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Add grad-div Vector FE Ex. 10
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‎configure.ac‎

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@@ -480,6 +480,7 @@ AS_IF([test "x$enableexamples" = "xyes"],
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examples/vector_fe/vector_fe_ex7/Makefile
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examples/vector_fe/vector_fe_ex8/Makefile
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examples/vector_fe/vector_fe_ex9/Makefile
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examples/vector_fe/vector_fe_ex10/Makefile
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examples/Makefile])
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])
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‎examples/Makefile.am‎

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@@ -74,7 +74,8 @@ SUBDIRS = \
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vector_fe/vector_fe_ex6 \
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vector_fe/vector_fe_ex7 \
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vector_fe/vector_fe_ex8 \
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vector_fe/vector_fe_ex9
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vector_fe/vector_fe_ex9 \
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vector_fe/vector_fe_ex10
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AUTOMAKE_OPTIONS = subdir-objects
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‎examples/vector_fe/vector_fe_ex10/Makefile.am‎

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example_name = vector_fe_ex10
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check_SCRIPTS = run.sh
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install_dir = $(examples_install_path)/vector_fe/ex10
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data = grad_div_exact_solution.h solution_function.h vector_fe_ex10.C vector_fe_ex10.in run.sh
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sources = $(data)
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CLEANFILES = out.e
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# also need to link files for VPATH builds
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if LIBMESH_VPATH_BUILD
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BUILT_SOURCES = .linkstamp
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.linkstamp:
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-rm -f vector_fe_ex10.in && $(LN_S) -f $(srcdir)/vector_fe_ex10.in .
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$(AM_V_GEN)touch .linkstamp
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CLEANFILES += vector_fe_ex10.in .linkstamp
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endif
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##############################################
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# include common example environment
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include $(top_srcdir)/examples/Make.common

‎examples/vector_fe/vector_fe_ex10/grad_div_exact_solution.h‎

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// The libMesh Finite Element Library.
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// Copyright (C) 2002-2024 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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#ifndef GRAD_DIV_EXACT_SOLUTION_H
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#define GRAD_DIV_EXACT_SOLUTION_H
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#include "libmesh/libmesh_common.h"
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#include "libmesh/vector_value.h"
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using namespace libMesh;
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class GradDivExactSolution
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{
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public:
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GradDivExactSolution() = default;
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~GradDivExactSolution() = default;
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RealGradient operator() (Real x, Real y, Real z)
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{
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libmesh_ignore(z);
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const Real ux = cos(k*x)*sin(k*y);
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const Real uy = sin(k*x)*cos(k*y);
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return RealGradient(ux, uy);
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}
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RealTensor grad(Real x, Real y, Real z)
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{
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libmesh_ignore(z);
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const Real dux_dx = -k*sin(k*x)*sin(k*y);
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const Real dux_dy = k*cos(k*x)*cos(k*y);
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const Real duy_dx = dux_dy;
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const Real duy_dy = dux_dx;
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return RealTensor(dux_dx, dux_dy, Real(0), duy_dx, duy_dy);
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}
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RealGradient forcing(Real x, Real y, Real z)
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{
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return (2*k*k + 1)*operator()(x, y, z);
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}
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private:
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const Real k = pi;
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};
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#endif // GRAD_DIV_EXACT_SOLUTION_H

‎examples/vector_fe/vector_fe_ex10/run.sh‎

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#!/bin/sh
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#set -x
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. "$LIBMESH_DIR"/examples/run_common.sh
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example_name=vector_fe_ex10
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# Note: these problems are particularly ill-conditioned, so we currently
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# resort to a direct solver.
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options="dim=2 element_type=TRI6 -pc_type lu"
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run_example "$example_name" "$options"
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options="dim=2 element_type=TRI7 -pc_type lu"
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run_example "$example_name" "$options"
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options="dim=2 element_type=QUAD8 -pc_type lu"
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run_example "$example_name" "$options"
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options="dim=2 element_type=QUAD9 -pc_type lu"
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run_example "$example_name" "$options"
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options="dim=2 order=3 element_type=TRI6 -pc_type lu"
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run_example "$example_name" "$options"
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options="dim=2 order=3 element_type=TRI7 -pc_type lu"
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run_example "$example_name" "$options"
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options="dim=2 order=3 element_type=QUAD8 -pc_type lu"
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run_example "$example_name" "$options"
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options="dim=2 order=3 element_type=QUAD9 -pc_type lu"
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run_example "$example_name" "$options"
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# Subdividing each hex into 24 tets gets expensive in dbg...
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options="dim=3 element_type=TET14 grid_size=6 -pc_type lu"
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run_example "$example_name" "$options"
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options="dim=3 element_type=HEX27 -pc_type lu"
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run_example "$example_name" "$options"

‎examples/vector_fe/vector_fe_ex10/solution_function.h‎

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// The libMesh Finite Element Library.
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// Copyright (C) 2002-2024 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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#ifndef SOLUTION_FUNCTION_H
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#define SOLUTION_FUNCTION_H
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// libMesh includes
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#include "libmesh/function_base.h"
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// Example includes
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#include "grad_div_exact_solution.h"
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// C++ includes
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#include <memory>
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using namespace libMesh;
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class SolutionFunction : public FunctionBase<Number>
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{
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public:
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SolutionFunction() = default;
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~SolutionFunction() = default;
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virtual Number operator() (const Point &,
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const Real = 0)
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{ libmesh_not_implemented(); }
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virtual void operator() (const Point & p,
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const Real,
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DenseVector<Number> & output)
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{
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output.zero();
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const Real x=p(0), y=p(1), z=p(2);
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output(0) = soln(x, y, z)(0);
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output(1) = soln(x, y, z)(1);
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output(2) = soln(x, y, z)(2);
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}
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virtual Number component(unsigned int component_in,
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const Point & p,
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const Real)
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{
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DenseVector<Number> outvec(3);
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(*this)(p, 0, outvec);
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return outvec(component_in);
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}
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virtual std::unique_ptr<FunctionBase<Number>> clone() const
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{ return std::make_unique<SolutionFunction>(); }
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private:
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GradDivExactSolution soln;
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};
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class SolutionGradient : public FunctionBase<Gradient>
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{
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public:
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SolutionGradient() = default;
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~SolutionGradient() = default;
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virtual Gradient operator() (const Point &, const Real = 0)
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{ libmesh_not_implemented(); }
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virtual void operator() (const Point & p,
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const Real,
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DenseVector<Gradient> & output)
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{
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output.zero();
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const Real x=p(0), y=p(1), z=p(2);
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output(0) = soln.grad(x, y, z).row(0);
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output(1) = soln.grad(x, y, z).row(1);
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output(2) = soln.grad(x, y, z).row(2);
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}
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virtual Gradient component(unsigned int component_in,
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const Point & p,
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const Real)
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{
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DenseVector<Gradient> outvec(3);
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(*this)(p, 0, outvec);
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return outvec(component_in);
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}
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virtual std::unique_ptr<FunctionBase<Gradient>> clone() const
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{ return std::make_unique<SolutionGradient>(); }
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private:
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GradDivExactSolution soln;
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};
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#endif // SOLUTION_FUNCTION_H

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