How to add a new scheme to Inciter

Control/Keywords.h

$ git diff src/Control/Keywords.h
diff --git a/src/Control/Keywords.h b/src/Control/Keywords.h
index 002869cb..c18f193a 100644
--- a/src/Control/Keywords.h
+++ b/src/Control/Keywords.h
@@ -4607,6 +4607,19 @@ struct diagcg_info {
 };
 using diagcg = keyword< diagcg_info, TAOCPP_PEGTL_STRING("diagcg") >;

+struct alecg_info {
+  static std::string name() { return "ALE-CG with RK"; }
+  static std::string shortDescription() { return "Select continuous Galerkin "
+    "with ALE + Runge-Kutta"; }
+  static std::string longDescription() { return
+    R"(This keyword is used to select the continuous Galerkin finite element
+    scheme in the arbitrary Lagrangian-Eulerian (ALE) reference frame combined
+    with Runge-Kutta (RK) time stepping. See Control/Inciter/Options/Scheme.h
+    for other valid options.)"; }
+};
+using alecg = keyword< alecg_info, TAOCPP_PEGTL_STRING("alecg") >;
+
 struct dg_info {
   static std::string name() { return "DG(P0) + RK"; }
   static std::string shortDescription() { return

We also add the new keyword to inciter's grammar's keywords pool:

Control/Inciter/InputDeck/InputDeck.h

$ git diff src/Control/Inciter/InputDeck/InputDeck.h
diff --git a/src/Control/Inciter/InputDeck/InputDeck.h b/src/Control/Inciter/InputDeck/InputDeck.h
index 83572480..20ce8975 100644
--- a/src/Control/Inciter/InputDeck/InputDeck.h
+++ b/src/Control/Inciter/InputDeck/InputDeck.h
@@ -144,6 +144,7 @@ class InputDeck :
                                    kw::scheme,
                                    kw::matcg,
                                    kw::diagcg,
+                                   kw::alecg,
                                    kw::dg,
                                    kw::dgp1,
                                    kw::flux,

This is required so that the compiler can generate a database containing the help for all the keywords in the grammar understood by inciter's control file parser. The above changes not only add the keyword but also some documentation that gets displayed when passing the -C or -H command line arguments to the inciter executable, so quick help is available at the user's fingertips:

$ inciter -C
inciter Control File Keywords:
             advdiff     string Specify the advection + diffusion physics configuration for a PDE
           advection     string Specify the advection physics configuration for a PDE
               alecg            Select continuous Galerkin with ALE + Runge-Kutta
           algorithm     string Select mesh partitioning algorithm
               alpha       real Set PDE parameter(s) alpha
...
$ inciter -H alecg
inciter control file keyword 'alecg'

   Select continuous Galerkin with ALE + Runge-Kutta (RK)

   This keyword is used to select the continuous Galerkin finite element scheme
   in the arbitrary Lagrangian-Eulerian (ALE) reference frame combined with
   Runge-Kutta (RK) time stepping. See Control/Inciter/Options/Scheme.h for other
   valid options.

Control/Inciter/Options/Scheme.h

$ git diff src/Control/Inciter/Options/Scheme.h
diff --git a/src/Inciter/SchemeBase.h b/src/Inciter/SchemeBase.h
index 61510d01..0cb3e9e8 100644
--- a/src/Inciter/SchemeBase.h
+++ b/src/Inciter/SchemeBase.h
@@ -22,6 +22,7 @@

 #include "NoWarning/matcg.decl.h"
 #include "NoWarning/diagcg.decl.h"
+#include "NoWarning/alecg.decl.h"
 #include "NoWarning/distfct.decl.h"
 #include "NoWarning/dg.decl.h"
 #include "NoWarning/discretization.decl.h"
@@ -52,8 +53,11 @@ class SchemeBase {
         proxy = static_cast< CProxy_DiagCG >( CProxy_DiagCG::ckNew(m_bound) );
         fctproxy= CProxy_DistFCT::ckNew(m_bound);
       } else if (scheme == ctr::SchemeType::DG ||
-                 scheme == ctr::SchemeType::DGP1) {
+                 scheme == ctr::SchemeType::DGP1)
+      {
         proxy = static_cast< CProxy_DG >( CProxy_DG::ckNew(m_bound) );
+      } else if (scheme == ctr::SchemeType::ALECG) {
+        proxy = static_cast< CProxy_ALECG >( CProxy_ALECG::ckNew(m_bound) );
       } else Throw( "Unknown discretization scheme" );
     }

