biharmonic demo

demo/demo_biharmonic.py

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+import json
+import logging
+import os
+import pdb
+import sys
+
+import numpy as np
+from irrevolutions.meshes.primitives import mesh_circle_gmshapi
+from irrevolutions.solvers import SNESSolver
+
+import petsc4py
+from dolfinx import log
+from dolfinx.io import XDMFFile
+from mpi4py import MPI
+from petsc4py import PETSc
+
+logging.basicConfig(level=logging.INFO)
+
+import sys
+
+import dolfinx
+import dolfinx.io
+import dolfinx.mesh
+import dolfinx.plot
+import ufl
+import yaml
+from dolfinx.fem import Constant, dirichletbc
+from dolfinx.io import XDMFFile, gmshio
+from mpi4py import MPI
+from ufl import (
+    avg,
+    div,
+    grad,
+    inner,
+    dot,
+    jump,
+)
+
+petsc4py.init(sys.argv)
+log.set_log_level(log.LogLevel.WARNING)
+
+comm = MPI.COMM_WORLD
+
+
+def monitor(snes, it, norm):
+    logging.info(f"Iteration {it}, residual {norm}")
+    return PETSc.SNES.ConvergedReason.ITERATING
+
+
+with open("default_parameters.yml") as f:
+    parameters = yaml.load(f, Loader=yaml.FullLoader)
+
+mesh_size = parameters["geometry"]["lc"]
+parameters["geometry"]["radius"] = 1
+parameters["geometry"]["geom_type"] = "circle"
+
+model_rank = 0
+tdim = 2
+
+gmsh_model, tdim = mesh_circle_gmshapi(
+    parameters["geometry"]["geom_type"], 1, mesh_size, tdim
+)
+mesh, mts, fts = gmshio.model_to_mesh(gmsh_model, comm, model_rank, tdim)
+
+outdir = "output"
+prefix = os.path.join(outdir, "biharmonic")
+order = 3
+
+V = dolfinx.fem.functionspace(mesh, ("Lagrange", order))
+mesh.topology.create_connectivity(mesh.topology.dim - 1, mesh.topology.dim)
+bndry_facets = dolfinx.mesh.exterior_facet_indices(mesh.topology)
+
+dofs = dolfinx.fem.locate_dofs_topological(V=V, entity_dim=1, entities=bndry_facets)
+
+bcs_u = [
+    dolfinx.fem.dirichletbc(value=np.array(0, dtype=PETSc.ScalarType), dofs=dofs, V=V)
+]
+bcs = {"bcs_u": bcs_u}
+u = dolfinx.fem.Function(V)
+D = dolfinx.fem.Constant(mesh, 1.0)
+α = dolfinx.fem.Constant(mesh, 10.0)
+load = dolfinx.fem.Constant(mesh, 1.0)
+h = ufl.CellDiameter(mesh)
+h_avg = (h("+") + h("-")) / 2.0
+
+tdim = mesh.topology.dim
+num_cells = mesh.topology.index_map(tdim).size_local
+_h = dolfinx.cpp.mesh.h(mesh._cpp_object, tdim, np.arange(num_cells, dtype=np.int32))
+
+n = ufl.FacetNormal(mesh)
+
+dx = ufl.Measure("dx")  # volume measure
+ds = ufl.Measure("ds")  # boundary measure
+dS = ufl.Measure("dS")  # interior facet measure
+
+bending = (D / 2 * (inner(div(grad(u)), div(grad(u))))) * dx
+W_ext = load * u * dx
+
+# DG terms implemented as in the paper
+# https://arxiv.org/abs/2501.15959
+
+
+def dg1(u):
+    return 1 / 2 * dot(jump(grad(u)), avg(grad(grad(u)) * n)) * dS
+
+
+def dg2(u):
+    return 1 / 2 * α / avg(h) * inner(jump(grad(u)), jump(grad(u))) * dS
+
+
+def dg3(u):
+    return 1 / 2 * α / h * inner(grad(u), grad(u)) * ds
+
+
+L = bending + dg1(u) + dg2(u) + dg3(u) - W_ext
+F = ufl.derivative(L, u, ufl.TestFunction(V))
+
+
+solver_parameters = {
+    "type": "SNES",
+    "prefix": "biharmonic_",
+    "snes": {
+        # "snes_type": "vinewtonrsls",
+        # "snes_type": "vinewtonssls",
+        "snes_type": "newtontr",
+        "snes_linesearch_type": "basic",
+        "ksp_type": "preonly",
+        "pc_type": "lu",
+        "pc_factor_mat_solver_type": "mumps",
+        "snes_atol": 1.0e-8,
+        "snes_rtol": 1.0e-8,
+        "snes_max_it": 50,
+        "snes_monitor": "",
+    },
+}
+biharmonic = SNESSolver(
+    F,
+    u,
+    bcs.get("bcs_u"),
+    petsc_options=solver_parameters.get("snes"),
+    prefix=solver_parameters.get("prefix"),
+)
+biharmonic.solve()
+
+convergedreason = biharmonic.solver.getConvergedReason()
+iterationnumber = biharmonic.solver.getIterationNumber()
+functionnorm = biharmonic.solver.getFunctionNorm()
+
+assert convergedreason > 0, "Convergence failed"
+assert functionnorm < 1.0e-8, "Function norm too large"
+
+print("Converged reason:", convergedreason)
+print("Iterations:", iterationnumber)
+print("Residual norm:", functionnorm)
+print("Norm of u:", u.x.petsc_vec.norm())