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feat/AA
RBPoly/mapping.cpp

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feat(mapping): major work on mapping implementation
2026-03-23 15:03:14 -04:00
//region Includes
#include <memory>
#include <mfem.hpp>
#include <print>
#include <format>
#include <string>
#include <functional>
#include <utility>
#include <vector>
#include <cmath>
#include <expected>
#include <CLI/CLI.hpp>
#include <XAD/XAD.hpp>
//endregion
//region Test Utilities
constexpr std::string_view ANSI_GREEN = "\033[32m";
constexpr std::string_view ANSI_RED = "\033[31m";
constexpr std::string_view ANSI_YELLOW = "\033[33m";
constexpr std::string_view ANSI_BLUE = "\033[34m";
constexpr std::string_view ANSI_RESET = "\033[0m";
enum class TEST_RESULT_TYPE : uint8_t {
SUCCESS,
FAILURE,
PARTIAL
};
std::string fmt_test_msg(const std::string_view test_name, const TEST_RESULT_TYPE type, size_t num_fails, size_t total) {
std::string_view color;
switch (type) {
case TEST_RESULT_TYPE::SUCCESS:
color = ANSI_GREEN;
break;
case TEST_RESULT_TYPE::FAILURE:
color = ANSI_RED;
break;
case TEST_RESULT_TYPE::PARTIAL:
color = ANSI_YELLOW;
break;
default:
color = ANSI_RESET;
}
return std::format("{}[TEST: {}] {}/{}{}", color, test_name, total-num_fails, total, ANSI_RESET);
}
//endregion
//region Constants
/********************
* Constants
*********************/
constexpr double G = 1.0;
constexpr double MASS = 1.0;
constexpr double RADIUS = 1.0;
constexpr double CENTRAL_DENSITY = 1.0;
constexpr char HOST[10] = "localhost";
constexpr int PORT = 19916;
//endregion
//region Concepts and Typedefs
/********************
* Concepts
*********************/
template <typename T>
concept is_xad =
std::is_same_v<T, xad::AReal<long double>>
|| std::is_same_v<T, xad::AReal<double>>
|| std::is_same_v<T, xad::AReal<float>>;
template <typename T>
concept is_real = std::is_floating_point_v<T> || is_xad<T>;
/********************
* Type Defs
*********************/
template <is_real T>
using EOS_P = std::function<T(T rho, T temp)>;
//endregion
//region User Argument Structs
/********************
* User Args
*********************/
struct potential {
double tol;
int max_iters;
};
struct rot {
bool enabled;
double omega;
};
struct Args {
std::string mesh_file;
potential p{};
rot r{};
bool verbose{};
double index{};
double mass{};
double c{};
int max_iters{};
double tol{};
};
//endregion
//region Misc Structs
struct OblatePotential {
bool use{false};
double a{1};
double c{1};
double rho_0{1};
};
struct Bounds {
double r_star_ref;
double r_inf_ref;
};
enum BoundsError : uint8_t {
CANNOT_FIND_VACUUM
};
//endregion
//region Domain Enums
enum class Domains : uint8_t {
NONE = 0,
CORE = 1 << 0,
ENVELOPE = 1 << 1,
VACUUM = 1 << 2,
ALL = 0x7
};
inline Domains operator|(Domains lhs, Domains rhs) {
return static_cast<Domains>(static_cast<uint8_t>(lhs) | static_cast<uint8_t>(rhs));
}
inline Domains operator&(Domains lhs, Domains rhs) {
return static_cast<Domains>(static_cast<uint8_t>(lhs) & static_cast<uint8_t>(rhs));
}
const Domains STELLAR = Domains::CORE | Domains::ENVELOPE;
//endregion
//region Domain Mapper
/********************
* Mappers
*********************/
class DomainMapper {
public:
DomainMapper(
const double r_star_ref,
const double r_inf_ref
) :
m_d(nullptr),
m_r_star_ref(r_star_ref),
m_r_inf_ref(r_inf_ref) {}
explicit DomainMapper(
const mfem::GridFunction &d,
const double r_star_ref,
const double r_inf_ref
) :
m_d(&d),
m_dim(d.FESpace()->GetMesh()->Dimension()),
m_r_star_ref(r_star_ref),
m_r_inf_ref(r_inf_ref) {};
[[nodiscard]] bool is_vacuum(const mfem::ElementTransformation &T) const {
if (T.ElementType == mfem::ElementTransformation::ELEMENT) {
return T.Attribute == m_vacuum_attr;
} else if (T.ElementType == mfem::ElementTransformation::BDR_ELEMENT) {
return T.Attribute == m_vacuum_attr - 1; // TODO: In a more robust code this should really be read from the stroid API to ensure that the vacuum boundary is really 1 - the vacuum material attribute
}
return false;
}
void SetDisplacement(const mfem::GridFunction &d) {
if (m_dim != d.FESpace()->GetMesh()->Dimension()) {
const std::string err_msg = std::format("Dimension mismatch: DomainMapper is initialized for dimension {}, but provided displacement field has dimension {}.", m_dim, d.FESpace()->GetMesh()->Dimension());
throw std::invalid_argument(err_msg);
}
m_d = &d;
}
[[nodiscard]] bool IsIdentity() const {
return (m_d == nullptr);
}
void ResetDisplacement() {
m_d = nullptr;
}
void ComputeJacobian(mfem::ElementTransformation &T, mfem::DenseMatrix &J) const {
mfem::DenseMatrix J_D(m_dim, m_dim);
J.SetSize(m_dim, m_dim);
J = 0.0;
J_D = 0.0;
if (IsIdentity()) {
for (int i = 0; i < m_dim; ++i) {
J_D(i, i) = 1.0; // Identity mapping
}
} else {
m_d->GetVectorGradient(T, J_D);
for (int i = 0; i < m_dim; ++i) {
J_D(i, i) += 1.0; // Add identity to get the total Jacobian of the mapping
}
}
if (is_vacuum(T)) {
mfem::Vector x_ref(m_dim);
T.Transform(T.GetIntPoint(), x_ref);
mfem::Vector d_val(m_dim), x_disp(m_dim);
if (IsIdentity()) {
x_disp = x_ref;
} else {
m_d->GetVectorValue(T, T.GetIntPoint(), d_val);
add(x_ref, d_val, x_disp);
}
mfem::DenseMatrix J_K(m_dim, m_dim);
ComputeKelvinJacobian(x_ref, x_disp, J_K);
mfem::Mult(J_K, J_D, J);
} else {
J = J_D;
}
}
double ComputeDetJ(mfem::ElementTransformation& T, const mfem::IntegrationPoint& ip) const {
if (IsIdentity() && !is_vacuum(T)) return 1.0; // If no mapping, the determinant of the Jacobian is 1
mfem::DenseMatrix J;
ComputeJacobian(T, J);
return J.Det();
}
void ComputeMappedDiffusionTensor(mfem::ElementTransformation &T, mfem::DenseMatrix &D) const {
mfem::DenseMatrix J(m_dim, m_dim), JInv(m_dim, m_dim);
ComputeJacobian(T, J);
const double detJ = J.Det();
mfem::CalcInverse(J, JInv);
D.SetSize(m_dim, m_dim);
mfem::MultABt(JInv, JInv, D);
D *= fabs(detJ);
}
void ComputeInverseJacobian(mfem::ElementTransformation &T, mfem::DenseMatrix &JInv) const {
mfem::DenseMatrix J(m_dim, m_dim);
ComputeJacobian(T, J);
JInv.SetSize(m_dim, m_dim);
mfem::CalcInverse(J, JInv);
}
void GetPhysicalPoint(mfem::ElementTransformation& T, const mfem::IntegrationPoint& ip, mfem::Vector& x_phys) const {
x_phys.SetSize(m_dim);
mfem::Vector x_ref(m_dim);
T.Transform(ip, x_ref);
if (IsIdentity()) {
x_phys = x_ref;
} else {
mfem::Vector d_val(m_dim);
m_d->GetVectorValue(T, ip, d_val);
add(x_ref, d_val, x_phys);
}
if (is_vacuum(T)) {
ApplyKelvinMapping(x_ref, x_phys);
}
}
[[nodiscard]] const mfem::GridFunction* GetDisplacement() const { return m_d; }
private:
void ApplyKelvinMapping(const mfem::Vector& x_ref, mfem::Vector& x_phys) const {
const double r_ref = x_ref.Norml2();
double xi = (r_ref - m_r_star_ref) / (m_r_inf_ref - m_r_star_ref);
xi = std::clamp(xi, 0.0, m_xi_clamp);
const double factor = m_r_star_ref / (r_ref * (1 - xi));
x_phys *= factor;
}
void ComputeKelvinJacobian(const mfem::Vector& x_ref, const mfem::Vector &x_disp, mfem::DenseMatrix& J_K) const {
const double r_ref = x_ref.Norml2();
const double delta_R = m_r_inf_ref - m_r_star_ref;
double xi = (r_ref - m_r_star_ref) / delta_R;
xi = std::clamp(xi, 0.0, m_xi_clamp);
const double denom = 1.0 - xi;
const double k = m_r_star_ref / (r_ref * denom);
const double dk_dr = m_r_star_ref * (( 1.0 / (delta_R* r_ref * denom * denom)) - ( 1.0 / (r_ref * r_ref * denom)));
J_K.SetSize(m_dim, m_dim);
const double outer_factor = dk_dr / r_ref;
for (int i = 0; i < m_dim; ++i) {
for (int j = 0; j < m_dim; ++j) {
J_K(i, j) = outer_factor * x_disp(i) * x_ref(j);
if (i == j) {
J_K(i, j) += k;
}
}
}
}
private:
const mfem::GridFunction *m_d;
std::unique_ptr<mfem::GridFunction> m_internal_d;
const int m_dim{3};
const int m_vacuum_attr{3};
const double m_r_star_ref{1.0};
const double m_r_inf_ref{2.0};
const double m_xi_clamp{0.999};
};
//endregion
//region State Types
/********************
* State Types
*********************/
struct FEM {
std::unique_ptr<mfem::Mesh> mesh;
std::unique_ptr<mfem::FiniteElementCollection> H1_fec;
std::unique_ptr<mfem::FiniteElementSpace> H1_fes;
std::unique_ptr<mfem::FiniteElementSpace> Vec_H1_fes;
std::unique_ptr<DomainMapper> mapping;
mfem::Array<int> block_offsets;
std::unique_ptr<mfem::GridFunction> reference_x;
mfem::Vector com;
mfem::DenseMatrix Q;
mfem::Array<int> ess_tdof_x;
std::unique_ptr<mfem::Array<int>> star_marker;
std::unique_ptr<mfem::Array<int>> vacuum_marker;
std::unique_ptr<mfem::Array<int>> surface_marker;
std::unique_ptr<mfem::Array<int>> inf_marker;
[[nodiscard]] bool okay() const { return (mesh != nullptr) && (H1_fec != nullptr) && (H1_fes != nullptr) && (Vec_H1_fes != nullptr); }
[[nodiscard]] bool has_mapping() const { return mapping != nullptr; }
};
struct CoupledState {
std::unique_ptr<mfem::BlockVector> U;
mfem::GridFunction rho;
mfem::GridFunction d; // Stability depends on solving for the displacement vector not the nodal position vector, those live on a reference domain.
