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// MFEM Example 37 - Serial/Parallel Shared Code
#include "mfem.hpp"
#include <fstream>
#include <iostream>
#include <functional>
namespace mfem
{
/// @brief Inverse sigmoid function
real_t inv_sigmoid(real_t x)
{
real_t tol = 1e-12;
x = std::min(std::max(tol,x), real_t(1.0)-tol);
return std::log(x/(1.0-x));
}
/// @brief Sigmoid function
real_t sigmoid(real_t x)
{
if (x >= 0)
{
return 1.0/(1.0+std::exp(-x));
}
else
{
return std::exp(x)/(1.0+std::exp(x));
}
}
/// @brief Derivative of sigmoid function
real_t der_sigmoid(real_t x)
{
real_t tmp = sigmoid(-x);
return tmp - std::pow(tmp,2);
}
/// @brief Returns f(u(x)) where u is a scalar GridFunction and f:R → R
class MappedGridFunctionCoefficient : public GridFunctionCoefficient
{
protected:
std::function<real_t(const real_t)> fun; // f:R → R
public:
MappedGridFunctionCoefficient()
:GridFunctionCoefficient(),
fun([](real_t x) {return x;}) {}
MappedGridFunctionCoefficient(const GridFunction *gf,
std::function<real_t(const real_t)> fun_,
int comp=1)
:GridFunctionCoefficient(gf, comp),
fun(fun_) {}
real_t Eval(ElementTransformation &T,
const IntegrationPoint &ip) override
{
return fun(GridFunctionCoefficient::Eval(T, ip));
}
void SetFunction(std::function<real_t(const real_t)> fun_) { fun = fun_; }
};
/// @brief Returns f(u(x)) - f(v(x)) where u, v are scalar GridFunctions and f:R → R
class DiffMappedGridFunctionCoefficient : public GridFunctionCoefficient
{
protected:
const GridFunction *OtherGridF;
GridFunctionCoefficient OtherGridF_cf;
std::function<real_t(const real_t)> fun; // f:R → R
public:
DiffMappedGridFunctionCoefficient()
:GridFunctionCoefficient(),
OtherGridF(nullptr),
OtherGridF_cf(),
fun([](real_t x) {return x;}) {}
DiffMappedGridFunctionCoefficient(const GridFunction *gf,
const GridFunction *other_gf,
std::function<real_t(const real_t)> fun_,
int comp=1)
:GridFunctionCoefficient(gf, comp),
OtherGridF(other_gf),
OtherGridF_cf(OtherGridF),
fun(fun_) {}
real_t Eval(ElementTransformation &T,
const IntegrationPoint &ip) override
{
const real_t value1 = fun(GridFunctionCoefficient::Eval(T, ip));
const real_t value2 = fun(OtherGridF_cf.Eval(T, ip));
return value1 - value2;
}
void SetFunction(std::function<real_t(const real_t)> fun_) { fun = fun_; }
};
/// @brief Solid isotropic material penalization (SIMP) coefficient
class SIMPInterpolationCoefficient : public Coefficient
{
protected:
GridFunction *rho_filter;
real_t min_val;
real_t max_val;
real_t exponent;
public:
SIMPInterpolationCoefficient(GridFunction *rho_filter_, real_t min_val_= 1e-6,
real_t max_val_ = 1.0, real_t exponent_ = 3)
: rho_filter(rho_filter_), min_val(min_val_), max_val(max_val_),
exponent(exponent_) { }
real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
{
real_t val = rho_filter->GetValue(T, ip);
real_t coeff = min_val + pow(val,exponent)*(max_val-min_val);
return coeff;
}
};
/// @brief Strain energy density coefficient
class StrainEnergyDensityCoefficient : public Coefficient
{
protected:
