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Albany_Application.hpp
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//*****************************************************************//
// Albany 3.0: Copyright 2016 Sandia Corporation //
// This Software is released under the BSD license detailed //
// in the file "license.txt" in the top-level Albany directory //
//*****************************************************************//
#ifndef ALBANY_APPLICATION_HPP
#define ALBANY_APPLICATION_HPP
#include "Albany_config.h"
#include "Albany_AbstractDiscretization.hpp"
#include "Albany_AbstractProblem.hpp"
#include "Albany_AbstractResponseFunction.hpp"
#include "Albany_StateManager.hpp"
#include "SolutionManager.hpp"
#include "Albany_DiscretizationFactory.hpp"
#include "PHAL_AlbanyTraits.hpp"
#include "PHAL_Setup.hpp"
#include "PHAL_Workset.hpp"
#include "Sacado_ParameterAccessor.hpp"
#include "Sacado_ParameterRegistration.hpp"
#include "Sacado_ScalarParameterLibrary.hpp"
#include "Sacado_ScalarParameterVector.hpp"
#include "Teuchos_ArrayRCP.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_TimeMonitor.hpp"
#include "Teuchos_VerboseObject.hpp"
#include <set>
namespace Albany {
class Application
{
public:
enum SolutionStatus
{
Converged,
NotConverged
} solutionStatus;
//! Constructor(s) and Destructor
Application (const Teuchos::RCP<const Teuchos_Comm>& comm,
const Teuchos::RCP<Teuchos::ParameterList>& params,
const Teuchos::RCP<const Thyra_Vector>& initial_guess = Teuchos::null);
Application(const Teuchos::RCP<const Teuchos_Comm>& comm);
Application(const Application&) = delete;
~Application() = default;
//! Prohibit copying/moving
Application& operator=(const Application&) = delete;
Application& operator=(Application&&) = delete;
void initialSetUp(const Teuchos::RCP<Teuchos::ParameterList>& params);
void createMeshSpecs();
void createMeshSpecs(Teuchos::RCP<Albany::AbstractMeshStruct> mesh);
void buildProblem();
void createDiscretization();
void finalSetUp(const Teuchos::RCP<Teuchos::ParameterList>& params,
const Teuchos::RCP<const Thyra_Vector>& initial_guess = Teuchos::null);
template<typename Traits>
void
setDynamicLayoutSizes(Teuchos::RCP<PHX::FieldManager<PHAL::AlbanyTraits>>& in_fm) const;
//! Get underlying abstract discretization
Teuchos::RCP<Albany::AbstractDiscretization>
getDiscretization() const;
//! Get problem object
Teuchos::RCP<Albany::AbstractProblem>
getProblem() const;
//! Get communicator
Teuchos::RCP<const Teuchos_Comm>
getComm() const;
//! Get Thyra DOF vector space
Teuchos::RCP<const Thyra_VectorSpace>
getVectorSpace() const;
//! Create Jacobian operator
Teuchos::RCP<Thyra_LinearOp>
createJacobianOp() const;
//! Get Preconditioner Operator
Teuchos::RCP<Thyra_LinearOp>
getPreconditioner();
bool
observeResponses() const
{
return observe_responses;
}
int
observeResponsesFreq() const
{
return response_observ_freq;
}
Teuchos::Array<unsigned int>
getMarkersForRelativeResponses() const
{
return relative_responses;
}
Teuchos::RCP<Albany::SolutionManager>
getAdaptSolMgr()
{
return solMgr;
}
//! Get parameter library
Teuchos::RCP<ParamLib>
getParamLib() const;
//! Get distributed parameter library
Teuchos::RCP<DistributedParameterLibrary>
getDistributedParameterLibrary() const;
//! Get solution method
SolutionMethodType
getSolutionMethod() const
{
return solMethod;
}
int
getNumTimeDerivs() const
{
return num_time_deriv;
}
//! Get number of responses
int
getNumResponses() const;
int
getNumEquations() const
{
return neq;
}
int
getSpatialDimension() const
{
return spatial_dimension;
}
int
getTangentDerivDimension() const
{
return tangent_deriv_dim;
}
Teuchos::RCP<Albany::AbstractDiscretization>
getDisc() const
{
return disc;
}
//! Get response function
Teuchos::RCP<AbstractResponseFunction>
getResponse(int i) const;
SolutionStatus getSolutionStatus() const {
return solutionStatus;
}
void setSolutionStatus(SolutionStatus status) {