explicit CoupledState(const FEM& fem) {
U = std::make_unique<mfem::BlockVector>(fem.block_offsets);
rho.MakeRef(fem.H1_fes.get(), U->GetBlock(0), 0);
d.MakeRef(fem.Vec_H1_fes.get(), U->GetBlock(1), 0);
*U = 0.0;
U->GetBlock(2) = 1.0;
}
};
//endregion
//region Function Definitions
/********************
* Core Setup Functions
*********************/
FEM setup_fem(const std::string& filename, bool verbose=true);
/********************
* Utility Functions
*********************/
void view_mesh(const std::string& host, int port, const mfem::Mesh& mesh, const mfem::GridFunction& gf, const std::string& title);
double domain_integrate_grid_function(const FEM& fem, const mfem::GridFunction& gf, Domains domain = Domains::ALL);
mfem::Vector get_com(const FEM& fem, const mfem::GridFunction &rho);
void get_physical_coordinates(const mfem::GridFunction& reference_pos, const mfem::GridFunction& displacement, mfem::GridFunction& physical_pos);
void populate_element_mask(const FEM& fem, Domains domain, mfem::Array<int>& mask);
std::expected<Bounds, BoundsError> DiscoverBounds(const mfem::Mesh *mesh, int vacuum_attr);
/********************
* Physics Functions
*********************/
double centrifugal_potential(const mfem::Vector& phys_x, double omega);
double get_moment_of_inertia(const FEM& fem, const mfem::GridFunction& rho);
double oblate_spheroid_surface_potential(const mfem::Vector& x, double a, double c, double total_mass);
std::unique_ptr<mfem::GridFunction> grav_potential(const FEM& fem, const Args &args, const mfem::GridFunction& rho);
std::unique_ptr<mfem::GridFunction> get_potential(const FEM& fem, const Args& args, const mfem::GridFunction& rho);
mfem::DenseMatrix compute_quadrupole_moment_tensor(const FEM& fem, const mfem::GridFunction& rho, const mfem::Vector& com);
double l2_multipole_potential(const FEM& fem, double total_mass, const mfem::Vector& phys_x);
/********************
* Conservation Functions
*********************/
void conserve_mass(const FEM& fem, mfem::GridFunction& rho, double target_mass);
//endregion
//region Mapping Coefficients
class MappedScalarCoefficient : public mfem::Coefficient {
public:
enum class EVAL_POINTS : uint8_t {
PHYSICAL,
REFERENCE
};
MappedScalarCoefficient(
const DomainMapper& map,
mfem::Coefficient& coeff,
const EVAL_POINTS eval_point=EVAL_POINTS::PHYSICAL
) :
m_map(map),
m_coeff(coeff),
m_eval_point(eval_point) {};
double Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
T.SetIntPoint(&ip);
double detJ = m_map.ComputeDetJ(T, ip);
double f_val = 0.0;
switch (m_eval_point) {
case EVAL_POINTS::PHYSICAL: {
f_val = eval_at_point(m_coeff, T, ip);
break;
}
case EVAL_POINTS::REFERENCE: {
f_val = m_coeff.Eval(T, ip);
break;
}
}
return f_val * fabs(detJ);
}
private:
static double eval_at_point(mfem::Coefficient& c, mfem::ElementTransformation& T, const mfem::IntegrationPoint& ip) {
return c.Eval(T, ip);
}
private:
const DomainMapper& m_map;
mfem::Coefficient& m_coeff;
EVAL_POINTS m_eval_point;
};
class MappedDiffusionCoefficient : public mfem::MatrixCoefficient {
public:
MappedDiffusionCoefficient(
const DomainMapper& map,
mfem::Coefficient& sigma,
const int dim
) :
mfem::MatrixCoefficient(dim),
m_map(map),
m_scalar(&sigma),
m_tensor(nullptr) {};
MappedDiffusionCoefficient(
const DomainMapper& map,
mfem::MatrixCoefficient& sigma
) :
mfem::MatrixCoefficient(sigma.GetHeight()),
m_map(map),
m_scalar(nullptr),
m_tensor(&sigma) {};
void Eval(mfem::DenseMatrix &K, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
const int dim = height;
T.SetIntPoint(&ip);
mfem::DenseMatrix J(dim, dim), JInv(dim, dim);
m_map.ComputeJacobian(T, J);
const double detJ = J.Det();
mfem::CalcInverse(J, JInv);
if (m_scalar) {
const double sig_val = m_scalar->Eval(T, ip);
mfem::MultABt(JInv, JInv, K);
K *= sig_val * fabs(detJ);
} else {
mfem::DenseMatrix sig_mat(dim, dim);
m_tensor->Eval(sig_mat, T, ip);
mfem::DenseMatrix temp(dim, dim);
Mult(JInv, sig_mat, temp);
MultABt(temp, JInv, K);
K *= fabs(detJ);
}
}
private:
const DomainMapper& m_map;
mfem::Coefficient* m_scalar;
mfem::MatrixCoefficient* m_tensor;
};
class MappedVectorCoefficient : public mfem::VectorCoefficient {
public:
MappedVectorCoefficient(
const DomainMapper& map,
mfem::VectorCoefficient& coeff
) :
mfem::VectorCoefficient(coeff.GetVDim()),
m_map(map),
m_coeff(coeff) {};
void Eval(mfem::Vector& V, mfem::ElementTransformation& T, const mfem::IntegrationPoint& ip) override {
const int dim = vdim;
T.SetIntPoint(&ip);
mfem::DenseMatrix JInv(dim, dim);
m_map.ComputeInverseJacobian(T, JInv);
double detJ = m_map.ComputeDetJ(T, ip);
mfem::Vector C_phys(dim);
m_coeff.Eval(C_phys, T, ip);
V.SetSize(dim);
JInv.Mult(C_phys, V);
V *= fabs(detJ);
}
private:
const DomainMapper& m_map;
mfem::VectorCoefficient& m_coeff;
};
class PhysicalPositionFunctionCoefficient : public mfem::Coefficient {
public:
using Func = std::function<double(const mfem::Vector& x)>;
PhysicalPositionFunctionCoefficient(
const DomainMapper& map,
Func f
) :
m_f(std::move(f)),
m_map(map) {};
double Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
T.SetIntPoint(&ip);
mfem::Vector x;
m_map.GetPhysicalPoint(T, ip, x);
return m_f(x);
}
private:
Func m_f;
const DomainMapper& m_map;
};
//endregion
//region Integrators
/********************
* Integrators
*********************/
template <is_xad EOS_T>
class FluidIntegrator : public mfem::NonlinearFormIntegrator {
using Scalar = EOS_T::value_type;
public:
explicit FluidIntegrator(
EOS_P<EOS_T> eos,
const DomainMapper* map = nullptr
) :
m_eos(std::move(eos)),
m_map(map)
{};
void AssembleElementVector(
const mfem::FiniteElement &el,
mfem::ElementTransformation &Tr,
const mfem::Vector &elfun,
mfem::Vector &elvect
) override {
const int dof = el.GetDof();
elvect.SetSize(dof);
elvect = 0.0;
const mfem::IntegrationRule *ir = IntRule ? IntRule : &mfem::IntRules.Get(el.GetGeomType(), 2 * el.GetOrder() + 1);
mfem::Vector shape(dof);
for (int i = 0; i < ir->GetNPoints(); i++) {
const mfem::IntegrationPoint& ip = ir->IntPoint(i);
Tr.SetIntPoint(&ip);
el.CalcShape(ip, shape);
double u = shape * elfun;
EOS_T rho = u;
const double val = m_eos(rho, 0.0).value();
double weight = ip.weight * Tr.Weight() * val;
if (m_map) weight *= fabs(m_map->ComputeDetJ(Tr, ip));
elvect.Add(weight, shape);
}
}
void AssembleElementGrad(
const mfem::FiniteElement &el,
mfem::ElementTransformation &Tr,
const mfem::Vector &elfun,
mfem::DenseMatrix &elmat
) override {
const int dof = el.GetDof();
elmat.SetSize(dof);
elmat = 0.0;
const mfem::IntegrationRule *ir = IntRule ? IntRule : &mfem::IntRules.Get(el.GetGeomType(), 2 * el.GetOrder() + 1);
mfem::Vector shape(dof);
for (int i = 0; i < ir->GetNPoints(); i++) {
const mfem::IntegrationPoint& ip = ir->IntPoint(i);
Tr.SetIntPoint(&ip);
el.CalcShape(ip, shape);
double u = shape * elfun;
double d_val_d_rho = 0.0;
if (u > 1e-15) {
xad::Tape<Scalar> tape;
EOS_T x_r = u;
EOS_T x_t = 0.0; // In future this is one area where we introduce a temp dependency
tape.registerInput(x_r);
EOS_T result = m_eos(x_r, x_t);
tape.registerOutput(result);
result.setAdjoint(1.0);
tape.computeAdjoints();
d_val_d_rho = x_r.getAdjoint();
}
double weight = ip.weight * Tr.Weight() * d_val_d_rho;
if (m_map) weight *= fabs(m_map->ComputeDetJ(Tr, ip));