Coefficient * lambda=nullptr;
Coefficient * mu=nullptr;
GridFunction *u = nullptr; // displacement
GridFunction *rho_filter = nullptr; // filter density
DenseMatrix grad; // auxiliary matrix, used in Eval
real_t exponent;
real_t rho_min;
public:
StrainEnergyDensityCoefficient(Coefficient *lambda_, Coefficient *mu_,
GridFunction * u_, GridFunction * rho_filter_, real_t rho_min_=1e-6,
real_t exponent_ = 3.0)
: lambda(lambda_), mu(mu_), u(u_), rho_filter(rho_filter_),
exponent(exponent_), rho_min(rho_min_)
{
MFEM_ASSERT(rho_min_ >= 0.0, "rho_min must be >= 0");
MFEM_ASSERT(rho_min_ < 1.0, "rho_min must be > 1");
MFEM_ASSERT(u, "displacement field is not set");
MFEM_ASSERT(rho_filter, "density field is not set");
}
real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
{
real_t L = lambda->Eval(T, ip);
real_t M = mu->Eval(T, ip);
u->GetVectorGradient(T, grad);
real_t div_u = grad.Trace();
real_t density = L*div_u*div_u;
int dim = T.GetSpaceDim();
for (int i=0; i<dim; i++)
{
for (int j=0; j<dim; j++)
{
density += M*grad(i,j)*(grad(i,j)+grad(j,i));
}
}
real_t val = rho_filter->GetValue(T,ip);
return -exponent * pow(val, exponent-1.0) * (1-rho_min) * density;
}
};
/// @brief Volumetric force for linear elasticity
class VolumeForceCoefficient : public VectorCoefficient
{
private:
real_t r;
Vector center;
Vector force;
public:
VolumeForceCoefficient(real_t r_,Vector & center_, Vector & force_) :
VectorCoefficient(center_.Size()), r(r_), center(center_), force(force_) { }
using VectorCoefficient::Eval;
void Eval(Vector &V, ElementTransformation &T,
const IntegrationPoint &ip) override
{
Vector xx; xx.SetSize(T.GetDimension());
T.Transform(ip,xx);
for (int i=0; i<xx.Size(); i++)
{
xx[i]=xx[i]-center[i];
}
real_t cr=xx.Norml2();
V.SetSize(T.GetDimension());
if (cr <= r)
{
V = force;
}
else
{
V = 0.0;
}
}
void Set(real_t r_,Vector & center_, Vector & force_)
{
r=r_;
center = center_;
force = force_;
}
};
/**
* @brief Class for solving Poisson's equation:
*
* - ∇ ⋅(κ ∇ u) = f in Ω
*
*/
class DiffusionSolver
{
private:
Mesh * mesh = nullptr;
int order = 1;
// diffusion coefficient
Coefficient * diffcf = nullptr;
// mass coefficient
Coefficient * masscf = nullptr;
Coefficient * rhscf = nullptr;
Coefficient * essbdr_cf = nullptr;
Coefficient * neumann_cf = nullptr;
VectorCoefficient * gradient_cf = nullptr;
// FEM solver
int dim;
FiniteElementCollection * fec = nullptr;
FiniteElementSpace * fes = nullptr;
Array<int> ess_bdr;
Array<int> neumann_bdr;
GridFunction * u = nullptr;
LinearForm * b = nullptr;
bool parallel;
#ifdef MFEM_USE_MPI
ParMesh * pmesh = nullptr;
ParFiniteElementSpace * pfes = nullptr;
#endif
public:
DiffusionSolver() { }
DiffusionSolver(Mesh * mesh_, int order_, Coefficient * diffcf_,
Coefficient * cf_);
void SetMesh(Mesh * mesh_)
{
mesh = mesh_;
parallel = false;
#ifdef MFEM_USE_MPI
pmesh = dynamic_cast<ParMesh *>(mesh);
if (pmesh) { parallel = true; }
#endif
}
void SetOrder(int order_) { order = order_ ; }
void SetDiffusionCoefficient(Coefficient * diffcf_) { diffcf = diffcf_; }