solutionStatus = status;
}
void forceWriteSolution()
{
force_write_solution = true;
}
bool getForceWriteSolution() const
{
return force_write_solution;
}
bool isAdjointSensitivities() const
{
return adjoint_sens;
}
//! Return whether problem wants to use its own preconditioner
bool
suppliesPreconditioner() const;
void
computeGlobalResidual(
const double current_time,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& x_dot,
const Teuchos::RCP<const Thyra_Vector>& x_dotdot,
const Teuchos::Array<ParamVec>& p,
const Teuchos::RCP<Thyra_Vector>& f,
const double dt = 0.0);
private:
void
computeGlobalResidualImpl(
const double current_time,
const Teuchos::RCP<const Thyra_Vector> x,
const Teuchos::RCP<const Thyra_Vector> x_dot,
const Teuchos::RCP<const Thyra_Vector> x_dotdot,
const Teuchos::Array<ParamVec>& p,
const Teuchos::RCP<Thyra_Vector>& f,
const double dt = 0.0);
PHAL::Workset
set_dfm_workset(
double const current_time,
const Teuchos::RCP<const Thyra_Vector> x,
const Teuchos::RCP<const Thyra_Vector> x_dot,
const Teuchos::RCP<const Thyra_Vector> x_dotdot,
const Teuchos::RCP<Thyra_Vector>& f,
const Teuchos::RCP<const Thyra_Vector>& x_post_SDBCs = Teuchos::null);
public:
//! Compute global Jacobian
/*!
* Set xdot to NULL for steady-state problems
*/
void
computeGlobalJacobian(
const double alpha,
const double beta,
const double omega,
const double current_time,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& p,
const Teuchos::RCP<Thyra_Vector>& f,
const Teuchos::RCP<Thyra_LinearOp>& jac,
const double dt = 0.0);
private:
void
computeGlobalJacobianImpl(
const double alpha,
const double beta,
const double omega,
const double current_time,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& p,
const Teuchos::RCP<Thyra_Vector>& f,
const Teuchos::RCP<Thyra_LinearOp>& jac,
const double dt = 0.0);
public:
//! Compute global Preconditioner
/*!
* Set xdot to NULL for steady-state problems
*/
void
computeGlobalTangent(
const double alpha,
const double beta,
const double omega,
const double current_time,
bool sum_derivs,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
Teuchos::Array<ParamVec>& par,
const int parameter_index,
const Teuchos::RCP<const Thyra_MultiVector>& Vx,
const Teuchos::RCP<const Thyra_MultiVector>& Vxdot,
const Teuchos::RCP<const Thyra_MultiVector>& Vxdotdot,
const Teuchos::RCP<const Thyra_MultiVector>& Vp,
const Teuchos::RCP<Thyra_Vector>& f,
const Teuchos::RCP<Thyra_MultiVector>& JV,
const Teuchos::RCP<Thyra_MultiVector>& fp);
public:
//! Compute df/dp*V or (df/dp)^T*V for distributed parameter p
/*!
* Set xdot to NULL for steady-state problems
*/
void
applyGlobalDistParamDerivImpl(
const double current_time,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& p,
const std::string& dist_param_name,
const bool trans,
const Teuchos::RCP<const Thyra_MultiVector>& V,
const Teuchos::RCP<Thyra_MultiVector>& fpV);
//! Evaluate response functions
/*!
* Set xdot to NULL for steady-state problems
*/
void
evaluateResponse(
int response_index,
const double current_time,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& p,
const Teuchos::RCP<Thyra_Vector>& g);
//! Evaluate tangent = alpha*dg/dx*Vx + beta*dg/dxdot*Vxdot + dg/dp*Vp
/*!
* Set xdot, dxdot_dp to NULL for steady-state problems
*/
void
evaluateResponseTangent(
int response_index,
int parameter_index,
const double alpha,
const double beta,
const double omega,
const double current_time,
bool sum_derivs,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
Teuchos::Array<ParamVec>& p,
const Teuchos::RCP<const Thyra_MultiVector>& Vx,
const Teuchos::RCP<const Thyra_MultiVector>& Vxdot,
const Teuchos::RCP<const Thyra_MultiVector>& Vxdotdot,
const Teuchos::RCP<const Thyra_MultiVector>& Vp,
const Teuchos::RCP<Thyra_Vector>& g,
const Teuchos::RCP<Thyra_MultiVector>& gx,
const Teuchos::RCP<Thyra_MultiVector>& gp);
//! Evaluate gradient = dg/dx, dg/dxdot, dg/dp
/*!
