tutorials/6_fenicsx.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 6: Coupling the finite and boundary element methods\n",
    "\n",
    "In this tutorial, we will look at how Bempp can be used alongside the finite element library FEniCSx to solve a transmission problem. To run this tutorial, you will need to have FEniCSx installed. FEniCSx is included in the [Bempp Docker image](https://bempp.com/installation.html), so you may like to use that rather than installing FEniCSx yourself.\n",
    "\n",
    "For this example, we let $\\Omega$ be a unit cube and we solve a transmission problem with different matrial properties inside and outside the cube.\n",
    "\n",
    "As an incident wave, we use\n",
    "\n",
    "$$\n",
    "p_\\text{inc}(\\mathbf{x})=\\mathrm{e}^{\\mathrm{i} k \\mathbf{x}\\cdot\\mathbf{d}},\n",
    "$$\n",
    "\n",
    "where $\\mathbf{x}=(x_0,x_1,x_2)$ and $\\mathbf{d} = \\frac{1}{\\sqrt{3}}(1,1,1)$ is the direction of the incident wave.\n",
    "\n",
    "The PDE we want to solve is\n",
    "\n",
    "$$\n",
    "\\Delta p + n(\\mathbf{x})^2 k^2 p = 0, \\quad \\text{ in } \\Omega\\\\\n",
    "\\Delta p + k^2 p = 0, \\quad \\text{ in } \\mathbb{R}^3 \\backslash \\Omega\n",
    "$$\n",
    "\n",
    "In this example, we use $n(\\mathbf{x}) = 0.5$. For simplicity we have chosen $n$ to be constant.\n",
    "\n",
    "As $n$ is constant, we could actually use BEM inside the domain too; but if $n$ were not constant, BEM could not be used, and the benefit of coupling with FEM is more apparent.\n",
    "\n",
    "## Formulation\n",
    "\n",
    "### FEM part\n",
    "\n",
    "In $\\Omega$, the FEM part is formulated as\n",
    "\n",
    "$$\n",
    "\\int_\\Omega \\nabla p\\cdot\\nabla v -k^2\\int_\\Omega n^2pv - \\int_{d\\Omega} v\\frac{\\partial p}{\\partial \\nu} = 0,\n",
    "$$\n",
    "\n",
    "or\n",
    "\n",
    "$$\n",
    "\\langle\\nabla p,\\nabla v\\rangle_\\Omega - k^2\\langle n^2p,v\\rangle_\\Omega - \\langle \\lambda,v\\rangle_\\Gamma=0,\n",
    "$$\n",
    "\n",
    "where $\\lambda=\\frac{\\partial p}{\\partial \\nu}$.\n",
    "\n",
    "Later, we will write this as an operator equation, as this more closely matches the BEM approach:\n",
    "\n",
    "$$\n",
    "\\mathsf{A}u-k^2 \\mathsf{M}u-\\mathsf{M}_\\Gamma \\lambda = 0.\n",
    "$$\n",
    "\n",
    "### BEM part\n",
    "\n",
    "Outside the cube, we split $p$ into $p_\\text{s}+p_\\text{inc}$.\n",
    "\n",
    "#### Representation formula\n",
    "\n",
    "$$\n",
    "p_\\text{s} = \\mathcal{D}p-\\mathcal{S}\\lambda,\n",
    "$$\n",
    "\n",
    "where $\\mathcal{S}$ is the single layer potential operator; $\\mathcal{D}$ is the double layer potential operator; and $\\lambda$ is the normal derivative of $p$ on the surface of the cube.\n",
    "\n",
    "#### Boundary integral equation\n",
    "\n",
    "$$\n",
    "\\left(\\tfrac{1}{2}\\mathsf{I}-\\mathsf{D}\\right)p+\\mathsf{S}\\lambda = p_\\text{inc},\n",
    "$$\n",
    "\n",
    "where $\\mathsf{S}$ is the single layer boundary operator; $\\mathsf{D}$ is the double layer boundary operator; and $\\mathsf{I}$ is the identity operator.\n",
    "\n",
    "### Overall formulation\n",
    "\n",
    "Combining the FEM and BEM parts of the formulation, we have two simultaneous operator equation in terms of $p$ and $\\lambda$. We can write this as a blocked system:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    \\mathsf{A}-k^2 \\mathsf{M} & -\\mathsf{M}_\\Gamma\\\\\n",