void SetMassCoefficient(Coefficient * masscf_) { masscf = masscf_; }
void SetRHSCoefficient(Coefficient * rhscf_) { rhscf = rhscf_; }
void SetEssentialBoundary(const Array<int> & ess_bdr_) { ess_bdr = ess_bdr_;};
void SetNeumannBoundary(const Array<int> & neumann_bdr_) { neumann_bdr = neumann_bdr_;};
void SetNeumannData(Coefficient * neumann_cf_) {neumann_cf = neumann_cf_;}
void SetEssBdrData(Coefficient * essbdr_cf_) {essbdr_cf = essbdr_cf_;}
void SetGradientData(VectorCoefficient * gradient_cf_) {gradient_cf = gradient_cf_;}
void ResetFEM();
void SetupFEM();
void Solve();
GridFunction * GetFEMSolution();
LinearForm * GetLinearForm() {return b;}
#ifdef MFEM_USE_MPI
ParGridFunction * GetParFEMSolution();
ParLinearForm * GetParLinearForm()
{
if (parallel)
{
return dynamic_cast<ParLinearForm *>(b);
}
else
{
MFEM_ABORT("Wrong code path. Call GetLinearForm");
return nullptr;
}
}
#endif
~DiffusionSolver();
};
/**
* @brief Class for solving linear elasticity:
*
* -∇ ⋅ σ(u) = f in Ω + BCs
*
* where
*
* σ(u) = λ ∇⋅u I + μ (∇ u + ∇uᵀ)
*
*/
class LinearElasticitySolver
{
private:
Mesh * mesh = nullptr;
int order = 1;
Coefficient * lambda_cf = nullptr;
Coefficient * mu_cf = nullptr;
VectorCoefficient * essbdr_cf = nullptr;
VectorCoefficient * rhs_cf = nullptr;
// FEM solver
int dim;
FiniteElementCollection * fec = nullptr;
FiniteElementSpace * fes = nullptr;
Array<int> ess_bdr;
Array<int> neumann_bdr;
GridFunction * u = nullptr;
LinearForm * b = nullptr;
bool parallel;
#ifdef MFEM_USE_MPI
ParMesh * pmesh = nullptr;
ParFiniteElementSpace * pfes = nullptr;
#endif
public:
LinearElasticitySolver() { }
LinearElasticitySolver(Mesh * mesh_, int order_,
Coefficient * lambda_cf_, Coefficient * mu_cf_);
void SetMesh(Mesh * mesh_)
{
mesh = mesh_;
parallel = false;
#ifdef MFEM_USE_MPI
pmesh = dynamic_cast<ParMesh *>(mesh);
if (pmesh) { parallel = true; }
#endif
}
void SetOrder(int order_) { order = order_ ; }
void SetLameCoefficients(Coefficient * lambda_cf_, Coefficient * mu_cf_) { lambda_cf = lambda_cf_; mu_cf = mu_cf_; }
void SetRHSCoefficient(VectorCoefficient * rhs_cf_) { rhs_cf = rhs_cf_; }
void SetEssentialBoundary(const Array<int> & ess_bdr_) { ess_bdr = ess_bdr_;};
void SetNeumannBoundary(const Array<int> & neumann_bdr_) { neumann_bdr = neumann_bdr_;};
void SetEssBdrData(VectorCoefficient * essbdr_cf_) {essbdr_cf = essbdr_cf_;}
void ResetFEM();
void SetupFEM();
void Solve();
GridFunction * GetFEMSolution();
LinearForm * GetLinearForm() {return b;}
#ifdef MFEM_USE_MPI
ParGridFunction * GetParFEMSolution();
ParLinearForm * GetParLinearForm()
{
if (parallel)
{
return dynamic_cast<ParLinearForm *>(b);
}
else
{
MFEM_ABORT("Wrong code path. Call GetLinearForm");
return nullptr;
}
}
#endif
~LinearElasticitySolver();
};
// Poisson solver
DiffusionSolver::DiffusionSolver(Mesh * mesh_, int order_,
Coefficient * diffcf_, Coefficient * rhscf_)
: mesh(mesh_), order(order_), diffcf(diffcf_), rhscf(rhscf_)
{
#ifdef MFEM_USE_MPI
pmesh = dynamic_cast<ParMesh *>(mesh);
if (pmesh) { parallel = true; }