@@ -75,11 +79,12 @@ class SchemeBase {
     const CkArrayOptions& arrayoptions() { return m_bound; }

     //! Variant type listing all chare proxy types modeling the same concept
-    using Proxy = boost::variant< CProxy_DiagCG, CProxy_DG >;
+    using Proxy =
+      boost::variant< CProxy_DiagCG, CProxy_DG, CProxy_ALECG >;
     //! Variant type listing all chare element proxy types (behind operator[])
     using ProxyElem =
       boost::variant< CProxy_DiagCG::element_t,
-                      CProxy_DG::element_t >;
+                      CProxy_DG::element_t, CProxy_ALECG::element_t >;

   protected:
     //! Variant storing one proxy to which this class is configured for

Inciter/SchemeBase.h

$ git diff src/Inciter/SchemeBase.h
diff --git a/src/Inciter/SchemeBase.h b/src/Inciter/SchemeBase.h
index 61510d01..dea3d78a 100644
--- a/src/Inciter/SchemeBase.h
+++ b/src/Inciter/SchemeBase.h
@@ -22,6 +22,7 @@

 #include "NoWarning/matcg.decl.h"
 #include "NoWarning/diagcg.decl.h"
+#include "NoWarning/alecg.decl.h"
 #include "NoWarning/distfct.decl.h"
 #include "NoWarning/dg.decl.h"
 #include "NoWarning/discretization.decl.h"
@@ -51,6 +52,8 @@ class SchemeBase {
       } else if (scheme == ctr::SchemeType::DiagCG) {
         proxy = static_cast< CProxy_DiagCG >( CProxy_DiagCG::ckNew(m_bound) );
         fctproxy= CProxy_DistFCT::ckNew(m_bound);
+      } else if (scheme == ctr::SchemeType::ALECG) {
+        proxy = static_cast< CProxy_ALECG >( CProxy_ALECG::ckNew(m_bound) );
       } else if (scheme == ctr::SchemeType::DG ||
                  scheme == ctr::SchemeType::DGP1) {
         proxy = static_cast< CProxy_DG >( CProxy_DG::ckNew(m_bound) );
@@ -75,11 +78,12 @@ class SchemeBase {
     const CkArrayOptions& arrayoptions() { return m_bound; }

     //! Variant type listing all chare proxy types modeling the same concept
-    using Proxy = boost::variant< CProxy_DiagCG, CProxy_DG >;
+    using Proxy =
+      boost::variant< CProxy_DiagCG, CProxy_ALECG, CProxy_DG >;
     //! Variant type listing all chare element proxy types (behind operator[])
     using ProxyElem =
       boost::variant< CProxy_DiagCG::element_t,
-                      CProxy_DG::element_t >;
+                      CProxy_ALECG::element_t, CProxy_DG::element_t >;

   protected:
     //! Variant storing one proxy to which this class is configured for

Inciter/Refiner.h

$ git diff src/Inciter/Refiner.h
diff --git a/src/Inciter/Refiner.h b/src/Inciter/Refiner.h
index dfcb1ffd..4fe743a4 100644
--- a/src/Inciter/Refiner.h
+++ b/src/Inciter/Refiner.h
@@ -29,6 +29,7 @@
 #include "SchemeBase.h"
 #include "DiagCG.h"
+#include "ALECG.h"
 #include "DG.h"

 #include "NoWarning/transporter.decl.h"

We also tell the build system about our new ALECG class and its Charm++ module:

Inciter/CMakeLists.txt

$ gd src/Inciter/CMakeLists.txt
diff --git a/src/Inciter/CMakeLists.txt b/src/Inciter/CMakeLists.txt
index 141055ec..e339b65b 100644
--- a/src/Inciter/CMakeLists.txt
+++ b/src/Inciter/CMakeLists.txt
@@ -14,6 +14,7 @@ add_library(Inciter
             Sorter.C
             DiagCG.C
+            ALECG.C
             DG.C
             FluxCorrector.C
             DistFCT.C
@@ -74,6 +75,7 @@ addCharmModule( "refiner" "Inciter" )
 addCharmModule( "sorter" "Inciter" )
 addCharmModule( "matcg" "Inciter" )
 addCharmModule( "diagcg" "Inciter" )
+addCharmModule( "alecg" "Inciter" )
 addCharmModule( "distfct" "Inciter" )
 addCharmModule( "dg" "Inciter" )

The addCharmModule cmake macro above, defined in cmake/charm.cmake, ensures that build target Inciter will properly depend on our new alecg Charm++ module, defined in Inciter/alecg.ci. The macro also tells cmake how the two files, alecg.decl.h and alecg.def.h, are generated from alecg.ci: using charmc, a compiler wrapper that generates Charm++-code to make the ALECG from an ordinary C++ class into a Charm++ chare array, with entry methods callable across the network, make it migratable, enable its structured DAGger, etc. See also the Charm++ manual.

