the restriction of the nodes is pointwise, e.g. coarse nodes are every other fine node

Subroutine to add a procedure to the hook on the given level

Apply a matrix (tmat or rmat) to src and add to dst. Mathematically this is dst= dst + amatsrc Where dst and src are vectors, mat is a matrix, and a is a scalar If the optional variable "zero" is provided and is true, then we compute dst= amatsrc

Apply a matrix (tmat or rmat) to src and add to dst.

PFASST controller for block mode When starting a new block, broadcast new initial conditions to all procs For initial block, this is done when initial conditions are set Reset some flags Pack away your last solution Everyone resets their q0 Just stick qend in q0 Update the step and t0 variables for new block Call the predictor to get an initial guess on all levels and all processors

Subroutine to broadcast the initial condition to all processors

Interfaces for subroutines

Subroutine to check if the current processor has converged and to update the next processor on the status Note that if the previous processor hasn't converged yet (pstatus), the current processor can't be converged yet either Check to see if tolerances are met

Test residuals to determine if the current processor has converged, adapted to optimal control. Can probably be removed, when pf_pfasst_block_oc is changed to use pf_check_convergence of pf_check_convergence_old.

Subroutine to test residuals to determine if the current processor has converged.

Subroutine to test residuals to determine if the current processor has converged.

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

This is the interface for the routine to compute the RHS function values

This is the interface for the routine to compute the RHS function values

Generic evaluate all Each sweeper can define its own evaluate_all or use this generic one

Generic residual Each sweeper can define its own residual, or use this generic one Compute the integral of F

Generic routine to spread initial conditions Each sweeper can define its own spreadq0 or use this generic one

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Deallocate PFASST level deallocate flat buffers for communcition deallocate nodes, flags, and integration matrices deallocate solution and function storage

Setup (allocate) PFASST level If the level is already setup, calling this again will allocate (or deallocate) tauQ appropriately. do some sanity checks (re)allocate tauQ (may to need create/destroy tauQ dynamically when doing AMR) skip the rest if we're already allocated allocate flat buffers for send, and recv allocate nodes, flags, and integration matrices make quadrature matrices Allocate and compute all the matrices initialize sweeper allocate solution and function arrays

Subroutine to add log hook

Subroutine defining log hook

Subroutine to create an MPI based PFASST communicator using the MPI communicator mpi_comm. assign communicator

Subroutine to destroy the PFASST communicator.

Subroutine to post receive requests.

Subroutine to receive solutions Note when blocking == .false. this is actually a wait because the nonblocking receive should have already been posted

Subroutine to receive convergence status information

Subroutine to send solutions

Subroutine to send convergence status information

Subroutine to set up the PFASST communicator. This should be called soon after adding levels to the PFASST controller set the rank

Routine to do the pfasst iterations for optimal control problems on one block of processors until completion. Each processor will do either a fixed number of iterations, or iterate until a tolerance is met On calling, it is assumed that the levels are already loaded with the initial guesses

Create a PFASST object gather some input from a file and command line fname present, read inputs from a file (and maybe command line) fname not present, only call read_opts if we want command line read set communicator

Deallocate PFASST object destroy all levels deallocate pfasst pointer arrays

This is the main interface to pfasst. It examines the parameters and decides which subroutine to call to execute the code correctly Set the number of time steps to do The user can either pass in the number of time steps or pass in the time step size and length of run Allocate stuff for holding results

Setup both the PFASST object and the comm object loop over levels to set parameters Loop over levels setting interpolation and restriction matrices (in time)

Subroutine to post a receive request for a new initial condition to be received after doing some work

Interfaces for subroutines

PFASST Predictor. Subroutine to initialize the solution on each processor The goal is to have a solution at each level and each node set to a consistent value When this is called, the value of q0 at the fine level on each processor has been set somehow (see q0_style below)

Step 1. Getting the initial condition on the finest level at each processor If we are doing multiple levels, then we need to coarsen to fine level Step 2: Proceed fine to coarse levels coarsening the fine solution and computing tau correction If RK_pred is true, just do some RK_steps

Subroutine to write out run parameters

Subroutine to create quadrature matrices

Subroutine to read pfasst options from file and command line define the namelist for reading set local variables to pf_pfasst defaults open the file "fname" and read the pfasst namelist overwrite parameters defined on command line re-assign the pfasst internals Sanity check

Subroutine to recieve the solution from the previous processor

Interfaces for subroutines

Subroutine to receive the convergence status from the previous processor

Interfaces for subroutines

Compute full residual at each node and measure it's size

Interfaces for subroutines

Interfaces for subroutines

Subroutine to send the solution to the next processor

Interfaces for subroutines

Subroutine to send this processor's convergence status to the next processor

Interfaces for subroutines

Interfaces for subroutines

Interfaces for subroutines

Subroutine to make the matrices for interpolation between noodes

Interfaces for subroutines

Execute a V-cycle between levels nfine and ncoarse

Post the nonblocking receives on the all the levels that will be recieving later (for single level this will be skipped) move from fine to coarse doing sweeps

Interfaces for subroutines

Subroutine to differentiate polynomial (in place)

Polynomial manipulation routines.

Function to evaluate complex polynomial

Subroutine to integrate polynomial (in place)

Subroutine to compute Legendre polynomial coefficients using Bonnet's recursion formula.

Subroutine to compute polynomial roots using the Durand-Kerner algorithm. The roots are assumed to be real.

Subroutine to sort (inplace) using the quick sort algorithm. Adapted from http://www.fortran.com/qsort_c.f95.

Restrict (in time and space) f_sol_array to c_sol_array Depending on the flag INTEGRAL, we may be restricting solutions, or integrals of F

Restrict (in time and space) fine level to coarse and set coarse level FAS correction.

Save current solution and function value so that future corrections can be computed

Subroutine to compute the quadrature matrices

Subroutine to compute high precision quadrature nodes.

Subroutine to start a timer

Destroy Verlet sweeper matrices

Subroutine to evaluate function value at node m

Subroutine to evaluate the function values at all nodes

Initialize integration matrices Array of substep sizes

Integrate (t_n to node)

Compute residual (t_n to node)

Spread the intial data for Verlet sweepers

Perform one SDC sweep on level lev_index and set qend appropriately Assign level pointer

Subroutine to compute y = a x + y where a is a scalar and x and y are arrays

Subroutine to allocate the array and set the size parameters

Subroutine to copy an array

Subroutine to create an array of arrays

Subroutine to create a single array

Subroutine to destroy array

Subroutine to destroy an array of arrays

Subroutine to destroy an single array

Interfaces to output routines in pf_numpy.c

Subroutine to print the array to the screen (mainly for debugging purposes)

Interfaces to output routines in pf_numpy.c

Subroutine to define the norm of the array (here the max norm)

Subroutine to pack an array into a flat array for sending

The following are the base subroutines that all encapsulations must provide

Subroutine to unpack a flatarray after receiving