mfem::AddMult_a_VVt(weight, shape, elmat);
}
}
[[nodiscard]] bool has_mapping() const { return m_map != nullptr; }
void set_mapping(const DomainMapper* map) { m_map = map; }
void clear_mapping() { m_map = nullptr; }
private:
EOS_P<EOS_T> m_eos;
const DomainMapper* m_map{nullptr};
};
//endregion
//region Coefficients
/********************
* Coefficient Defs
*********************/
template <is_xad EOS_T>
class PressureBoundaryForce : public mfem::VectorCoefficient {
public:
PressureBoundaryForce(
const int dim,
const FEM& fem,
const mfem::GridFunction& rho,
const EOS_P<EOS_T>& eos,
const double P_fit
) : VectorCoefficient(dim), m_fem(fem), m_rho(rho), m_eos(eos), m_P_fit(P_fit) {};
void Eval(mfem::Vector &V, mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
V.SetSize(vdim);
V = 0.0;
double rho = m_rho.GetValue(T, ip);
EOS_T x_rho = rho;
const double P_curr = m_eos(x_rho, 0.0).value();
const double delta_P = P_curr - m_P_fit;
mfem::Vector phys(vdim);
T.Transform(ip, phys);
mfem::Vector normal(vdim);
mfem::CalcOrtho(T.Jacobian(), normal);
for (int i = 0; i < vdim; ++i) {
V(i) = delta_P * normal(i);
}
}
private:
const FEM& m_fem;
const mfem::GridFunction& m_rho;
const EOS_P<EOS_T>& m_eos;
double m_P_fit;
};
template <is_xad EOS_T>
class MappingDetJacobianCoefficient : public mfem::Coefficient {
public:
MappingDetJacobianCoefficient(
const mfem::GridFunction& d,
const mfem::FiniteElementSpace& fes
) :
m_d(d),
m_fes(fes) {}
double Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) override {
const int dim = T.GetSpaceDim();
mfem::DenseMatrix grad_d(dim, dim);
m_d.GetVectorGradient(T, grad_d);
for (int i = 0; i < dim; ++i) {
grad_d(i, i) += 1.0;
}
return grad_d.Det();
}
private:
const mfem::GridFunction& m_d; // Displacement vector
const mfem::FiniteElementSpace &m_fes;
};
//endregion
//region Operators
/********************
* Operator Defs
*********************/
template <is_xad EOS_T>
class VectorOperator : public mfem::Operator {
public:
VectorOperator() = default;
VectorOperator(
const mfem::Vector& v,
const bool is_col
) :
Operator(is_col ? v.Size() : 1, is_col ? 1 : v.Size()),
m_v(v),
m_is_col(is_col),
m_is_initialized(true) {}
void SetVector(const mfem::Vector& v, const bool is_col) {
if (v.Size() != m_v.Size()) {
m_v.SetSize(v.Size());
}
m_v = v;
m_is_col = is_col;
height = is_col ? v.Size() : 1;
width = is_col ? 1 : v.Size();
m_is_initialized = true;
}
void Mult(const mfem::Vector &x, mfem::Vector &y) const override {
if (!m_is_initialized) throw std::runtime_error("VectorOperator Not initialized");
if (m_is_col) {
y.SetSize(m_v.Size());
y = 0.0;
y.Add(x(0), m_v);
} else {
y.SetSize(1);
y(0) = m_v * x;
}
}
private:
mfem::Vector m_v;
bool m_is_col{false};
bool m_is_initialized{false};
};
template <is_xad EOS_T>
class PressureDensityCoupling : public mfem::Operator {
public:
PressureDensityCoupling(
FEM& fem,
const mfem::GridFunction& rho,
const EOS_P<EOS_T>& eos_pressure)
: Operator(fem.Vec_H1_fes->GetTrueVSize(), fem.H1_fes->GetTrueVSize()),
m_fem(fem),
m_rho(rho),
m_eos(eos_pressure) {
Assemble();
}
void Assemble() {
const int dim = m_fem.mesh->Dimension();
const int scalar_size = m_fem.H1_fes->GetTrueVSize();
const int vector_size = m_fem.Vec_H1_fes->GetTrueVSize();
m_mat = std::make_unique<mfem::SparseMatrix>(vector_size, scalar_size);
for (int be = 0; be < m_fem.mesh->GetNBE(); ++be) {
auto* ftr = m_fem.mesh->GetBdrFaceTransformations(be);
if (!ftr) continue;
const int elem = ftr->Elem1No;
const auto& scalar_fe = *m_fem.H1_fes->GetFE(elem);
const int sdof = scalar_fe.GetDof();
mfem::Array<int> scalar_dofs, vector_dofs;
m_fem.H1_fes->GetElementDofs(elem, scalar_dofs);
m_fem.Vec_H1_fes->GetElementDofs(elem, vector_dofs);
mfem::DenseMatrix elmat(vector_dofs.Size(), scalar_dofs.Size());
elmat = 0.0;
const auto& face_ir = mfem::IntRules.Get(ftr->GetGeometryType(), 2 * scalar_fe.GetOrder() + 2);
mfem::Vector shape(sdof);
mfem::Vector normal(dim);
for (int q = 0; q < face_ir.GetNPoints(); ++q) {
const auto& face_ip = face_ir.IntPoint(q);
ftr->SetAllIntPoints(&face_ip);
const mfem::IntegrationPoint& vol_ip = ftr->GetElement1IntPoint();
scalar_fe.CalcShape(vol_ip, shape);
mfem::CalcOrtho(ftr->Face->Jacobian(), normal);
mfem::ElementTransformation& vol_trans = ftr->GetElement1Transformation();
vol_trans.SetIntPoint(&vol_ip);
double rho_val = m_rho.GetValue(vol_trans, vol_ip);
double dPdrho = 0.0;
if (rho_val > 1e-15) {
using Scalar = EOS_T::value_type;
xad::Tape<Scalar> tape;
EOS_T x_rho = rho_val;
tape.registerInput(x_rho);
EOS_T P = m_eos(x_rho, EOS_T(0.0));
tape.registerOutput(P);
P.setAdjoint(1.0);
tape.computeAdjoints();
dPdrho = x_rho.getAdjoint();
}
const double w = face_ip.weight;
for (int k = 0; k < sdof; ++k) {
for (int j = 0; j < sdof; ++j) {
double base = -dPdrho * shape(j) * shape(k) * w;
for (int c = 0; c < dim; ++c) {
elmat(k + c * sdof, j) += base * normal(c);
}
}
}
}
m_mat->AddSubMatrix(vector_dofs, scalar_dofs, elmat);
}
m_mat->Finalize();
}
void Mult(const mfem::Vector &x, mfem::Vector &y) const override {
m_mat->Mult(x, y);
}
[[nodiscard]] mfem::SparseMatrix& SpMat() const { return *m_mat; }
private:
FEM& m_fem;
const mfem::GridFunction& m_rho;
const EOS_P<EOS_T>& m_eos;
std::unique_ptr<mfem::SparseMatrix> m_mat;
};
template <is_xad EOS_T>
class MassDisplacementCoupling : public mfem::Operator {
public:
MassDisplacementCoupling(
FEM& fem,
const mfem::GridFunction& rho,
const bool is_col
) :
Operator(
is_col ? fem.Vec_H1_fes->GetTrueVSize() : 1,
is_col ? 1 : fem.Vec_H1_fes->GetTrueVSize()
),
m_fem(fem),
m_rho(rho),
m_is_col(is_col){
m_D.SetSize(m_fem.Vec_H1_fes->GetTrueVSize());
Assemble();
}
void Assemble() const {
const int dim = m_fem.mesh->Dimension();
m_D = 0.0;
for (int elemID = 0; elemID < m_fem.mesh->GetNE(); ++elemID) {
auto* trans = m_fem.mesh->GetElementTransformation(elemID);
const auto& fe = *m_fem.Vec_H1_fes->GetFE(elemID);
const int dof = fe.GetDof();
mfem::Array<int> vdofs;
m_fem.Vec_H1_fes->GetElementDofs(elemID, vdofs);
const auto& ir = mfem::IntRules.Get(trans->GetGeometryType(), 2 * fe.GetOrder() + 1);
mfem::DenseMatrix dshape(dof, dim);
mfem::Vector elvec(dof * dim);
elvec = 0.0;
for (int q = 0; q < ir.GetNPoints(); ++q) {
const auto& ip = ir.IntPoint(q);
trans->SetIntPoint(&ip);
fe.CalcPhysDShape(*trans, dshape);
double rho_val = m_rho.GetValue(elemID, ip);
double ref_weight = trans->Weight() * ip.weight;
mfem::DenseMatrix J_map(dim, dim), J_inv(dim, dim);
m_fem.mapping->ComputeJacobian(*trans, J_map);
double detJ = J_map.Det();
mfem::CalcInverse(J_map, J_inv);
for (int k = 0; k < dof; ++k) {
for (int c = 0; c < dim; ++c) {
double trace_contrib = 0.0;
for (int j = 0; j < dim; ++j) {
trace_contrib += J_inv(j, c) * dshape(k, j);
}
elvec(k + c * dof) += rho_val * fabs(detJ) * trace_contrib * ref_weight;
}
}
}
m_D.AddElementVector(vdofs, elvec);
}
}
[[nodiscard]] mfem::Vector& GetVec() const {
return m_D;
}
void Mult(const mfem::Vector &x, mfem::Vector &y) const override {
if (m_is_col) {
y.SetSize(m_D.Size());
y = 0.0;
y.Add(x(0), m_D);
} else {
y.SetSize(1);
y(0) = m_D * x;
}
}
private:
const FEM& m_fem;
const mfem::GridFunction& m_rho;
const bool m_is_col;
mutable mfem::Vector m_D;
};
template <is_xad EOS_T>
class ResidualOperator : public mfem::Operator {