* Set xdot, dg_dxdot to NULL for steady-state problems
*/
void
evaluateResponseDerivative(
int response_index,
const double current_time,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& p,
const int parameter_index,
const Teuchos::RCP<Thyra_Vector>& g,
const Thyra_Derivative& dg_dx,
const Thyra_Derivative& dg_dxdot,
const Thyra_Derivative& dg_dxdotdot,
const Thyra_Derivative& dg_dp);
void
evaluateResponseDistParamDeriv(
int response_index,
const double current_time,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const std::string& dist_param_name,
const Teuchos::RCP<Thyra_MultiVector>& dg_dp);
/**
* \brief evaluateResponse_HessVecProd_xx function
*
* This function is used to compute contributions of the application of the Hessian \f$\boldsymbol{H}(g)\f$ of the <tt>response[response_index]</tt>
* (i.e. the response_index-th response) to a direction vector \f$\boldsymbol{v}\f$.
*
* Representing the Hessian \f$\boldsymbol{H}(g)\f$ as a block matrix:
* \f[
* \boldsymbol{H}(g) :=
* \begin{bmatrix}
* \frac{\partial^{2} g}{\partial \boldsymbol{x}^{2}} & \frac{\partial^{2} g}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{n}} \\
* \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{x}} & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1}^{2}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{p}_{n}} \\
* \vdots & \vdots & \ddots & \vdots\\
* \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n} \partial \boldsymbol{x}} & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n}\partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n}^{2}}
* \end{bmatrix} =
* \begin{bmatrix}
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_n}(g) \\
* \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_n}(g) \\
* \vdots & \vdots & \ddots & \vdots\\
* \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_n}(g)
* \end{bmatrix},
* \f]
* where \f$g\f$ is the response, \f$\boldsymbol{x}\f$ is the solution vector, \f$\boldsymbol{p}_1\f$ is a first parameter, \f$\ldots\f$, and \f$\boldsymbol{p}_n\f$ is the \f$n\f$-th
* parameter, this function computes the contribution:
* \f[
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(g)\boldsymbol{v}_{\boldsymbol{x}}.
* \f]
*
* This function can currently compute only one block contribution at a time; for one function call \f$\boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(g)\boldsymbol{v}_{\boldsymbol{x}}\f$
* can be computed only for one fixed response index at a time.
*
* \param response_index [in] Response index of the response which the Hessian is computed.
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param v [in] Direction vector on which the Hessian is applied: \f$\boldsymbol{v}_{\boldsymbol{x}}\f$.
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$.
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param Hv_g_xx [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(g)\boldsymbol{v}_{\boldsymbol{x}}\f$.
*
* This implementation relies on:
* <ul>
* <li> PHAL::GatherSolution<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarExtruded2DNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::SeparableScatterScalarResponse<PHAL::AlbanyTraits::HessianVec,Traits>.
* </ul>
*/
void
evaluateResponse_HessVecProd_xx(
int response_index,
const double current_time,
const Teuchos::RCP<const Thyra_MultiVector>& v,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const Teuchos::RCP<Thyra_MultiVector>& Hv_g_xx);
/**
* \brief evaluateResponse_HessVecProd_xp function
*
* This function is used to compute contributions of the application of the Hessian \f$\boldsymbol{H}(g)\f$ of the <tt>response[response_index]</tt>
* (i.e. the response_index-th response) to a direction vector \f$\boldsymbol{v}\f$.
*
* Representing the Hessian \f$\boldsymbol{H}(g)\f$ as a block matrix:
* \f[
* \boldsymbol{H}(g) :=
* \begin{bmatrix}
* \frac{\partial^{2} g}{\partial \boldsymbol{x}^{2}} & \frac{\partial^{2} g}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{n}} \\
* \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{x}} & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1}^{2}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{p}_{n}} \\
* \vdots & \vdots & \ddots & \vdots\\
* \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n} \partial \boldsymbol{x}} & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n}\partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n}^{2}}
* \end{bmatrix} =
* \begin{bmatrix}
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_n}(g) \\
* \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_n}(g) \\
* \vdots & \vdots & \ddots & \vdots\\
* \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_n}(g)
* \end{bmatrix},
* \f]
* where \f$g\f$ is the response, \f$\boldsymbol{x}\f$ is the solution vector, \f$\boldsymbol{p}_1\f$ is a first parameter, \f$\ldots\f$, and \f$\boldsymbol{p}_n\f$ is the \f$n\f$-th
* parameter, this function computes the contribution:
* \f[
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_j}(g)\boldsymbol{v}_{\boldsymbol{p}_j},
* \f]
* where \f$i\f$ and \f$j\f$ are 2 (potentially different) indices included in the range \f$\left[1,n\right]\f$.