Now to the new files. First is the new Charm++ interface file, Inciter/alecg.ci:

Inciter/alecg.ci

This is the file that is parsed by Charm++'s compiler which then generates additional code that makes ALECG a Charm++ chare array, makes it migratable, etc. The full listing is at Inciter/alecg.ci some of whose details are discussed below.

  extern module transporter;
  extern module discretization;

  include "UnsMesh.h";
  include "PUPUtil.h";

    array [1D] ALECG {

      entry ALECG( const CProxy_Discretization& disc,
                   const std::map< int, std::vector< std::size_t > >& /* bface */,
                   const std::map< int, std::vector< std::size_t > >& bnode,
                   const std::vector< std::size_t >& /* triinpoel */ );
      initnode void registerReducers();
      entry void setup( tk::real v );
      entry void init();
      entry void diag();
      entry void sendinit();
      entry void advance( tk::real newdt );
      entry void comlhs( const std::vector< std::size_t >& gid,
                         const std::vector< std::vector< tk::real > >& L );
      entry void comrhs( const std::vector< std::size_t >& gid,
                         const std::vector< std::vector< tk::real > >& R );
      entry void resized();
      entry void lhs();
      entry void step();

      entry void wait4lhs() {
        when ownlhs_complete(), comlhs_complete() serial "lhs" { lhsmerge(); } };

      entry void wait4rhs() {
        when ownrhs_complete(), comrhs_complete() serial "rhs" { solve(); } };

      entry void wait4out() {
        when diag_complete(), ref_complete(), lhs_complete(),
             resize_complete() serial "out" { out(); } };

      entry void ownlhs_complete();
      entry void ownrhs_complete();
      entry void comlhs_complete();
      entry void comrhs_complete();
      entry void diag_complete();
      entry void ref_complete();
      entry void lhs_complete();
      entry void resize_complete();

NoWarning/alecg.decl.h and NoWarning/alecg.def.h

The newly added files to the NoWarning/ directory simply include the Charm++-generated alecg.decl.h and alecg.def.h files and locally, around the include, turn off specific compiler warnings for various compilers – we will not discuss them here further. Full listings are at NoWarning/alecg.decl.h and NoWarning/alecg.def.h.

ALECG::ALECG – Constructor

{
  usesAtSync = true;    // enable migration at AtSync

  // Size communication buffers
  resizeComm();

  // Activate SDAG wait for initially computing the left-hand side
  thisProxy[ thisIndex ].wait4lhs();

  // Signal the runtime system that the workers have been created
  contribute( sizeof(int), &m_initial, CkReduction::sum_int,
    CkCallback(CkReductionTarget(Transporter,comfinal), Disc()->Tr()) );
}

As discussed in Section Creating workers on the Inciter software design page, the worker chare array elements, such as ALECG, are created using Charm++'s dynamic array insertion feature. This is an asynchronous call, issued from Sorter::createWorkers(), and it signals the runtime system that it is time to start calling individual constructors of ALECG, passing them the appropriate data, required for each of them to initialize and operate on a mesh partition each is assigned (held by their companion Discretization "base" class). Thus running Sorter::createWorkers() eventually triggers calling ALECG's constructors distributed across the whole problem and available PEs.

In the constructor's body, listed above, we first enable migration for the class, then the local communication buffers are initialized by sizing them for the first time. Finally, we signal the runtime system that extra communication buffers, specific to this particular discretization scheme, have been created. This is a reduction call, issued by all array elements, eventually calling the reduction target Transporter::comfinal() a single time.