    "    \\tfrac{1}{2}\\mathsf{I}-\\mathsf{D} & \\mathsf{S}\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "    p\\\\\n",
    "    \\lambda\n",
    "\\end{bmatrix}=\\begin{bmatrix}\n",
    "    0\\\\\n",
    "    p_\\text{inc}\n",
    "\\end{bmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving with Bempp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by importing DOLFINx (the FEniCSx python library), UFL (FEniCS's unified form language), MPI, Bempp and Numpy. We also disable Bempp's logging messages (as otherwise a lot will appear during the solve step)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import dolfinx\n",
    "import dolfinx.geometry\n",
    "import ufl\n",
    "from mpi4py import MPI\n",
    "import bempp.api\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we set the wavenumber ``k`` and the direction ``d`` of the incoming wave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 6.\n",
    "d = np.array([1., 1., 1])\n",
    "d /= np.linalg.norm(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a mesh of a cube using DOLFINx. This will be mesh of tetrahedral cells to be used for the interior FEM part of the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mesh = dolfinx.UnitCubeMesh(MPI.COMM_WORLD, 10, 10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we make the DOLFINx and Bempp function spaces.\n",
    "\n",
    "The function ``fenics_to_bempp_trace_data`` will extract the trace space from the DOLFINx space and create the matrix ``trace_matrix``, which maps between the dofs (degrees of freedom) in DOLFINx and Bempp."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FEM dofs: 1331\n",
      "BEM dofs: 1200\n"
     ]
    }
   ],
   "source": [
    "from bempp.api.external import fenicsx\n",
    "\n",
    "fenics_space = dolfinx.FunctionSpace(mesh, (\"CG\", 1))\n",
    "trace_space, trace_matrix = \\\n",
    "    fenicsx.fenics_to_bempp_trace_data(fenics_space)\n",
    "bempp_space = bempp.api.function_space(trace_space.grid, \"DP\", 0)\n",
    "\n",
    "fem_size = fenics_space.dofmap.index_map.size_global\n",
    "bem_size = bempp_space.global_dof_count\n",
    "\n",
    "print(\"FEM dofs: {0}\".format(fem_size))\n",
    "print(\"BEM dofs: {0}\".format(bem_size))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the boundary operators that we need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "identity = bempp.api.operators.boundary.sparse.identity(\n",
    "    trace_space, bempp_space, bempp_space)\n",
    "mass = bempp.api.operators.boundary.sparse.identity(\n",
    "    bempp_space, bempp_space, trace_space)\n",
    "double_layer = bempp.api.operators.boundary.helmholtz.double_layer(\n",
    "    trace_space, bempp_space, bempp_space, k)\n",
    "single_layer = bempp.api.operators.boundary.helmholtz.single_layer(\n",
    "    bempp_space, bempp_space, bempp_space, k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the UFL trial function, test function, and define $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = ufl.TrialFunction(fenics_space)\n",
    "v = ufl.TestFunction(fenics_space)\n",
    "n = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We make the vectors on the right hand side of the formulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "@bempp.api.complex_callable\n",
    "def u_inc(x, n, domain_index, result):\n",