*
* This function can currently compute only one block contribution at a time; for one function call \f$\boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_j}(g)\boldsymbol{v}_{\boldsymbol{p}_j}\f$
* can be computed only for one fixed \f$j\f$ and one fixed response index at a time.
*
* \param response_index [in] Response index of the response which the Hessian is computed.
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param v [in] Direction vector on which the Hessian is applied: \f$\boldsymbol{v}_{\boldsymbol{p}_j}\f$.
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$.
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param param_direction_name [in] Name of the parameter used for the second differentiation: \f$\boldsymbol{p}_j\f$.
*
* \param Hv_g_xp [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_j}(g)\boldsymbol{v}_{\boldsymbol{p}_j}\f$.
*
* This implementation relies on:
* <ul>
* <li> PHAL::GatherSolution<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarExtruded2DNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::SeparableScatterScalarResponse<PHAL::AlbanyTraits::HessianVec,Traits>.
* </ul>
*/
void
evaluateResponse_HessVecProd_xp(
int response_index,
const double current_time,
const Teuchos::RCP<const Thyra_MultiVector>& v,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const std::string& param_direction_name,
const Teuchos::RCP<Thyra_MultiVector>& Hv_g_xp);
/**
* \brief evaluateResponse_HessVecProd_px function
*
* This function is used to compute contributions of the application of the Hessian \f$\boldsymbol{H}(g)\f$ of the <tt>response[response_index]</tt>
* (i.e. the response_index-th response) to a direction vector \f$\boldsymbol{v}\f$.
*
* Representing the Hessian \f$\boldsymbol{H}(g)\f$ as a block matrix:
* \f[
* \boldsymbol{H}(g) :=
* \begin{bmatrix}
* \frac{\partial^{2} g}{\partial \boldsymbol{x}^{2}} & \frac{\partial^{2} g}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{n}} \\
* \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{x}} & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1}^{2}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{p}_{n}} \\
* \vdots & \vdots & \ddots & \vdots\\
* \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n} \partial \boldsymbol{x}} & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n}\partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n}^{2}}
* \end{bmatrix} =
* \begin{bmatrix}
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_n}(g) \\
* \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_n}(g) \\
* \vdots & \vdots & \ddots & \vdots\\
* \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_n}(g)
* \end{bmatrix},
* \f]
* where \f$g\f$ is the response, \f$\boldsymbol{x}\f$ is the solution vector, \f$\boldsymbol{p}_1\f$ is a first parameter, \f$\ldots\f$, and \f$\boldsymbol{p}_n\f$ is the \f$n\f$-th
* parameter, this function computes the contribution:
* \f[
* \boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{x}}(g)\boldsymbol{v}_{\boldsymbol{x}},
* \f]
* where \f$i\f$ is an index included in the range \f$\left[1,n\right]\f$.
*
* This function can currently compute only one block contribution at a time; for one function call \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{x}}(g)\boldsymbol{v}_{\boldsymbol{x}}\f$
* can be computed only for one fixed \f$i\f$ and one fixed response index at a time.
*
* \param response_index [in] Response index of the response which the Hessian is computed.
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param v [in] Direction vector on which the Hessian is applied: \f$\boldsymbol{v}_{\boldsymbol{x}}\f$
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param param_name [in] Name of the parameter used for the first differentiation: \f$\boldsymbol{p}_i\f$.
*
* \param Hv_g_px [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{x}}(g)\boldsymbol{v}_{\boldsymbol{x}}\f$.
*
* This implementation relies on:
* <ul>
* <li> PHAL::GatherSolution<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarExtruded2DNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::SeparableScatterScalarResponse<PHAL::AlbanyTraits::HessianVec,Traits>.
* </ul>
*/
void
evaluateResponse_HessVecProd_px(
int response_index,
const double current_time,
const Teuchos::RCP<const Thyra_MultiVector>& v,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const std::string& param_name,
const Teuchos::RCP<Thyra_MultiVector>& Hv_g_px);
/**
* \brief evaluateResponse_HessVecProd_pp function
*
* This function is used to compute contributions of the application of the Hessian \f$\boldsymbol{H}(g)\f$ of the <tt>response[response_index]</tt>
* (i.e. the response_index-th response) to a direction vector \f$\boldsymbol{v}\f$.
