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Update non-linear poisson problem.
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‎.github/workflows/build-publish.yml‎

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build:
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# The type of runner that the job will run on
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runs-on: ubuntu-latest
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container: dokken92/dolfinx_custom:08052021
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container: dokken92/dolfinx_custom:13052021
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env:
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HDF5_MPI: "ON"

‎.github/workflows/docker-image.yml‎

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run: echo ${{ secrets.DOCKERHUB_TOKEN }} | docker login -u ${{ secrets.DOCKERHUB_USERNAME }} --password-stdin
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- name: Push to the DockerHub registry
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run: |
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docker push dokken92/dolfinx_custom:08052021
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docker push dokken92/dolfinx_custom:13052021

‎Dockerfile‎

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FROM dokken92/dolfinx_custom:08052021
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FROM dokken92/dolfinx_custom:13052021
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# create user with a home directory
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ARG NB_USER

‎chapter2/nonlinpoisson_code.ipynb‎

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@@ -84,8 +84,8 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The next step is to solve the non-linear problem. To do so, we use [Newtons method](https://en.wikipedia.org/wiki/Newton%27s_method). \n",
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"We start by creating a class containing the core functions that we require to solve the problem."
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"The next step is to define the non-linear problem. As it is non-linear we will use [Newtons method](https://en.wikipedia.org/wiki/Newton%27s_method).\n",
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"Newton's method requires methods for evaluating the residual `F` (including application of boundary conditions), as well as a method for computing the Jacobian matrix. DOLFINx provides the function `NonlinearProblem` that implements these methods. In addition to the boundary conditions, you can supply the variational form for the Jacobian (computed if not supplied), and form and jit parameters, see the [JIT parameters section](../chapter4/compiler_parameters.ipynb)."
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]
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},
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{
@@ -94,77 +94,61 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"from typing import List\n",
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"class NonlinearPDEProblem:\n",
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" \"\"\"Nonlinear problem class for solving the non-linear problem\n",
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" F(u, v) = 0 for all v in V\n",
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" \"\"\"\n",
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" def __init__(self, F: ufl.form.Form, u: dolfinx.Function, bcs: List[dolfinx.DirichletBC]):\n",
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" \"\"\"\n",
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" Input:\n",
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" - F: The PDE residual F(u, v)\n",
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" - u: The unknown\n",
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" - bcs: List of Dirichlet boundary conditions\n",
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" This class set up structures for solving the non-linear problem using Newton's method, \n",
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" dF/du(u) du = -F(u)\n",
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" \"\"\"\n",
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" V = u.function_space\n",
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" du = ufl.TrialFunction(V)\n",
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" self.L = F\n",
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" # Create the Jacobian matrix, dF/du\n",
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" self.a = ufl.derivative(F, u, du)\n",
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" self.bcs = bcs\n",
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"\n",
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" # Create matrix and vector to be used for assembly\n",
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" # of the non-linear problem\n",
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" self.matrix = dolfinx.fem.create_matrix(self.a)\n",
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" self.vector = dolfinx.fem.create_vector(self.L)\n",
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"\n",
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" def form(self, x: PETSc.Vec):\n",
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" \"\"\"\n",
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" This function is called before the residual or Jacobian is computed. This is usually used to update ghost values.\n",
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" Input: \n",
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" x: The vector containing the latest solution\n",
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" \"\"\"\n",
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" x.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)\n",
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"\n",
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" def F(self, x: PETSc.Vec, b: PETSc.Vec):\n",
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" \"\"\"Assemble the residual F into the vector b. \n",
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" Input:\n",
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" x: The vector containing the latest solution\n",
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" b: Vector to assemble the residual into\n",
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" \"\"\"\n",
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" # Reset the residual vector\n",
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" with b.localForm() as b_local:\n",
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" b_local.set(0.0)\n",
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" dolfinx.fem.assemble_vector(b, self.L)\n",
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" # Apply boundary condition\n",
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" dolfinx.fem.apply_lifting(b, [self.a], [self.bcs], [x], -1.0)\n",