#endif
SetupFEM();
}
void DiffusionSolver::SetupFEM()
{
dim = mesh->Dimension();
fec = new H1_FECollection(order, dim);
#ifdef MFEM_USE_MPI
if (parallel)
{
pfes = new ParFiniteElementSpace(pmesh, fec);
u = new ParGridFunction(pfes);
b = new ParLinearForm(pfes);
}
else
{
fes = new FiniteElementSpace(mesh, fec);
u = new GridFunction(fes);
b = new LinearForm(fes);
}
#else
fes = new FiniteElementSpace(mesh, fec);
u = new GridFunction(fes);
b = new LinearForm(fes);
#endif
*u=0.0;
if (!ess_bdr.Size())
{
if (mesh->bdr_attributes.Size())
{
ess_bdr.SetSize(mesh->bdr_attributes.Max());
ess_bdr = 1;
}
}
}
void DiffusionSolver::Solve()
{
OperatorPtr A;
Vector B, X;
Array<int> ess_tdof_list;
#ifdef MFEM_USE_MPI
if (parallel)
{
pfes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
}
else
{
fes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
}
#else
fes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
#endif
*u=0.0;
if (b)
{
delete b;
#ifdef MFEM_USE_MPI
if (parallel)
{
b = new ParLinearForm(pfes);
}
else
{
b = new LinearForm(fes);
}
#else
b = new LinearForm(fes);
#endif
}
if (rhscf)
{
b->AddDomainIntegrator(new DomainLFIntegrator(*rhscf));
}
if (neumann_cf)
{
MFEM_VERIFY(neumann_bdr.Size(), "neumann_bdr attributes not provided");
b->AddBoundaryIntegrator(new BoundaryLFIntegrator(*neumann_cf),neumann_bdr);
}
else if (gradient_cf)
{
MFEM_VERIFY(neumann_bdr.Size(), "neumann_bdr attributes not provided");
b->AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(*gradient_cf),
neumann_bdr);
}
b->Assemble();
BilinearForm * a = nullptr;
#ifdef MFEM_USE_MPI
if (parallel)
{
a = new ParBilinearForm(pfes);
}
else
{
a = new BilinearForm(fes);
}
#else
a = new BilinearForm(fes);
#endif
a->AddDomainIntegrator(new DiffusionIntegrator(*diffcf));
if (masscf)
{
a->AddDomainIntegrator(new MassIntegrator(*masscf));
}
a->Assemble();
if (essbdr_cf)
{
u->ProjectBdrCoefficient(*essbdr_cf,ess_bdr);
}
a->FormLinearSystem(ess_tdof_list, *u, *b, A, X, B);
CGSolver * cg = nullptr;
Solver * M = nullptr;
#ifdef MFEM_USE_MPI
if (parallel)
{
M = new HypreBoomerAMG;
dynamic_cast<HypreBoomerAMG*>(M)->SetPrintLevel(0);
cg = new CGSolver(pmesh->GetComm());
}
else
{
M = new GSSmoother((SparseMatrix&)(*A));
cg = new CGSolver;
}
#else
M = new GSSmoother((SparseMatrix&)(*A));
cg = new CGSolver;
#endif
cg->SetRelTol(1e-12);
cg->SetMaxIter(10000);
cg->SetPrintLevel(0);
cg->SetPreconditioner(*M);
cg->SetOperator(*A);
cg->Mult(B, X);
delete M;
delete cg;
a->RecoverFEMSolution(X, *b, *u);
delete a;
}
GridFunction * DiffusionSolver::GetFEMSolution()
{
return u;
}
#ifdef MFEM_USE_MPI
ParGridFunction * DiffusionSolver::GetParFEMSolution()
{
if (parallel)
{
return dynamic_cast<ParGridFunction*>(u);
}
else
{
MFEM_ABORT("Wrong code path. Call GetFEMSolution");
return nullptr;
}
}
#endif
DiffusionSolver::~DiffusionSolver()
{
delete u; u = nullptr;
delete fes; fes = nullptr;
#ifdef MFEM_USE_MPI
delete pfes; pfes=nullptr;
#endif
delete fec; fec = nullptr;
delete b;
}
// Elasticity solver
LinearElasticitySolver::LinearElasticitySolver(Mesh * mesh_, int order_,