Transporter::comfinal() – Complete communication maps

{
  if (initial > 0) {
    m_progWork.end();
    m_scheme.setup( m_V );
    // Turn on automatic load balancing
    tk::CProxy_LBSwitch::ckNew( g_inputdeck.get<tag::cmd,tag::verbose>() );
  } else {
    m_scheme.lhs();
  }
}

Though asynchronously executed, the reduction operation targeting Transporter::comfinal() is a global synchronization point: all chares arrive in that function body, synchronized, and all continue from there again by calling ALECG::setup().

Transporter::comfinal() is a global synchronization point because all worker chares must finish resizing and/or constructing their communication maps before their setup() member function can be invoked. This is because setup() starts using those communication maps, e.g., when it starts computing and assembling the left hand side matrix or vector. When a chare receives data from others this data must be correctly sized and ready on all chares before these data containers can be used. If a global synchronization point did not precede setup(), chares that finish their constructor early might go ahead all the way to calling ALECG::comlhs(), which then will attempt to write to a communication buffer on the receiving side, which would lead to corrupt data and errors.

ALECG::setup() – Set initial conditions and compute the left hand side

void
ALECG::init()
// *****************************************************************************
// Initially compute left hand side diagonal matrix
// *****************************************************************************
{
  // Compute left-hand side of PDEs
  lhs();
}

In the ALECG::setup() code snippet above we first tell the runtime system to start listening for the completion of tasks leading to computing the left-hand side (lhs). This is done by the call wait4lhs(), which activates the relevant part of the DAG, discussed above in Section Inciter/alecg.ci – Structured DAG. Then we call ALECG::lhs() which starts by computing the own contribution of the lhs followed by sending out contributions to those chares the given chare shares at least a single mesh node with.

ALECG::lhs() – Compute own and send lhs on chare-boundary

void
ALECG::lhs()
// *****************************************************************************
// Compute the left-hand side of transport equations
// *****************************************************************************
{
  auto d = Disc();

  // Compute own portion of the lhs
  // m_lhs = ...

  if (d->Msum().empty())        // in serial we are done
    comlhs_complete();
  else // send contributions of lhs to chare-boundary nodes to fellow chares
    for (const auto& n : d->Msum()) {
      std::vector< std::vector< tk::real > > l( n.second.size() );
      std::size_t j = 0;
      for (auto i : n.second) l[ j++ ] = m_lhs[ tk::cref_find(d->Lid(),i) ];
      thisProxy[ n.first ].comlhs( n.second, l );
    }

  ownlhs_complete();
}

As the above ALECG::lhs() code snippet shows, to communicate the lhs first we check if the node communication map is empty. If so, we are running in serial and the communication part is a no-op – we call comlhs_complete() right away. If the map is not empty, we loop through the map and for each chare the given chare shares a node (or multiple nodes) with we collect the values of the lhs in those nodes into a vector and send it to the given destination chare. The send is done via the entry method function call thisProxy[n.first].comlhs(), which sends its arguments to chare id n.first in a point-point fashion.

ALECG::comlhs() – Receive left hand side on chare boundary

void
ALECG::comlhs( const std::vector< std::size_t >& gid,
               const std::vector< std::vector< tk::real > >& L )
// *****************************************************************************
//  Receive contributions to left-hand side diagonal matrix on chare-boundaries
//! \param[in] gid Global mesh node IDs at which we receive LHS contributions
//! \param[in] L Partial contributions of LHS to chare-boundary nodes
//! \details This function receives contributions to m_lhs, which stores the
//!   diagonal (lumped) mass matrix at mesh nodes. While m_lhs stores
//!   own contributions, m_lhsc collects the neighbor chare contributions during
//!   communication. This way work on m_lhs and m_lhsc is overlapped. The two
//!   are combined in lhsmerge().
// *****************************************************************************
{
  Assert( L.size() == gid.size(), "Size mismatch" );

  using tk::operator+=;

  auto d = Disc();

  for (std::size_t i=0; i<gid.size(); ++i) {
    auto bid = tk::cref_find( d->Bid(), gid[i] );
    Assert( bid < m_lhsc.size(), "Indexing out of bounds" );
    m_lhsc[ bid ] += L[i];
  }

  // When we have heard from all chares we communicate with, this chare is done
  if (++m_nlhs == d->Msum().size()) {
    m_nlhs = 0;
    comlhs_complete();
  }
}