    "    result[0] = np.exp(1j * k * np.dot(x, d))\n",
    "u_inc = bempp.api.GridFunction(bempp_space, fun=u_inc)\n",
    "\n",
    "# The rhs from the FEM\n",
    "rhs_fem = np.zeros(fem_size)\n",
    "# The rhs from the BEM\n",
    "rhs_bem = u_inc.projections(bempp_space)\n",
    "# The combined rhs\n",
    "rhs = np.concatenate([rhs_fem, rhs_bem])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready to create a ``BlockedLinearOperator`` containing all four parts of the discretisation of\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    \\mathsf{A}-k^2 \\mathsf{M} & -\\mathsf{M}_\\Gamma\\\\\n",
    "    \\tfrac{1}{2}\\mathsf{I}-\\mathsf{D} & \\mathsf{S}\n",
    "\\end{bmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from bempp.api.assembly.blocked_operator import BlockedDiscreteOperator\n",
    "from scipy.sparse.linalg.interface import LinearOperator\n",
    "blocks = [[None,None],[None,None]]\n",
    "\n",
    "trace_op = LinearOperator(trace_matrix.shape, lambda x:trace_matrix @ x)\n",
    "\n",
    "A = fenicsx.FenicsOperator((ufl.inner(ufl.grad(u), ufl.grad(v)) - k**2 * n**2 * ufl.inner(u, v)) * ufl.dx)\n",
    "\n",
    "blocks[0][0] = A.weak_form()\n",
    "blocks[0][1] = -trace_matrix.T * mass.weak_form().to_sparse()\n",
    "blocks[1][0] = (.5 * identity - double_layer).weak_form() * trace_op\n",
    "blocks[1][1] = single_layer.weak_form()\n",
    "\n",
    "blocked = BlockedDiscreteOperator(np.array(blocks))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we solve the system, then split the solution into the parts assosiated with p and $\\lambda$. For an efficient solve, preconditioning is required."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of iterations: 312\n"
     ]
    }
   ],
   "source": [
    "from bempp.api.assembly.discrete_boundary_operator import InverseSparseDiscreteBoundaryOperator\n",
    "from scipy.sparse.linalg import LinearOperator\n",
    "\n",
    "# Compute the sparse inverse of the Helmholtz operator\n",
    "# Although it is not a boundary operator we can use\n",
    "# the SparseInverseDiscreteBoundaryOperator function from\n",
    "# BEM++ to turn its LU decomposition into a linear operator.\n",
    "P1 = InverseSparseDiscreteBoundaryOperator(\n",
    "    blocked[0,0].to_sparse().tocsc())\n",
    "\n",
    "# For the Laplace slp we use a simple mass matrix preconditioner. \n",
    "# This is sufficient for smaller low-frequency problems.\n",
    "P2 = InverseSparseDiscreteBoundaryOperator(\n",
    "    bempp.api.operators.boundary.sparse.identity(\n",
    "        bempp_space, bempp_space, bempp_space).weak_form())\n",
    "\n",
    "# Create a block diagonal preconditioner object using the Scipy LinearOperator class\n",
    "def apply_prec(x):\n",
    "    \"\"\"Apply the block diagonal preconditioner\"\"\"\n",
    "    m1 = P1.shape[0]\n",
    "    m2 = P2.shape[0]\n",
    "    n1 = P1.shape[1]\n",
    "    n2 = P2.shape[1]\n",
    "    \n",
    "    res1 = P1.dot(x[:n1])\n",
    "    res2 = P2.dot(x[n1:])\n",
    "    return np.concatenate([res1, res2])\n",
    "\n",
    "p_shape = (P1.shape[0] + P2.shape[0], P1.shape[1] + P2.shape[1])\n",
    "P = LinearOperator(p_shape, apply_prec, dtype=np.dtype('complex128'))\n",
    "\n",
    "# Create a callback function to count the number of iterations\n",
    "it_count = 0\n",
    "def count_iterations(x):\n",
    "    global it_count\n",