public:
ResidualOperator(
FEM& fem,
const Args& args,
const EOS_P<EOS_T>& eos_enthalpy,
const EOS_P<EOS_T>& eos_pressure,
const double alpha
) :
Operator(fem.block_offsets.Last()),
m_fem(fem),
m_args(args),
m_eos_enthalpy(eos_enthalpy),
m_eos_pressure(eos_pressure),
m_alpha(std::make_unique<mfem::ConstantCoefficient>(alpha)),
m_fluid_nlf(m_fem.H1_fes.get()),
m_reference_stiffness(m_fem.Vec_H1_fes.get())
{
m_fluid_nlf.AddDomainIntegrator(new FluidIntegrator<EOS_T>(m_eos_enthalpy, m_fem.mapping.get()));
m_reference_stiffness.AddDomainIntegrator(new mfem::VectorMassIntegrator(*m_alpha));
m_reference_stiffness.AddDomainIntegrator(new mfem::VectorDiffusionIntegrator());
m_reference_stiffness.Assemble();
m_reference_stiffness.Finalize();
std::println("ResidualOperator initialized with XAD-enabled FluidIntegrator and reference stiffness.");
};
void Mult(const mfem::Vector &u, mfem::Vector &r) const override {
mfem::GridFunction rho, d;
rho.MakeRef(m_fem.H1_fes.get(), u.GetData() + m_fem.block_offsets[0]);
d.MakeRef(m_fem.Vec_H1_fes.get(), u.GetData() + m_fem.block_offsets[1]);
double lambda = u(m_fem.block_offsets[2]);
m_fem.mapping->SetDisplacement(d);
m_fem.com = get_com(m_fem, rho);
m_fem.Q = compute_quadrupole_moment_tensor(m_fem, rho, m_fem.com);
mfem::GridFunction r_rho, r_d;
r_rho.MakeRef(m_fem.H1_fes.get(), r.GetData() + m_fem.block_offsets[0]);
r_d.MakeRef(m_fem.Vec_H1_fes.get(), r.GetData() + m_fem.block_offsets[1]);
double &r_lambda = r(m_fem.block_offsets[2]);
m_fluid_nlf.Mult(rho, r_rho);
auto phi = get_potential(m_fem, m_args, rho);
mfem::GridFunctionCoefficient phi_c(phi.get());
MappedScalarCoefficient mapped_phi_c(*m_fem.mapping, phi_c);
mfem::LinearForm phi_lf(m_fem.H1_fes.get());
phi_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(mapped_phi_c));
phi_lf.Assemble();
r_rho += phi_lf;
mfem::ConstantCoefficient lambda_c(lambda);
MappedScalarCoefficient mapped_lambda_c(*m_fem.mapping, lambda_c);
mfem::LinearForm mass_grad_lf(m_fem.H1_fes.get());
mass_grad_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(mapped_lambda_c));
mass_grad_lf.Assemble();
// ReSharper disable once CppDFAUnusedValue
r_rho += mass_grad_lf;
m_reference_stiffness.Mult(d, r_d);
PressureBoundaryForce<EOS_T> pbf(
m_fem.H1_fes->GetMesh()->Dimension(),
m_fem,
rho,
m_eos_pressure,
m_args.c
);
mfem::LinearForm pbf_lf(m_fem.Vec_H1_fes.get());
pbf_lf.AddBoundaryIntegrator(new mfem::VectorBoundaryLFIntegrator(pbf));
pbf_lf.Assemble();
r_d -= pbf_lf;
for (int i = 0; i < m_fem.ess_tdof_x.Size(); ++i) {
r_d(m_fem.ess_tdof_x[i]) = 0.0;
}
double current_mass = domain_integrate_grid_function(m_fem, rho);
r_lambda = current_mass - m_args.mass;
}
[[nodiscard]] Operator& GetGradient(const mfem::Vector &u) const override {
mfem::GridFunction rho, d;
rho.MakeRef(m_fem.H1_fes.get(), u.GetData() + m_fem.block_offsets[0]);
d.MakeRef(m_fem.Vec_H1_fes.get(), u.GetData() + m_fem.block_offsets[1]);
m_fem.mapping->SetDisplacement(d);
m_approx_jacobian = std::make_unique<mfem::BlockOperator>(m_fem.block_offsets);
const mfem::GridFunction grad(m_fem.Vec_H1_fes.get(), u.GetData() + m_fem.block_offsets[1]);
// m_fem.mesh->SetNodes(grad);
m_approx_jacobian->SetBlock(0, 0, &m_fluid_nlf.GetGradient(rho));
m_approx_jacobian->SetBlock(1, 1, &m_reference_stiffness);
B_vec.SetSize(m_fem.H1_fes->GetTrueVSize());
B_vec = 0.0;
mfem::ConstantCoefficient one(1.0);
MappedScalarCoefficient mapped_b_vec(*m_fem.mapping, one);
mfem::LinearForm b_lf(m_fem.H1_fes.get());
b_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(mapped_b_vec));
b_lf.Assemble();
B_vec += b_lf;
m_B_vec_op_col.SetVector(B_vec, true);
m_B_vec_op_row.SetVector(B_vec, false);
m_approx_jacobian->SetBlock(0, 2, &m_B_vec_op_col);
m_approx_jacobian->SetBlock(2, 0, &m_B_vec_op_row);
m_C = std::make_unique<PressureDensityCoupling<EOS_T>>(m_fem, rho, m_eos_pressure);
m_D = std::make_unique<MassDisplacementCoupling<EOS_T>>(m_fem, rho, false);
m_approx_jacobian->SetBlock(1, 0, m_C.get());
m_approx_jacobian->SetBlock(2, 1, m_D.get());
return *m_approx_jacobian;
}
private:
FEM& m_fem;
const Args& m_args;
const EOS_P<EOS_T>& m_eos_enthalpy;
const EOS_P<EOS_T>& m_eos_pressure;
const std::unique_ptr<mfem::ConstantCoefficient> m_alpha;
mutable mfem::NonlinearForm m_fluid_nlf;
mutable mfem::BilinearForm m_reference_stiffness;
mutable std::unique_ptr<mfem::BlockOperator> m_approx_jacobian = nullptr;
mutable mfem::Vector B_vec;
mutable VectorOperator<EOS_T> m_B_vec_op_col;
mutable VectorOperator<EOS_T> m_B_vec_op_row;
mutable std::unique_ptr<PressureDensityCoupling<EOS_T>> m_C;
mutable std::unique_ptr<MassDisplacementCoupling<EOS_T>> m_D;
};
//endregion
//region Utility Functions
FEM setup_fem(const std::string& filename, const bool verbose) {
FEM fem;
fem.mesh = std::make_unique<mfem::Mesh>(filename, 0, 0);
fem.mesh->EnsureNodes();
int dim = fem.mesh->Dimension();
fem.H1_fec = std::make_unique<mfem::H1_FECollection>(2, dim);
fem.H1_fes = std::make_unique<mfem::FiniteElementSpace>(fem.mesh.get(), fem.H1_fec.get());
fem.Vec_H1_fes = std::make_unique<mfem::FiniteElementSpace>(fem.mesh.get(), fem.H1_fec.get(), dim, mfem::Ordering::byNODES);
auto [r_star_ref, r_inf_ref] = DiscoverBounds(fem.mesh.get(), 3)
.or_else([](const BoundsError& err)->std::expected<Bounds, BoundsError> {
throw std::runtime_error("Unable to determine vacuum domain reference boundary...");
}).value();
fem.mapping = std::make_unique<DomainMapper>(r_star_ref, r_inf_ref);
fem.block_offsets.SetSize(4);
fem.block_offsets[0] = 0;
fem.block_offsets[1] = fem.H1_fes->GetTrueVSize();
fem.block_offsets[2] = fem.block_offsets[1] + fem.Vec_H1_fes->GetTrueVSize();
fem.block_offsets[3] = fem.block_offsets[2] + 1;
// Setup Domain Markers to constrain integration
fem.star_marker = std::make_unique<mfem::Array<int>>(fem.mesh->attributes.Max());
fem.star_marker->operator=(0);
fem.star_marker.operator->()[0] = 1; // core
fem.star_marker.operator->()[1] = 1; // envelope
fem.vacuum_marker = std::make_unique<mfem::Array<int>>(fem.mesh->attributes.Max());
fem.vacuum_marker->operator=(0);
fem.vacuum_marker.operator->()[2] = 1; // vacuum
fem.surface_marker = std::make_unique<mfem::Array<int>>(fem.mesh->bdr_attributes.Max());
fem.surface_marker->operator=(0);
fem.surface_marker.operator->()[0] = 1; // surface
fem.vacuum_marker = std::make_unique<mfem::Array<int>>(fem.mesh->bdr_attributes.Max());
fem.vacuum_marker->operator=(0);
fem.vacuum_marker.operator->()[1] = 1; // Infinity
// Initial COM should be 0, initial mass distribution should be uniform
fem.com.SetSize(dim); fem.com = 0.0;
fem.Q.SetSize(dim, dim); fem.Q = 0.0;
fem.reference_x = std::make_unique<mfem::GridFunction>(fem.Vec_H1_fes.get());
fem.mesh->GetNodes(*fem.reference_x);
fem.ess_tdof_x.SetSize(0); // No essential boundary conditions for the displacement, the null space here is handled with a weak penalty term
return fem;
}
void view_mesh(const std::string& host, int port, const mfem::Mesh& mesh, const mfem::GridFunction& gf, const std::string& title) {
mfem::socketstream sol_sock(host.c_str(), port);
if (!sol_sock.is_open()) return;
sol_sock << "solution\n" << mesh << gf;
sol_sock << "window_title '" << title << "'\n" << std::flush;
}
double domain_integrate_grid_function(const FEM& fem, const mfem::GridFunction& gf, Domains domain) {
