twist.cpp

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// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.
//
//          -------------------------------------------------------
//          Twist Miniapp:  Generate simple twisted periodic meshes
//          -------------------------------------------------------
//
// This miniapp generates simple periodic meshes to demonstrate MFEM's handling
// of periodic domains. MFEM's strategy is to use a discontinuous vector field
// to define the mesh coordinates on a topologically periodic mesh. It works by
// defining a stack of individual elements and stitching together the top and
// bottom of the mesh. The stack can also be twisted so that the vertices of the
// bottom and top can be joined with any integer offset (for tetrahedral and
// wedge meshes only even offsets are supported).
//
// Compile with: make twist
//
// Sample runs:  twist
//               twist -no-pm
//               twist -nt -2 -no-pm
//               twist -nt 2 -e 4
//               twist -nt 2 -e 6
//               twist -nt 3 -e 8
//
#include "mfem.hpp"
#include <fstream>
#include <iostream>
 
using namespace std;
using namespace mfem;
 
static Element::Type el_type_ = Element::WEDGE;
static int    order_ = 3;
static int    nz_    = 3;
static int    nt_    = 2;
static real_t a_     = 1.0;
static real_t b_     = 1.0;
static real_t c_     = 3.0;
 
void pts(int iphi, int t, real_t x[]);
void trans(const Vector &x, Vector &p);
 
int main(int argc, char *argv[])
{
   int ser_ref_levels = 0;
   int el_type = 8;
   bool per_mesh = true;
   bool dg_mesh  = false;
   int visport = 19916;
   bool visualization = true;
 
   OptionsParser args(argc, argv);
   args.AddOption(&nz_, "-nz", "--num-elements-z",
                  "Number of elements in z-direction.");
   args.AddOption(&nt_, "-nt", "--num-twists",
                  "Number of node positions to twist the top of the mesh.");
   args.AddOption(&order_, "-o", "--mesh-order",
                  "Order (polynomial degree) of the mesh elements.");
   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
                  "Number of times to refine the mesh uniformly in serial.");
   args.AddOption(&a_, "-a", "--base-x",
                  "Width of the base in x-direction.");
   args.AddOption(&b_, "-b", "--base-y",
                  "Width of the base in y-direction.");
   args.AddOption(&c_, "-c", "--height",
                  "Height in z-direction.");
   args.AddOption(&el_type, "-e", "--element-type",
                  "Element type: 4 - Tetrahedron, 6 - Wedge, 8 - Hexahedron.");
   args.AddOption(&per_mesh, "-pm", "--periodic-mesh",
                  "-no-pm", "--non-periodic-mesh",
                  "Enforce periodicity in z-direction "
                  "(requires discontinuous mesh).");
   args.AddOption(&dg_mesh, "-dm", "--discont-mesh", "-cm", "--cont-mesh",
                  "Use discontinuous or continuous space for the mesh nodes.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.AddOption(&visport, "-p", "--send-port", "Socket for GLVis.");
   args.Parse();
   if (!args.Good())
   {
      args.PrintUsage(cout);
      return 1;
   }
   args.PrintOptions(cout);
 
   // The output mesh could be tetrahedra, hexahedra, or prisms
   switch (el_type)
   {
      case 4:
         el_type_ = Element::TETRAHEDRON;
         break;
      case 6:
         el_type_ = Element::WEDGE;
         break;
      case 8:
         el_type_ = Element::HEXAHEDRON;
         break;
      default:
         cout << "Unsupported element type" << endl;
         exit(1);
         break;
   }
 
   // Define the mesh
   Mesh mesh = Mesh::MakeCartesian3D(1, 1, nz_, el_type_, a_, b_, c_, false);
 
   // Promote to high order mesh and transform into a twisted shape
   if (order_ > 1 || dg_mesh || per_mesh)
   {
      mesh.SetCurvature(order_, dg_mesh || per_mesh, 3, Ordering::byVDIM);
   }
   if (nt_ != 0 )
   {
      mesh.Transform(trans);
   }
 
   while (per_mesh)
   {
      // Verify geometric compatibility
      if (nt_ % 2 == 1 && std::abs(a_ - b_) > 1e-6 * a_)
      {
         cout << "Base is rectangular so number of shifts must be even "
              << "for a periodic mesh!" << endl;
         exit(1);
      }
 