The above code snippet from ALECG::comlhs() shows the implementation of the receive side of the lhs communication step. The function receives two vectors: in gid the list of global node IDs and in L the list of lhs values, one for each scalar component of the number of equations solved (in a system of systems). The sizes of the two vectors must equal – this is the number of nodes we receive data for from one other chare. Then we loop over all incoming data, find the local IDs for the global IDs and store them by adding their contributions at each node received. As the comment says, when this chare has received all contributions it supposed to receive, we tell the runtime system that on this chare communication of the lhs is finished by calling comlhs_cmplete(). The completion condition is implemented via a counter, whose value is incremented upon each call to this function and testing its equality with the size of the symmetric node communication map (Discretization::m_msum), which has data for as many chares as many other chare a given chare must communicate with. As discussed in Inciter/alecg.ci – Structured DAG, when both own and communicated parts of the lhs are complete, the runtime system calls lhsmerge().

ALECG::lhsmerge() – Merge left hand side and continue

void
ALECG::lhsmerge()
// *****************************************************************************
// The own and communication portion of the left-hand side is complete
// *****************************************************************************
{
  // Combine own and communicated contributions to left hand side
  auto d = Disc();

  // Combine own and communicated contributions to LHS and ICs
  for (const auto& b : d->Bid()) {
    auto lid = tk::cref_find( d->Lid(), b.first );
    const auto& blhsc = m_lhsc[ b.second ];
    for (ncomp_t c=0; c<m_lhs.nprop(); ++c) m_lhs(lid,c,0) += blhsc[c];
  }

  // Zero communication buffers for next time step
  for (auto& b : m_rhsc) std::fill( begin(b), end(b), 0.0 );

  // Continue after lhs is complete
  if (m_initial) start(); else lhs_complete();
}

When the own and communicated contributions to the lhs are in place, the communication buffer for the lhs, ALECG::m_lhsc, is merged into ALECG::m_lhs. As the above code snippet of ALECG::lhsmerge() shows, we loop through the global IDs of all chare-boundary nodes and add the received contributions to the lhs. After preparing (zeroing) the communication buffers for the right hand side (rhs), at the end of ALECG::lhsmerge() we continue in different directions depending on whether this is the first step or we are during time stepping. If lhsmerge() was called during the first step, we call ALECG::start() but if it was called during time stepping, we just tell the runtime system that the lhs is complete. (This latter happens after a mesh refinement step, in which case we need to regenerate the lhs, and in that case, completing the lhs is only part of a DAG, wait4eval, waiting for multiple overlapping tasks, required for continuing.) ALECG::start() calls ALECG::dt(), which is the first step in a time step.

ALECG::dt() – Start time step

    for (const auto& eq : g_cgpde) {
      auto eqdt = eq.dt( d->Coord(), d->Inpoel(), m_u );
      if (eqdt < mindt) mindt = eqdt;
    }

    // Scale smallest dt with CFL coefficient
    mindt *= g_inputdeck.get< tag::discr, tag::cfl >();

The above code snippet from ALECG::dt() shows a for loop that calls the the dt() member function of all types of PDEs configured by the user and finds the minimum size of the time step.

  // Actiavate SDAG waits for time step
  thisProxy[ thisIndex ].wait4rhs();
  thisProxy[ thisIndex ].wait4out();

  // Contribute to minimum dt across all chares the advance to next step
  contribute( sizeof(tk::real), &mindt, CkReduction::min_double,
              CkCallback(CkReductionTarget(Transporter,advance), d->Tr()) );

Once we have the time step size, we enable a couple of SDAG waits and issue a reduction to Transporter::advance() which yields the global minimum across all chares then issues a broadcast to ALECG::advance(). advance() saves the new time step in Discretization::m_dt, which is the master copy, then calls ALECG::rhs(), which starts computing the right hand sides of all PDEs integrated.

ALECG::rhs() & ALECG::comrhs() – Compute and communicate right hand side

Computing the right hand sides (rhs) of all PDE operators and communicating the rhs values in chare boundary nodes look exactly the same as the analogous functions for the lhs. When both the own and communicated contributions are complete on a chare, the runtime system calls ALECG::solve(), which first combines the own and received contributions then solves the system.