mfem::LinearForm lf(fem.H1_fes.get());
mfem::GridFunctionCoefficient gf_c(&gf);
double integral;
mfem::Array<int> elem_markers;
populate_element_mask(fem, domain, elem_markers);
if (fem.has_mapping()) {
MappedScalarCoefficient mapped_gf_c(*fem.mapping, gf_c);
lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(mapped_gf_c), elem_markers);
lf.Assemble();
integral = lf.Sum();
} else {
lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(gf_c), elem_markers);
lf.Assemble();
integral = lf.Sum();
}
return integral;
}
mfem::Vector get_com(const FEM& fem, const mfem::GridFunction &rho) {
const int dim = fem.mesh->Dimension();
mfem::Vector com(dim);
com = 0.0;
double total_mass = 0.0;
for (int i = 0; i < fem.H1_fes->GetNE(); ++i) {
mfem::ElementTransformation *trans = fem.H1_fes->GetElementTransformation(i);
const mfem::IntegrationRule &ir = mfem::IntRules.Get(trans->GetGeometryType(), fem.H1_fes->GetOrder(0) + trans->OrderW());
for (int j = 0; j < ir.GetNPoints(); ++j) {
const mfem::IntegrationPoint &ip = ir.IntPoint(j);
trans->SetIntPoint(&ip);
double weight = trans->Weight() * ip.weight;
if (fem.has_mapping()) {
weight *= fem.mapping->ComputeDetJ(*trans, ip);
}
double rho_val = rho.GetValue(i, ip);
mfem::Vector phys_point(dim);
if (fem.has_mapping()) {
fem.mapping->GetPhysicalPoint(*trans, ip, phys_point);
} else {
trans->Transform(ip, phys_point);
}
const double mass_term = rho_val * weight;
total_mass += mass_term;
for (int d = 0; d < dim; ++d) {
com(d) += phys_point(d) * mass_term;
}
}
}
com /= total_mass;
return com;
}
void get_physical_coordinates(const mfem::GridFunction& reference_pos, const mfem::GridFunction& displacement, mfem::GridFunction& physical_pos) {
add(reference_pos, displacement, physical_pos);
}
void populate_element_mask(const FEM &fem, Domains domain, mfem::Array<int> &mask) {
mask.SetSize(fem.mesh->attributes.Max());
mask = 0;
if ((domain & Domains::CORE) == Domains::CORE) {
mask[0] = 1;
}
if ((domain & Domains::ENVELOPE) == Domains::ENVELOPE) {
mask[1] = 1;
}
if ((domain & Domains::VACUUM) == Domains::VACUUM) {
mask[2] = 1;
}
}
std::expected<Bounds, BoundsError> DiscoverBounds(const mfem::Mesh *mesh, const int vacuum_attr) {
double min_r = std::numeric_limits<double>::max();
double max_r = -std::numeric_limits<double>::max();
bool found_vacuum = false;
for (int i = 0; i < mesh->GetNE(); ++i) {
if (mesh->GetAttribute(i) == vacuum_attr) {
found_vacuum = true;
mfem::Array<int> vertices;
mesh->GetElementVertices(i, vertices);
for (const int v: vertices) {
const double* coords = mesh->GetVertex(v);
double r = std::sqrt(coords[0] * coords[0] + coords[1] * coords[1] + coords[2] * coords[2]);
min_r = std::min(min_r, r);
max_r = std::max(max_r, r);
}
}
}
if (found_vacuum) {
return Bounds(min_r, max_r);
}
return std::unexpected(BoundsError::CANNOT_FIND_VACUUM);
}
void conserve_mass(const FEM& fem, mfem::GridFunction& rho, const double target_mass) {
if (const double current_mass = domain_integrate_grid_function(fem, rho); current_mass > 1e-15) rho *= (target_mass / current_mass);
}
//endregion
//region Physics Functions
double centrifugal_potential(const mfem::Vector& phys_x, double omega) {
const double s2 = std::pow(phys_x(0), 2) + std::pow(phys_x(1), 2);
return -0.5 * s2 * std::pow(omega, 2);
}
double get_moment_of_inertia(const FEM& fem, const mfem::GridFunction& rho) {
auto s2_func = [](const mfem::Vector& x) {
return std::pow(x(0), 2) + std::pow(x(1), 2);
};
std::unique_ptr<mfem::Coefficient> s2_coeff;
if (fem.has_mapping()) {
s2_coeff = std::make_unique<PhysicalPositionFunctionCoefficient>(*fem.mapping, s2_func);
} else {
s2_coeff = std::make_unique<mfem::FunctionCoefficient>(s2_func);
}
mfem::GridFunctionCoefficient rho_coeff(&rho);
mfem::ProductCoefficient I_integrand(rho_coeff, *s2_coeff);
mfem::LinearForm I_lf(fem.H1_fes.get());
double I = 0.0;
if (fem.has_mapping()) {
MappedScalarCoefficient mapped_integrand(*fem.mapping, I_integrand);
I_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(mapped_integrand));
I_lf.Assemble();
I = I_lf.Sum();
} else {
I_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(I_integrand));
I_lf.Assemble();
I = I_lf.Sum();
}
return I;
}
//endregion
//region Analytic External Potential for an oblate spheroid (doi.10.16.j.pss.2018.01.005)
inline double sq(const double x) { return x * x; }
double eccentricity(const double a, const double c) {
return std::sqrt(1.0 - sq(c)/sq(a));
}
double equatorial_radius(const mfem::Vector& x) {
return std::sqrt(sq(x(0)) + sq(x(1)));
}
double beta_ext(const mfem::Vector& x, const double a, const double c) {
const double e = eccentricity(a, c);
const double z = x(2);
const double r = equatorial_radius(x);
const double ae_sq = sq(a*e);
if (std::abs(r) < 1e-12) {
return std::atan2(a*e, std::abs(x(2)));
}
const double fraction = (sq(z) + ae_sq) / sq(r);
const double first_term = -fraction;
const double radical_one = sq(1.0 + fraction);
const double radical_two = 4.0 * ae_sq / sq(r);
const double second_term = std::sqrt(std::max(0.0, radical_one - radical_two));
const double cos_term = first_term + second_term;
return 0.5 * std::acos(std::clamp(cos_term, -1.0, 1.0));
}
double oblate_spheroid_surface_potential(const mfem::Vector& x, const double a, const double c, const double total_mass) {
const double beta = beta_ext(x, a, c);
const double r = equatorial_radius(x);
const double e = eccentricity(a, c);
const double z = x(2);
const double G_M = G * total_mass;
const double e3a3 = std::pow(e, 3) * std::pow(a, 3);
const double t1 = (3.0 * G_M * beta) / (2.0 * e * a);
const double t2aa = (3.0 * G_M * sq(r)) / (2.0 * e3a3);
const double t2ab = beta - std::sin(beta) * std::cos(beta);
const double t2ba = (3.0 * G_M * sq(z)) / e3a3;
const double t2bb = std::tan(beta) - beta;
return -t1 + 0.5 * (t2aa * t2ab + t2ba * t2bb);
}
//endregion End Analytic Potential
//region potentials
std::unique_ptr<mfem::GridFunction> grav_potential(const FEM& fem, const Args& args, const mfem::GridFunction& rho) {
auto phi = std::make_unique<mfem::GridFunction>(fem.H1_fes.get());
mfem::Array<int> ess_bdr(fem.mesh->bdr_attributes.Max());
ess_bdr = 0;
assert(ess_bdr.Size() == 2);
ess_bdr[1] = 1; // The only boundary condition is that the potential goes to 0 at infinity
// mfem::ConstantCoefficient zero(0.0);
// phi->ProjectBdrCoefficient(zero, ess_bdr); // Set the potential to 0 at infinity;
double total_mass = domain_integrate_grid_function(fem, rho, STELLAR);
auto bdr_func = [&fem, total_mass](const mfem::Vector& x) {
double r = x.Norml2();
double theta = std::atan2(x(1), x(0));
double phi = std::acos(x(2) / r);
double val = l2_multipole_potential(fem, total_mass, x);
// std::println("{},{},{},{},{}", r, theta, phi, val, -G*total_mass / r);
return l2_multipole_potential(fem, total_mass, x);
};
std::unique_ptr<mfem::Coefficient> phi_bdr_coeff;
if (fem.has_mapping()) {
phi_bdr_coeff = std::make_unique<PhysicalPositionFunctionCoefficient>(*fem.mapping, bdr_func);
} else {
phi_bdr_coeff = std::make_unique<mfem::FunctionCoefficient>(bdr_func);
}
phi->ProjectBdrCoefficient(*phi_bdr_coeff, ess_bdr);
mfem::Array<int> ess_tdof_list;
fem.H1_fes->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
mfem::Array<int> stellar_marker;