      // Verify topological compatibility
      if (nt_ % 2 == 1 && (el_type_ == Element::TETRAHEDRON ||
                           el_type_ == Element::WEDGE))
      {
         cout << "Diagonal cuts on the base and top must line up "
              << "for a periodic mesh!" << endl;
         exit(1);
      }
 
      int nnode = 4;
      int noff = (nt_ >= 0) ? 0 : (nnode * (1 - nt_ / nnode));
 
      Array<int> v2v(mesh.GetNV());
      for (int i = 0; i < v2v.Size() - nnode; i++)
      {
         v2v[i] = i;
      }
      // identify vertices at the extremes of the stack
      switch ((noff + nt_) % nnode)
      {
         case 0:
            v2v[v2v.Size() - nnode + 0] = 0;
            v2v[v2v.Size() - nnode + 1] = 1;
            v2v[v2v.Size() - nnode + 2] = 2;
            v2v[v2v.Size() - nnode + 3] = 3;
            break;
         case 1:
            v2v[v2v.Size() - nnode + 0] = 2;
            v2v[v2v.Size() - nnode + 1] = 0;
            v2v[v2v.Size() - nnode + 2] = 3;
            v2v[v2v.Size() - nnode + 3] = 1;
            break;
         case 2:
            v2v[v2v.Size() - nnode + 0] = 3;
            v2v[v2v.Size() - nnode + 1] = 2;
            v2v[v2v.Size() - nnode + 2] = 1;
            v2v[v2v.Size() - nnode + 3] = 0;
            break;
         case 3:
            v2v[v2v.Size() - nnode + 0] = 1;
            v2v[v2v.Size() - nnode + 1] = 3;
            v2v[v2v.Size() - nnode + 2] = 0;
            v2v[v2v.Size() - nnode + 3] = 2;
            break;
      }
      // renumber elements
      for (int i = 0; i < mesh.GetNE(); i++)
      {
         Element *el = mesh.GetElement(i);
         int *v = el->GetVertices();
         int nv = el->GetNVertices();
         for (int j = 0; j < nv; j++)
         {
            v[j] = v2v[v[j]];
         }
      }
      // renumber boundary elements
      for (int i = 0; i < mesh.GetNBE(); i++)
      {
         Element *el = mesh.GetBdrElement(i);
         int *v = el->GetVertices();
         int nv = el->GetNVertices();
         for (int j = 0; j < nv; j++)
         {
            v[j] = v2v[v[j]];
         }
      }
      mesh.RemoveUnusedVertices();
      mesh.RemoveInternalBoundaries();
 
      break;
   }
 
   // Refine the mesh if desired
   for (int lev = 0; lev < ser_ref_levels; lev++)
   {
      mesh.UniformRefinement();
   }
 
   // Output the resulting mesh to a file
   {
      ostringstream oss;
      if (el_type_ == Element::TETRAHEDRON)
      {
         oss << "twist-tet";
      }
      else if (el_type_ == Element::WEDGE)
      {
         oss << "twist-wedge";
      }
      else
      {
         oss << "twist-hex";
      }
      oss << "-o" << order_ << "-s" << nt_;
      if (ser_ref_levels > 0)
      {
         oss << "-r" << ser_ref_levels;
      }
      if (per_mesh)
      {
         oss << "-p";
      }
      else if (dg_mesh)
      {
         oss << "-d";
      }
      else
      {
         oss << "-c";
      }
 
      oss << ".mesh";
      ofstream ofs(oss.str().c_str());
      ofs.precision(8);
      mesh.Print(ofs);
      ofs.close();
   }
 
   // Output the resulting mesh to GLVis
   if (visualization)
   {
      char vishost[] = "localhost";
      socketstream sol_sock(vishost, visport);
      sol_sock.precision(8);
      sol_sock << "mesh\n" << mesh << flush;
   }
 
   // Clean up and exit
   return 0;
}
 
void trans(const Vector &x, Vector &p)
{
   real_t z = x[2];
   real_t phi = 0.5 * M_PI * nt_ * z / c_;
   real_t cp = cos(phi);
   real_t sp = sin(phi);
 
   p[0] = 0.5 * a_ + (x[0] - 0.5 * a_) * cp - (x[1] - 0.5 * b_) * sp;
   p[1] = 0.5 * b_ + (x[0] - 0.5 * a_) * sp + (x[1] - 0.5 * b_) * cp;
   p[2] = z;
}