ALECG::solve() – Solve, diagnostics, refine

  // Compute diagnostics, e.g., residuals
  auto diag_computed = m_diag.compute( *d, m_u );
  // Increase number of iterations and physical time
  d->next();
  // Signal that diagnostics have been computed (or in this case, skipped)
  if (!diag_computed) diag();
  // Optionally refine mesh
  refine();

The above code snippet shows what happens immediately after solving the linear system on a chare. First we compute diagnostics, which is a catch-all phrase for various norms and integral quantities, see Inciter/NodeDiagnostics.C for details. Note that computing diagnostics only happens every few time step, depending on user configuration. If m_diag.compute() returns true, diagnostics have been computed in this time step. If diagnostics have been computed, their correct values require global reduction operations, performing different aggregation operations depending on the value. As all reductions, diagnostics are also collected by Transporter, this time in target Transporter::diagnostics(), which calls back, via a broadcast, to ALECG::diag(), which signals, on the ALECG chare, that diagnostics have been computed. If diagnostics have not been computed in this time step, we call ALECG::diag() right away. Next we increase the number of iterations taken and update physical time on the master copies, Discretization::m_it and Discretization::m_t. This is followed by (optionally) refining the mesh, calling ALECG::refine().

ALECG::refine() – Optionally refine mesh

  auto d = Disc();

  auto dtref = g_inputdeck.get< tag::amr, tag::dtref >();
  auto dtfreq = g_inputdeck.get< tag::amr, tag::dtfreq >();

  // if t>0 refinement enabled and we hit the frequency
  if (dtref && !(d->It() % dtfreq)) {   // refine

    d->Ref()->dtref( {}, m_bnode, {} );

  } else {      // do not refine

    ref_complete();
    lhs_complete();
    resize_complete();

  }

The above snippet shows that mesh refinement happens only at every few time step with its frequency configured by the user. If the mesh is not refined, we simply enable the SDAG waits associated to the tasks of the mesh refinement step. If the mesh is refined, we call a member function of the mesh refiner object held by Discretization, Refiner::dtref(), which when done, eventually calls back to ALECG::resize(), passing back the new mesh and associated data structures.

ALECG::resize() – Resize data after mesh refinement

void
ALECG::resizeAfterRefined(
  const std::vector< std::size_t >& /*ginpoel*/,
  const tk::UnsMesh::Chunk& chunk,
  const tk::UnsMesh::Coords& coord,
  const std::unordered_map< std::size_t, tk::UnsMesh::Edge >& addedNodes,
  const std::unordered_map< std::size_t, std::size_t >& /*addedTets*/,
  const std::unordered_map< int, std::vector< std::size_t > >& msum,
  const std::map< int, std::vector< std::size_t > >& /*bface*/,
  const std::map< int, std::vector< std::size_t > >& bnode,
  const std::vector< std::size_t >& /*triinpoel*/ )
// *****************************************************************************
//  Receive new mesh from Refiner
//! \param[in] ginpoel Mesh connectivity with global node ids
//! \param[in] chunk New mesh chunk (connectivity and global<->local id maps)
//! \param[in] coord New mesh node coordinates
//! \param[in] addedNodes Newly added mesh nodes and their parents (local ids)
//! \param[in] addedTets Newly added mesh cells and their parents (local ids)
//! \param[in] msum New node communication map
//! \param[in] bface Boundary-faces mapped to side set ids
//! \param[in] bnode Boundary-node lists mapped to side set ids
//! \param[in] triinpoel Boundary-face connectivity
// *****************************************************************************
{
  auto d = Disc();

  // Set flag that indicates that we are during time stepping
  m_initial = 0;

  // Zero field output iteration count between two mesh refinement steps
  d->Itf() = 0;

  // Increase number of iterations with mesh refinement
  ++d->Itr();

  // Resize mesh data structures
  d->resize( chunk, coord, msum );

  // Resize auxiliary solution vectors
  auto npoin = coord[0].size();
  auto nprop = m_u.nprop();
  m_u.resize( npoin, nprop );
  m_du.resize( npoin, nprop );
  m_lhs.resize( npoin, nprop );
  m_rhs.resize( npoin, nprop );

  // Update solution on new mesh
  for (const auto& n : addedNodes)
    for (std::size_t c=0; c<nprop; ++c)
      m_u(n.first,c,0) = (m_u(n.second[0],c,0) + m_u(n.second[1],c,0))/2.0;

  // Update physical-boundary node lists
  m_bnode = bnode;

  // Resize communication buffers
  resizeComm();