populate_element_mask(fem, STELLAR, stellar_marker);
auto laplacian = std::make_unique<mfem::BilinearForm>(fem.H1_fes.get());
mfem::ConstantCoefficient one_coeff(1.0);
std::unique_ptr<MappedDiffusionCoefficient> mapped_diff_coeff;
if (fem.has_mapping()) {
mapped_diff_coeff = std::make_unique<MappedDiffusionCoefficient>(*fem.mapping, one_coeff, fem.mesh->Dimension());
laplacian->AddDomainIntegrator(new mfem::DiffusionIntegrator(*mapped_diff_coeff)); // The laplacian is global
} else {
laplacian->AddDomainIntegrator(new mfem::DiffusionIntegrator());
}
laplacian->Assemble();
laplacian->Finalize();
mfem::LinearForm b(fem.H1_fes.get());
mfem::ConstantCoefficient four_pi_G(-4.0 * M_PI * G);
mfem::GridFunctionCoefficient rho_coeff(&rho);
mfem::ProductCoefficient rhs_coeff(rho_coeff, four_pi_G);
auto mapped_rhs = std::make_unique<MappedScalarCoefficient>(*fem.mapping, rhs_coeff, MappedScalarCoefficient::EVAL_POINTS::REFERENCE);
if (fem.has_mapping()) {
b.AddDomainIntegrator(new mfem::DomainLFIntegrator(*mapped_rhs), stellar_marker); // The mass contribution is local to the stellar domain
} else {
b.AddDomainIntegrator(new mfem::DomainLFIntegrator(rhs_coeff), stellar_marker);
}
b.Assemble();
mfem::OperatorPtr A;
mfem::Vector B, X;
laplacian->FormLinearSystem(ess_tdof_list, *phi, b, A, X, B);
mfem::GSSmoother prec;
mfem::CGSolver cg;
cg.SetPreconditioner(prec);
cg.SetOperator(*A);
cg.SetRelTol(args.p.tol);
cg.SetMaxIter(args.p.max_iters);
cg.Mult(B, X);
laplacian->RecoverFEMSolution(X, b, *phi);
return phi;
}
// std::unique_ptr<mfem::GridFunction> grav_potential(const FEM& fem, const Args &args, const mfem::GridFunction& rho, std::optional<OblatePotential> oblate) {
// auto phi = std::make_unique<mfem::GridFunction>(fem.H1_fes.get());
//
// mfem::Array<int> ess_bdr(fem.mesh->bdr_attributes.Max());
// ess_bdr = 1;
//
// mfem::GridFunctionCoefficient rho_coeff(&rho);
// double total_mass = domain_integrate_grid_function(fem, rho);
//
// auto grav_potential = [&fem, &total_mass, &oblate](const mfem::Vector& x) {
// if (!oblate.has_value() or oblate->use == false) {
// return l2_multipole_potential(fem, total_mass, x);
// }
// return oblate_spheroid_surface_potential(x, oblate->a, oblate->c, total_mass);
// };
//
// std::unique_ptr<mfem::Coefficient> phi_bdr_coeff;
// if (fem.has_mapping()) {
// phi_bdr_coeff = std::make_unique<PhysicalPositionFunctionCoefficient>(*fem.mapping, grav_potential);
// } else {
// phi_bdr_coeff = std::make_unique<mfem::FunctionCoefficient>(grav_potential);
// }
// phi->ProjectBdrCoefficient(*phi_bdr_coeff, ess_bdr);
//
// mfem::Array<int> ess_tdof_list;
// fem.H1_fes->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
//
// auto laplacian = std::make_unique<mfem::BilinearForm>(fem.H1_fes.get());
// // ReSharper disable once CppTooWideScope
// std::unique_ptr<mfem::ConstantCoefficient> one_coeff;
// // ReSharper disable once CppTooWideScope
// std::unique_ptr<MappedDiffusionCoefficient> mapped_diff_coeff;
// if (fem.has_mapping()) {
// one_coeff = std::make_unique<mfem::ConstantCoefficient>(1.0);
// mapped_diff_coeff = std::make_unique<MappedDiffusionCoefficient>(*fem.mapping, *one_coeff, fem.mesh->Dimension());
// laplacian->AddDomainIntegrator(new mfem::DiffusionIntegrator(*mapped_diff_coeff));
// } else {
// laplacian->AddDomainIntegrator(new mfem::DiffusionIntegrator());
// }
// laplacian->Assemble();
// laplacian->Finalize();
//
// mfem::ConstantCoefficient four_pi_G(-4.0 * M_PI * G);
// mfem::ProductCoefficient rhs_coeff(rho_coeff, four_pi_G);
// mfem::LinearForm b(fem.H1_fes.get());
//
// // ReSharper disable once CppTooWideScope
// std::unique_ptr<MappedScalarCoefficient> mapped_rhs;
// if (fem.has_mapping()) {
// mapped_rhs = std::make_unique<MappedScalarCoefficient>(*fem.mapping, rhs_coeff, MappedScalarCoefficient::EVAL_POINTS::REFERENCE);
// b.AddDomainIntegrator(new mfem::DomainLFIntegrator(*mapped_rhs));
// } else {
// b.AddDomainIntegrator(new mfem::DomainLFIntegrator(rhs_coeff));
// }
// b.Assemble();
//
// mfem::OperatorPtr A;
// mfem::Vector B, X;
// laplacian->FormLinearSystem(ess_tdof_list, *phi, b, A, X, B);
//
// mfem::GSSmoother prec;
// mfem::CGSolver cg;
// cg.SetPreconditioner(prec);
// cg.SetOperator(*A);
// cg.SetRelTol(args.p.tol);
// cg.SetMaxIter(args.p.max_iters);
// cg.SetPrintLevel(0);
//
// cg.Mult(B, X);
// laplacian->RecoverFEMSolution(X, b, *phi);
// return phi;
// }
std::unique_ptr<mfem::GridFunction> get_potential(const FEM &fem, const Args &args, const mfem::GridFunction &rho) {
auto phi = grav_potential(fem, args, rho);
if (args.r.enabled) {
auto rot = [&args](const mfem::Vector& x) {
return centrifugal_potential(x, args.r.omega);
};
std::unique_ptr<mfem::Coefficient> centrifugal_coeff;
if (fem.has_mapping()) {
centrifugal_coeff = std::make_unique<PhysicalPositionFunctionCoefficient>(*fem.mapping, rot);
} else {
centrifugal_coeff = std::make_unique<mfem::FunctionCoefficient>(rot);
}
mfem::GridFunction centrifugal_gf(fem.H1_fes.get());
centrifugal_gf.ProjectCoefficient(*centrifugal_coeff);
(*phi) += centrifugal_gf;
}
return phi;
}
mfem::DenseMatrix compute_quadrupole_moment_tensor(const FEM& fem, const mfem::GridFunction& rho, const mfem::Vector& com) {
const int dim = fem.mesh->Dimension();
mfem::DenseMatrix Q(dim, dim);
Q = 0.0;
for (int i = 0; i < fem.H1_fes->GetNE(); ++i) {
mfem::ElementTransformation *trans = fem.mesh->GetElementTransformation(i);
const mfem::IntegrationRule &ir = mfem::IntRules.Get(trans->GetGeometryType(), 2 * fem.H1_fes->GetOrder(0) + trans->OrderW());
for (int j = 0; j < ir.GetNPoints(); ++j) {
const mfem::IntegrationPoint &ip = ir.IntPoint(j);
trans->SetIntPoint(&ip);
double weight = trans->Weight() * ip.weight;
if (fem.has_mapping()) {
weight *= fem.mapping->ComputeDetJ(*trans, ip);
}
const double rho_val = rho.GetValue(i, ip);
mfem::Vector phys_point(dim);
if (fem.has_mapping()) {
fem.mapping->GetPhysicalPoint(*trans, ip, phys_point);
} else {
trans->Transform(ip, phys_point);
}
mfem::Vector x_prime(dim);
double r_sq = 0.0;
for (int d = 0; d < dim; ++d) {
x_prime(d) = phys_point(d) - com(d);
r_sq += x_prime(d) * x_prime(d);
}
for (int m = 0; m < dim; ++m) {
for (int n = 0; n < dim; ++n) {
const double delta = (m == n) ? 1.0 : 0.0;
const double contrib = 3.0 * x_prime(m) * x_prime(n) - delta * r_sq;
Q(m, n) += rho_val * contrib * weight;
}
}
}
}
return Q;
}
double l2_multipole_potential(const FEM &fem, const double total_mass, const mfem::Vector &phys_x) {
const double r = phys_x.Norml2();
if (r < 1e-12) return 0.0;
const int dim = fem.mesh->Dimension();
mfem::Vector n(phys_x);
n /= r;
double l2_mult_factor = 0.0;
for (int i = 0; i < dim; ++i) {
for (int j = 0; j < dim; ++j) {
l2_mult_factor += fem.Q(i, j) * n(i) * n(j);
}
}
const double l2_contrib = (G / (2.0 * std::pow(r, 3))) * l2_mult_factor;
const double l0_contrib = -G * total_mass / r;
// l1 contribution is zero for a system centered on its COM
return l0_contrib + l2_contrib;
}
//endregion
//region Tests
void test_mesh_load(const FEM& fem) {
size_t failed = 0;
if (not fem.okay()) ++failed;
const int dim = fem.mesh->Dimension();
if (dim != 3) ++failed;
const int n_scalar = fem.H1_fes->GetTrueVSize();
const int n_vector = fem.Vec_H1_fes->GetTrueVSize();