Coefficient * lambda_cf_, Coefficient * mu_cf_)
: mesh(mesh_), order(order_), lambda_cf(lambda_cf_), mu_cf(mu_cf_)
{
#ifdef MFEM_USE_MPI
pmesh = dynamic_cast<ParMesh *>(mesh);
if (pmesh) { parallel = true; }
#endif
SetupFEM();
}
void LinearElasticitySolver::SetupFEM()
{
dim = mesh->Dimension();
fec = new H1_FECollection(order, dim,BasisType::Positive);
#ifdef MFEM_USE_MPI
if (parallel)
{
pfes = new ParFiniteElementSpace(pmesh, fec, dim);
u = new ParGridFunction(pfes);
b = new ParLinearForm(pfes);
}
else
{
fes = new FiniteElementSpace(mesh, fec,dim);
u = new GridFunction(fes);
b = new LinearForm(fes);
}
#else
fes = new FiniteElementSpace(mesh, fec, dim);
u = new GridFunction(fes);
b = new LinearForm(fes);
#endif
*u=0.0;
if (!ess_bdr.Size())
{
if (mesh->bdr_attributes.Size())
{
ess_bdr.SetSize(mesh->bdr_attributes.Max());
ess_bdr = 1;
}
}
}
void LinearElasticitySolver::Solve()
{
GridFunction * x = nullptr;
OperatorPtr A;
Vector B, X;
Array<int> ess_tdof_list;
#ifdef MFEM_USE_MPI
if (parallel)
{
x = new ParGridFunction(pfes);
pfes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
}
else
{
x = new GridFunction(fes);
fes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
}
#else
x = new GridFunction(fes);
fes->GetEssentialTrueDofs(ess_bdr,ess_tdof_list);
#endif
*u=0.0;
if (b)
{
delete b;
#ifdef MFEM_USE_MPI
if (parallel)
{
b = new ParLinearForm(pfes);
}
else
{
b = new LinearForm(fes);
}
#else
b = new LinearForm(fes);
#endif
}
if (rhs_cf)
{
b->AddDomainIntegrator(new VectorDomainLFIntegrator(*rhs_cf));
}
b->Assemble();
*x = 0.0;
BilinearForm * a = nullptr;
#ifdef MFEM_USE_MPI
if (parallel)
{
a = new ParBilinearForm(pfes);
}
else
{
a = new BilinearForm(fes);
}
#else
a = new BilinearForm(fes);
#endif
a->AddDomainIntegrator(new ElasticityIntegrator(*lambda_cf, *mu_cf));
a->Assemble();
if (essbdr_cf)
{
u->ProjectBdrCoefficient(*essbdr_cf,ess_bdr);
}
a->FormLinearSystem(ess_tdof_list, *x, *b, A, X, B);
CGSolver * cg = nullptr;
Solver * M = nullptr;
#ifdef MFEM_USE_MPI
if (parallel)
{
M = new HypreBoomerAMG;
dynamic_cast<HypreBoomerAMG*>(M)->SetPrintLevel(0);
cg = new CGSolver(pmesh->GetComm());
}
else
{
M = new GSSmoother((SparseMatrix&)(*A));
cg = new CGSolver;
}
#else
M = new GSSmoother((SparseMatrix&)(*A));
cg = new CGSolver;
#endif
cg->SetRelTol(1e-10);
cg->SetMaxIter(10000);
cg->SetPrintLevel(0);
cg->SetPreconditioner(*M);
cg->SetOperator(*A);
cg->Mult(B, X);
delete M;
delete cg;
a->RecoverFEMSolution(X, *b, *x);
*u+=*x;
delete a;
delete x;
}
GridFunction * LinearElasticitySolver::GetFEMSolution()
{
return u;
}
#ifdef MFEM_USE_MPI
ParGridFunction * LinearElasticitySolver::GetParFEMSolution()
{
if (parallel)
{
return dynamic_cast<ParGridFunction*>(u);
}
else
{
MFEM_ABORT("Wrong code path. Call GetFEMSolution");
return nullptr;
}
}
#endif
LinearElasticitySolver::~LinearElasticitySolver()
{
delete u; u = nullptr;
delete fes; fes = nullptr;
#ifdef MFEM_USE_MPI
delete pfes; pfes=nullptr;
#endif
delete fec; fec = nullptr;
delete b;
}
} // namespace mfem