    "    it_count += 1\n",
    "\n",
    "from scipy.sparse.linalg import gmres\n",
    "soln, info = gmres(blocked, rhs, M=P, callback=count_iterations)\n",
    "\n",
    "soln_fem = soln[:fem_size]\n",
    "soln_bem = soln[fem_size:]\n",
    "\n",
    "print(\"Number of iterations: {0}\".format(it_count))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we make DOLFINx and Bempp functions from the solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Store the real part of the FEM solution\n",
    "u = dolfinx.Function(fenics_space)\n",
    "u.vector[:] = np.ascontiguousarray(np.real(soln_fem))\n",
    "\n",
    "# Solution function with dirichlet data on the boundary\n",
    "dirichlet_data = trace_matrix * soln_fem\n",
    "dirichlet_fun = bempp.api.GridFunction(trace_space, coefficients=dirichlet_data)\n",
    "\n",
    "# Solution function with Neumann data on the boundary\n",
    "neumann_fun = bempp.api.GridFunction(bempp_space, coefficients=soln_bem)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now evaluate the solution on the slice $z=0.5$ and plot it. For the exterior domain, we use the respresentation formula\n",
    "\n",
    "$$\n",
    "p_\\text{s} = \\mathcal{D}p-\\mathcal{S}\\frac{\\partial u}{\\partial \\nu}\n",
    "$$\n",
    "\n",
    "to evaluate the solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "Nx=200\n",
    "Ny=200\n",
    "xmin, xmax, ymin, ymax=[-1,3,-1,3]\n",
    "plot_grid = np.mgrid[xmin:xmax:Nx*1j,ymin:ymax:Ny*1j]\n",
    "points = np.vstack((plot_grid[0].ravel(),\n",
    "                    plot_grid[1].ravel(),\n",
    "                    np.array([0.5]*plot_grid[0].size)))\n",
    "plot_me = np.zeros(points.shape[1], dtype=np.complex128)\n",
    "\n",
    "x,y,z = points\n",
    "bem_x = np.logical_not((x>0) * (x<1) * (y>0) * (y<1) * (z>0) * (z<1))\n",
    "\n",
    "slp_pot= bempp.api.operators.potential.helmholtz.single_layer(\n",
    "    bempp_space, points[:, bem_x], k)\n",
    "dlp_pot= bempp.api.operators.potential.helmholtz.double_layer(\n",
    "    trace_space, points[:, bem_x], k)\n",
    "\n",
    "plot_me[bem_x] += np.exp(1j * k * (points[0, bem_x] * d[0] \\\n",
    "                                 + points[1, bem_x] * d[1] \\\n",
    "                                 + points[2, bem_x] * d[2]))\n",
    "plot_me[bem_x] += dlp_pot.evaluate(dirichlet_fun).flat\n",
    "plot_me[bem_x] -= slp_pot.evaluate(neumann_fun).flat\n",
    "\n",
    "fem_points = points[:, np.logical_not(bem_x)].transpose()\n",
    "tree = dolfinx.geometry.BoundingBoxTree(mesh, 3)\n",
    "entities = []\n",
    "for point in fem_points:\n",
    "    entities.append(dolfinx.geometry.compute_closest_entity(tree, point, mesh)[0])\n",
    "fem_val = u.eval(fem_points, entities)\n",
    "\n",
    "plot_me[np.logical_not(bem_x)] += fem_val.T[0]\n",
    "\n",
    "plot_me = plot_me.reshape((Nx, Ny))\n",
    "\n",
    "plot_me = plot_me.transpose()[::-1]\n",
    "\n",
    "vmax = max(np.abs(np.real(plot_me.flat)))\n",
    "\n",
    "# Plot the image\n",
    "from matplotlib import pyplot as plt\n",
    "fig=plt.figure(figsize=(10, 8))\n",
    "plt.imshow(np.real(plot_me), extent=[xmin, xmax, ymin, ymax],\n",
    "           cmap=plt.get_cmap(\"bwr\"), vmin=-vmax, vmax=vmax)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.colorbar()\n",
    "plt.title(\"FEM-BEM Coupling for Helmholtz\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}