if (n_vector != dim * n_scalar) ++failed;
if (fem.block_offsets[0] != 0) ++failed;
if (fem.block_offsets[1] != n_scalar) ++failed;
if (fem.block_offsets[2] != n_scalar + n_vector) ++failed;
if (fem.block_offsets[3] != n_scalar + n_vector + 1) ++failed;
constexpr size_t num_tests = 6;
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
std::string test_msg = fmt_test_msg("Mesh Load Test", result_type, failed, num_tests);
std::println("{}", test_msg);
assert(dim == 3);
assert(n_vector == (n_scalar * dim));
assert (fem.block_offsets[0] == 0);
assert (fem.block_offsets[1] == n_scalar);
assert (fem.block_offsets[2] == n_scalar + n_vector);
assert (fem.block_offsets[3] == n_scalar + n_vector + 1);
}
void test_ref_coord_storage(const FEM& fem) {
size_t failed = 0;
if (not fem.mapping->IsIdentity()) ++failed;
const size_t num_elemIDs = std::min(30, fem.mesh->GetNE());
for (int elemID = 0; elemID < num_elemIDs; ++elemID) {
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ir = mfem::IntRules.Get(trans->GetGeometryType(), 2);
const auto& ip = ir.IntPoint(0);
trans->SetIntPoint(&ip);
mfem::Vector x_ref, x_phys;
trans->Transform(ip, x_ref);
fem.mapping->GetPhysicalPoint(*trans, ip, x_phys);
x_ref -= x_phys;
if (not (x_ref.Norml2() < 1e-12)) ++failed;
}
const size_t num_tests = num_elemIDs + 1;
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
std::string test_msg = fmt_test_msg("Mesh Ref Coord", result_type, failed, num_tests);
std::println("{}", test_msg);
}
void test_reference_volume_integral(const FEM& fem) {
size_t failed = 0;
mfem::GridFunction ones(fem.H1_fes.get());
ones = 1.0;
double vol = domain_integrate_grid_function(fem, ones, STELLAR);
double expected = (4.0/3.0) * M_PI * std::pow(RADIUS, 3.0);
double rel_err = std::abs(vol - expected) / expected;
if (rel_err > 1e-2) ++failed;
constexpr size_t num_tests = 1;
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
}
std::println("{}", fmt_test_msg("Reference Volume Integral", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: Volume: {}, Expected: {}, Error (rel): {}", vol, expected, rel_err);
}
}
void test_spherically_symmetric_com(const FEM& fem) {
mfem::GridFunction rho(fem.H1_fes.get());
rho = 1.0;
mfem::Vector com = get_com(fem, rho);
size_t failed = 0;
const size_t dim = fem.mesh->Dimension();
const size_t num_tests = dim;
for (int dimID = 0; dimID < num_tests; ++dimID) {
if (std::abs(com(dimID)) > 1e-12) ++failed;
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
std::println("{}", fmt_test_msg("Uniform COM", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\t COM=<{:+0.3E}, {:+0.3E}, {:+0.3E}>", com(0), com(1), com(2));
}
}
void test_com_variance_to_displacement(const FEM& fem) {
size_t failed = 0;
mfem::GridFunction linear_displacement(fem.Vec_H1_fes.get());
linear_displacement = 10.0; // This will linearly displace the domain by 10 unit along all axes
fem.mapping->SetDisplacement(linear_displacement);
mfem::GridFunction rho(fem.H1_fes.get());
rho = 1.0;
mfem::Vector mapped_com = get_com(fem, rho);
const size_t dim = fem.mesh->Dimension();
const size_t num_tests = dim;
for (int dimID = 0; dimID < num_tests; ++dimID) {
if (10 - std::abs(mapped_com(dimID)) > 1e-12) ++failed;
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
std::println("{}", fmt_test_msg("COM variance to displacement", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE COM=<{:+0.2E}, {:+0.2E}, {:+0.2E}>", mapped_com(0), mapped_com(1), mapped_com(2));
}
fem.mapping->ResetDisplacement();
}
void test_volume_invariance_to_displacement(const FEM& fem) {
size_t failed = 0;
mfem::GridFunction linear_displacement(fem.Vec_H1_fes.get());
linear_displacement = 10.0; // This will linearly displace the domain by 10 unit along all axes
fem.mapping->SetDisplacement(linear_displacement);
mfem::GridFunction ones(fem.H1_fes.get());
ones = 1.0;
double mapped_vol = domain_integrate_grid_function(fem, ones, STELLAR);
double expected = (4.0/3.0) * M_PI * std::pow(RADIUS, 3.0);
double rel_err = std::abs(mapped_vol - expected) / expected;
if (rel_err > 1e-2) ++failed;
constexpr size_t num_tests = 1;
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
}
std::println("{}", fmt_test_msg("Invariance of volume against translation", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: Volume: {}, Expected: {}", mapped_vol, expected);
}
fem.mapping->ResetDisplacement();
}
void test_volume_ellipsoid_deformation(const FEM& fem) {
size_t failed = 0;
size_t num_tests = 0;
constexpr double a = 2.0; // x-axis
constexpr double b = 0.5; // y-axis
constexpr double c = 1.5; // z-axis
constexpr double expected_vol = (4.0 / 3.0) * M_PI * a * b * c;
mfem::GridFunction ellipsoid_displacement(fem.Vec_H1_fes.get());
{
const int dim = fem.mesh->Dimension();
mfem::VectorFunctionCoefficient disp_coeff(dim, [&](const mfem::Vector& x, mfem::Vector& d) {
d.SetSize(x.Size());
d(0) = (a - 1.0) * x(0);
d(1) = (b - 1.0) * x(1);
d(2) = (c - 1.0) * x(2);
});
ellipsoid_displacement.ProjectCoefficient(disp_coeff);
}
fem.mapping->SetDisplacement(ellipsoid_displacement);
{
++num_tests;
mfem::GridFunction ones(fem.H1_fes.get());
ones = 1.0;
const double mapped_vol = domain_integrate_grid_function(fem, ones, STELLAR);
const double rel_err = std::abs(mapped_vol - expected_vol) / expected_vol;
if (rel_err > 1e-3) {
++failed;
std::println("\tFAILURE Test 1: Mapped volume = {:.6f}, expected = {:.6f}, rel_err = {:.2e}",
mapped_vol, expected_vol, rel_err);
}
}
{
++num_tests;
const double expected_x2_integral = std::pow(a, 3) * b * c * (4.0 * M_PI / 15.0);
mfem::GridFunction x_ref_sq(fem.H1_fes.get());
mfem::FunctionCoefficient x_sq_coeff([](const mfem::Vector& x) {
return x(0) * x(0);
});
x_ref_sq.ProjectCoefficient(x_sq_coeff);
mfem::GridFunction x_phys_sq(fem.H1_fes.get());
PhysicalPositionFunctionCoefficient x_phys_sq_coeff(*fem.mapping,
[](const mfem::Vector& x_phys) {
return x_phys(0) * x_phys(0);
}
);
x_phys_sq.ProjectCoefficient(x_phys_sq_coeff);
const double mapped_x2_integral = domain_integrate_grid_function(fem, x_phys_sq, STELLAR);
const double rel_err = std::abs(mapped_x2_integral - expected_x2_integral) / expected_x2_integral;
if (rel_err > 1e-3) {
++failed;
std::println("\tFAILURE Test 2: integral x_phys^2 = {:.6f}, expected = {:.6f}, rel_err = {:.2e}",
mapped_x2_integral, expected_x2_integral, rel_err);
}
}
{
++num_tests;
constexpr double expected_detJ = a * b * c;
double max_detJ_err = 0.0;
for (int e = 0; e < std::min(5, fem.mesh->GetNE()); ++e) {
auto* trans = fem.mesh->GetElementTransformation(e);
const auto& ir = mfem::IntRules.Get(trans->GetGeometryType(), 2);
for (int q = 0; q < ir.GetNPoints(); ++q) {
const auto& ip = ir.IntPoint(q);
trans->SetIntPoint(&ip);
const double detJ = fem.mapping->ComputeDetJ(*trans, ip);
max_detJ_err = std::max(max_detJ_err, std::abs(detJ - expected_detJ));
}
}
if (max_detJ_err > 1e-10) {
++failed;
std::println("\tFAILURE Test 3: max pointwise |det(J) - a*b*c| = {:.2e}", max_detJ_err);
}
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
std::println("{}", fmt_test_msg("Volume under ellipsoidal deformation", result_type, failed, num_tests));
fem.mapping->ResetDisplacement();
}
void test_uniform_potential(FEM& fem, const Args& args) {