  // Activate SDAG waits for re-computing the left-hand side
  thisProxy[ thisIndex ].wait4lhs();

  ref_complete();

  contribute( CkCallback(CkReductionTarget(Transporter,workresized), d->Tr()) );
}

The above snippet shows ALECG::resize() called by Refiner when it finished mesh refinement. Besides resizing the mesh-related data held locally by ALECG, e.g., ALECG::m_u, ALECG::m_du, etc., as well as the communication buffers in ALECG::resizeComm(), we also call Discretization::resize(), which resizes all mesh-related data structures in Discretization. We also prepare for recomputing the lhs on the new mesh by enabling its SDAG wait, wait4lhs(). When all of this is done, we issue a reduction to Transporter::workresized(), which when called will mean that all workers have resized their data after mesh refinement. However, this is only one concurrent (asynchronous) thread of execution. Another one is started within d->resize(), which calls Discretization::resize(), which eventually reduces to Transporter::discresized(). When both of these independent threads finished, Transporter::resized() is called, see Transporter::wait4resize(). Transporter::resized() then starts two new asynchronous threads, issuing two broadcasts: one to Discretization::vol() and another one to ALECG::lhs(). The former recomputes the nodal volumes, stored in Discretization, while the latter recomputes the lhs stored in ALECG::m_lhs. Both of these threads require multiple steps and involve communication, but they are independent and thus we let the runtime system schedule them arbitrarily. The first thread, doing communication in parallel and going through Transporter::vol(), ends up in Transporter::totalvol(). The second one, after recomputing and communicating the chare-boundary values of the lhs, ends up in ALECG::lhsmerge(). Note that execution can arrive at both end-points, Transporter::totalvol() and ALECG::lhsmerge(), during setup, i.e., before time stepping, or during time stepping, due to code reuse. Thus both of these end-points check whether execution is before or during time stepping, indicated by the booleans ALECG::m_initial and the one appearing as the function argument of Transporter::totalvol(). During time stepping these bools are false, and ALECG enables lhs_complete(), while Transporter calls ALECG::resized() which enables resize_complete().

When all the end-of-time-step, independent threads have finished, we call ALECG::eval(), which decides whether we start a new time step or call Transporter::finish() for terminating at the end of time stepping. These end-of-time-step threads are (1) computing diagnostics, discussed above, (2) mesh refinement (and resizing of some of the mesh data structures), (3) resized (complete resize of mesh data structures, i.e., also those that require communication, e.g., nodal volumes), and (4) recomputing the lhs. The code-snippet on Inciter/alecg.ci in Section Inciter/alecg.ci – Structured DAG, above shows the DAG that tells the runtime system this logic, involving the four tasks.

Main/inciter.ci

$ git diff src/Main/inciter.ci
diff --git a/src/Main/inciter.ci b/src/Main/inciter.ci
index bf7eac98..e9b114b6 100644
--- a/src/Main/inciter.ci
+++ b/src/Main/inciter.ci
@@ -14,6 +14,7 @@ mainmodule inciter {
   extern module partitioner;
   extern module matcg;
   extern module diagcg;
+  extern module alecg;
   extern module dg;
   extern module charestatecollector;

The second, and final, step is to enable triggering the instantiation of specialized CGPDE class objects for our new ALECG scheme when the system of systems is instantiated. This associates the type of generic PDE systems that is used to instantiate the PDE classes, selected by user configuration. Since ALECG will be a node-centered scheme, we assign it to use the CGPDE polymorphic interface (instead of DGPDE, which is tailored for cell-centered discretizations).

PDE/PDEStack.C

$ git diff src/PDE/PDEStack.C
diff --git a/src/PDE/PDEStack.C b/src/PDE/PDEStack.C
index 438cb5e3..9b2e14e7 100644
--- a/src/PDE/PDEStack.C
+++ b/src/PDE/PDEStack.C
@@ -108,7 +108,9 @@ PDEStack::selectedCG() const
   std::vector< CGPDE > pdes;                // will store instantiated PDEs

   const auto sch = g_inputdeck.get< tag::discr, tag::scheme >();
-  if (sch == ctr::SchemeType::DiagCG) {
+  if (sch == ctr::SchemeType::DiagCG || sch == ctr::SchemeType::ALECG) {

     for (const auto& d : g_inputdeck.get< tag::selected, tag::pde >()) {
       if (d == ctr::PDEType::TRANSPORT)
         pdes.push_back( createCG< tag::transport >( d, cnt ) );
       else if (d == ctr::PDEType::COMPFLOW)
         pdes.push_back( createCG< tag::compflow >( d, cnt ) );
       else Throw( "Can't find selected CGPDE" );
     }

   }