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" b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)\n",
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" dolfinx.fem.set_bc(b, self.bcs, x, -1.0)\n",
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"\n",
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" def J(self, x: PETSc.Vec, A: PETSc.Mat):\n",
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" \"\"\"Assemble the Jacobian matrix.\n",
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" Input:\n",
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" - x: The vector containing the latest solution\n",
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" - A: The matrix to assemble the Jacobian into\n",
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" \"\"\"\n",
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" A.zeroEntries()\n",
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" dolfinx.fem.assemble_matrix(A, self.a, self.bcs)\n",
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" A.assemble()"
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"problem = dolfinx.fem.NonlinearProblem(F, uh, bcs=[bc])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"As we have now defined the the solution strategy, we can use the built-in Newton-solver in dolfin-X to solve the variational problem. We can set the convergence criterions for the solver by changing the absolute tolerance (`atol`), relative tolerance (`rtol`) or the convergence criterion (`residual` or `incremental`)."
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"Next, we use the dolfinx Newton solver. We can set the convergence criterions for the solver by changing the absolute tolerance (`atol`), relative tolerance (`rtol`) or the convergence criterion (`residual` or `incremental`)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"solver = dolfinx.NewtonSolver(MPI.COMM_WORLD, problem)\n",
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"solver.convergence_criterion = \"incremental\"\n",
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"solver.rtol = 1e-6\n",
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"solver.report = True"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We can modify the linear solver in each Newton iteration by accessing the underlying `PETSc` object."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"ksp = solver.krylov_solver\n",
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"opts = PETSc.Options()\n",
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"option_prefix = ksp.getOptionsPrefix()\n",
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"opts[f\"{option_prefix}ksp_type\"] = \"cg\"\n",
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"opts[f\"{option_prefix}pc_type\"] = \"gamg\"\n",
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"opts[f\"{option_prefix}pc_factor_mat_solver_type\"] = \"mumps\"\n",
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"ksp.setFromOptions()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We are now ready to solve the non-linear problem. We assert that the solver has converged and print the number of iterations."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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}
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],
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"source": [
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"# Create nonlinear problem\n",
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"problem = NonlinearPDEProblem(F, uh, [bc])\n",
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"\n",
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"# Create Newton solver\n",
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"solver = dolfinx.cpp.nls.NewtonSolver(MPI.COMM_WORLD)\n",
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"\n",
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"# Set Newton solver options\n",
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"solver.atol = 1e-8\n",
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"solver.rtol = 1e-8\n",
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"solver.convergence_criterion = \"residual\"\n",
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"\n",
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"# Set non-linear problem for Newton solver\n",
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"solver.setF(problem.F, problem.vector)\n",
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"solver.setJ(problem.J, problem.matrix)\n",
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"solver.set_form(problem.form)\n",
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"\n",
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"# Solve non-linear problem\n",
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"dolfinx.log.set_log_level(dolfinx.log.LogLevel.INFO)\n",
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"n, converged = solver.solve(uh.vector)\n",
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"n, converged = solver.solve(uh)\n",
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"dolfinx.cpp.la.scatter_forward(uh.x)\n",
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"assert(converged)\n",
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"print(f\"Number of interations: {n:d}\")"
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"ename": "NameError",
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"evalue": "name 'dolfinx' is not defined",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-1-1940f870bef7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Compute L2 error and error at nodes\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mV_ex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdolfinx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFunctionSpace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmesh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m\"CG\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0mu_ex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdolfinx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mV_ex\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mu_ex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minterpolate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mu_exact\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mdolfinx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcpp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mla\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter_forward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mu_ex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mNameError\u001b[0m: name 'dolfinx' is not defined"
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"L2-error: 3.65e-15\n",
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"Error_max: 1.42e-14\n"
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]
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}
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],

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