const double analytic_vol = (4.0/3.0) * M_PI * std::pow(RADIUS, 3);
const double rho0 = MASS / analytic_vol;
mfem::GridFunction rho_uniform(fem.H1_fes.get());
rho_uniform = rho0;
fem.com = get_com(fem, rho_uniform);
fem.Q = compute_quadrupole_moment_tensor(fem, rho_uniform, fem.com);
const auto phi = grav_potential(fem, args, rho_uniform);
double max_abs_err = 0.0;
double max_rel_err = 0.0;
constexpr double tol = 1e-3;
size_t failed = 0;
size_t num_tests = 0;
const size_t num_elemIDs = std::min(30, fem.mesh->GetNE());
for (int elemID = 0; elemID < num_elemIDs; ++elemID) {
num_tests++;
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ir = mfem::IntRules.Get(trans->GetGeometryType(), 2);
const auto& ip = ir.IntPoint(0);
trans->SetIntPoint(&ip);
mfem::Vector x_ref, x_phys;
trans->Transform(ip, x_ref);
fem.mapping->GetPhysicalPoint(*trans, ip, x_phys);
const double r = x_phys.Norml2();
if (r < 1e-9) continue;
const double phi_analytic = (-G * MASS / (2.0 * std::pow(RADIUS, 3.0))) * (3.0*RADIUS*RADIUS - r*r);
const double phi_fem = phi->GetValue(elemID, ip);
const double abs_err = std::abs(phi_fem - phi_analytic);
const double rel_err = abs_err / std::abs(phi_analytic);
max_abs_err = std::max(max_abs_err, abs_err);
max_rel_err = std::max(max_rel_err, rel_err);
if (rel_err > tol) ++failed;
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
std::println("{}", fmt_test_msg("Test Uniform Potential", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: max abs error: {:+0.2E}, max rel error: {:+0.2E}", max_abs_err, max_rel_err);
}
}
void test_ellipsoidal_potential(FEM& fem, const Args& args) {
constexpr double a = 1.0 * RADIUS;
constexpr double b = a; // oblate
constexpr double c = 0.99 * RADIUS;
constexpr double expected_vol = (4.0 / 3.0) * M_PI * a * b * c;
constexpr double rho0 = MASS / expected_vol;
mfem::GridFunction ellipsoidal_disp(fem.Vec_H1_fes.get());
mfem::VectorFunctionCoefficient disp_coeff(3, [&](const mfem::Vector& x, mfem::Vector& d) {
d.SetSize(3);
d(0) = (a/RADIUS - 1.0) * x(0);
d(1) = (b/RADIUS - 1.0) * x(1);
d(2) = (c/RADIUS - 1.0) * x(2);
});
ellipsoidal_disp.ProjectCoefficient(disp_coeff);
fem.mapping->SetDisplacement(ellipsoidal_disp);
mfem::GridFunction rho(fem.H1_fes.get());
rho = rho0;
fem.com = get_com(fem, rho);
fem.Q = compute_quadrupole_moment_tensor(fem, rho, fem.com);
// OblatePotential oblate{.use=true, .a=a, .c=c,.rho_0=rho0};
const auto phi = grav_potential(fem, args, rho);
constexpr double e_sq = 1.0 - (c * c)/(a*a);
const double e = std::sqrt(e_sq);
const double I_const = (2.0 * std::sqrt(1.0 - e_sq) / e) * std::asin(e);
const double A_R = (std::sqrt(1.0-e_sq) / std::pow(e, 3.0)) * std::asin(e) - (1.0 - e_sq)/e_sq;
const double A_z = (2.0 / e_sq) * (1.0 - (std::sqrt(1.0-e_sq) / e) * std::asin(e));
size_t failed = 0;
size_t num_tests = 0;
double max_rel_err = 0.0;
double total_err = 0.0;
const size_t check_count = std::min(50, fem.mesh->GetNE());
for (int elemID = 0; elemID < check_count; ++elemID) {
auto* trans = fem.mesh->GetElementTransformation(elemID);
const auto& ip = mfem::IntRules.Get(trans->GetGeometryType(), 2).IntPoint(0);
trans->SetIntPoint(&ip);
mfem::Vector x_phys;
fem.mapping->GetPhysicalPoint(*trans, ip, x_phys);
const double R2 = x_phys(0)*x_phys(0) + x_phys(1)*x_phys(1);
const double z2 = x_phys(2)*x_phys(2);
const double phi_analytic = -M_PI * G * rho0 * (a*a*I_const - A_R * R2 - A_z * z2);
const double phi_fem = phi->GetValue(elemID, ip);
const double rel_err = std::abs(phi_fem - phi_analytic) / std::abs(phi_analytic);
max_rel_err = std::max(max_rel_err, rel_err);
total_err += rel_err;
num_tests++;
if (rel_err > 1e-3) ++failed;
}
auto result_type = TEST_RESULT_TYPE::FAILURE;
if (failed == 0) {
result_type = TEST_RESULT_TYPE::SUCCESS;
} else if (failed < num_tests) {
result_type = TEST_RESULT_TYPE::PARTIAL;
}
std::println("{}", fmt_test_msg("Test Ellipsoidal Potential", result_type, failed, num_tests));
if (result_type == TEST_RESULT_TYPE::FAILURE) {
std::println("\tFAILURE: max rel error: {:+0.2E}, mean rel error: {:+0.2E}", max_rel_err, total_err/static_cast<double>(num_tests));
}
}
//endregion
int main(int argc, char** argv) {
Args args;
CLI::App app{"Mapped Coordinates XAD-Enabled Non-Linear Solver"};
app.add_option("-m,--mesh", args.mesh_file)->required()->check(CLI::ExistingFile);
app.add_option("--max-iters", args.max_iters)->default_val(20);
app.add_option("--index", args.index)->default_val(1);
app.add_option("--mass", args.mass)->default_val(MASS);
app.add_option("--surface-pressure-scalar", args.c)->default_val(1e-4);
args.r.enabled = false;
args.p.tol = 1e-6;
args.p.max_iters = 1000;
CLI11_PARSE(app, argc, argv);
FEM fem = setup_fem(args.mesh_file, true);
// fem.mesh->UniformRefinement();
test_mesh_load(fem);
test_ref_coord_storage(fem);
test_reference_volume_integral(fem);
test_spherically_symmetric_com(fem);
test_com_variance_to_displacement(fem);
test_volume_invariance_to_displacement(fem);
test_volume_ellipsoid_deformation(fem);
// test_kelvin_jacobian(fem);
test_uniform_potential(fem, args);
test_ellipsoidal_potential(fem, args); // Note that this test is currently predicated on an analytic solution for the surface boundary potential
CoupledState state(fem);
// typedef xad::AReal<double> adouble;
//
// EOS_P<adouble> eos_enthalpy = [index = args.index](const adouble& rho, const adouble& temp) -> adouble {
// if (rho.value() < 1e-15) return {0.0};
// return (index + 1.0) * pow(rho, 1.0 / index);
// };
//
// EOS_P<adouble> eos_pressure = [index = args.index](const adouble& rho, const adouble& temp) -> adouble {
// if (rho.value() < 1e-15) return {0.0};
// return pow(rho, 1.0 + (1.0 / index));
// };
//
// auto init_rho_func = [&](const mfem::Vector& pt) {
// const double r = pt.Norml2();
// return (r < RADIUS) ? (1.0 - r/RADIUS) : 0.0;
// };
// mfem::FunctionCoefficient init_rho_coeff(init_rho_func);
// state.rho.ProjectCoefficient(init_rho_coeff);
// conserve_mass(fem, state.rho, args.mass);
// view_mesh(HOST, PORT, *fem.mesh, state.rho, "Initial Density Solution with XAD AD");
// view_mesh(HOST, PORT, *fem.mesh, state.d, "Initial Position Solution with XAD AD");
//
// std::println("Starting Coupled Block Solver with XAD AD...");
//
// ResidualOperator coupled_operator(fem, args, eos_enthalpy, eos_pressure);
//
// mfem::NewtonSolver newton_solver;
// newton_solver.SetOperator(coupled_operator);
// newton_solver.SetMaxIter(500);
// newton_solver.SetRelTol(1e-6);
// newton_solver.SetPrintLevel(1);
//
// mfem::GMRESSolver jfnk_solver;
// jfnk_solver.SetMaxIter(100);
// jfnk_solver.SetRelTol(1e-4);
// newton_solver.SetSolver(jfnk_solver);
// newton_solver.SetAdaptiveLinRtol(2, 0.5, 0.9, 0.9, 1.1);
//
// mfem::Vector zero_rhs(fem.block_offsets.Last());
// zero_rhs = 0.0;
// newton_solver.Mult(zero_rhs, *state.U);
//
// mfem::GridFunction rho(fem.H1_fes.get(), state.U->GetBlock(0), 0);
// mfem::GridFunction x(fem.Vec_H1_fes.get(), state.U->GetBlock(1), 0);
// view_mesh(HOST, PORT, *fem.mesh, rho, "Final Density Solution with XAD AD");
// view_mesh(HOST, PORT, *fem.mesh, x, "Final Position Solution with XAD AD");
//
// std::println("Solver finished using XAD machine-precision gradients.");
// return 0;
}
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