*
* Representing the Hessian \f$\boldsymbol{H}(g)\f$ as a block matrix:
* \f[
* \boldsymbol{H}(g) :=
* \begin{bmatrix}
* \frac{\partial^{2} g}{\partial \boldsymbol{x}^{2}} & \frac{\partial^{2} g}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{n}} \\
* \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{x}} & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1}^{2}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{p}_{n}} \\
* \vdots & \vdots & \ddots & \vdots\\
* \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n} \partial \boldsymbol{x}} & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n}\partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} g}{\partial \boldsymbol{p}_{n}^{2}}
* \end{bmatrix} =
* \begin{bmatrix}
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_n}(g) \\
* \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_n}(g) \\
* \vdots & \vdots & \ddots & \vdots\\
* \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{x}}(g) & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_1}(g) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_n}(g)
* \end{bmatrix},
* \f]
* where \f$g\f$ is the response, \f$\boldsymbol{x}\f$ is the solution vector, \f$\boldsymbol{p}_1\f$ is a first parameter, \f$\ldots\f$, and \f$\boldsymbol{p}_n\f$ is the \f$n\f$-th
* parameter, this function computes the contribution:
* \f[
* \boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{p}_j}(g)\boldsymbol{v}_{\boldsymbol{p}_j},
* \f]
* where \f$i\f$ and \f$j\f$ are 2 (potentially different) indices included in the range \f$\left[1,n\right]\f$.
*
* This function can currently compute only one block contribution at a time; for one function call \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{p}_j}(g)\boldsymbol{v}_{\boldsymbol{p}_j}\f$
* can be computed only for one fixed \f$i\f$, one fixed \f$j\f$, and one fixed response index at a time.
*
* \param response_index [in] Response index of the response which the Hessian is computed.
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param v [in] Direction vector on which the Hessian is applied: \f$\boldsymbol{v}_{\boldsymbol{p}_j}\f$.
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$.
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param param_name [in] Name of the parameter used for the first differentiation: \f$\boldsymbol{p}_i\f$.
*
* \param param_direction_name [in] Name of the parameter used for the second differentiation: \f$\boldsymbol{p}_j\f$.
*
* \param Hv_g_pp [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{p}_j}(g)\boldsymbol{v}_{\boldsymbol{p}_j}\f$.
*
* This implementation relies on:
* <ul>
* <li> PHAL::GatherSolution<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarExtruded2DNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::SeparableScatterScalarResponse<PHAL::AlbanyTraits::HessianVec,Traits>.
* </ul>
*/
void
evaluateResponse_HessVecProd_pp(
int response_index,
const double current_time,
const Teuchos::RCP<const Thyra_MultiVector>& v,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const std::string& param_name,
const std::string& param_direction_name,
const Teuchos::RCP<Thyra_MultiVector>& Hv_g_pp);
/**
* \brief evaluateResponseHessian_pp function
*
* This function is used to compute the Hessian \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{p}_i}(g)\f$ of the <tt>response[response_index]</tt>
* (i.e. the response_index-th response) where \f$g\f$ is the response and \f$\boldsymbol{p}_i\f$ is a parameter.
*
* \param response_index [in] Response index of the response which the Hessian is computed.
*
* \param parameter_index [in] Parameter index of the parameter.
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$.
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param param_name [in] Name of the parameter.
*
* \param H [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{p}_i}(g)\f$.
*/
void
evaluateResponseHessian_pp(
int response_index,
int parameter_index,
const double current_time,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const std::string& param_name,
const Teuchos::RCP<Thyra_LinearOp>& H);
/**
* \brief evaluateResidual_HessVecProd_xx function
*
* This function is used to compute contributions of the application of the Hessian \f$\boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\f$ of the inner product of the residual vector \f$\boldsymbol{f}\f$
* and a Lagrange multiplier vector \f$\boldsymbol{z}\f$ to a direction vector \f$\boldsymbol{v}\f$.
*
* Representing the Hessian \f$\boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\f$ as a block matrix:
* \f[
* \boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) :=
* \begin{bmatrix}
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x}^{2}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{n}} \\
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{x}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1}^{2}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{p}_{n}} \\
* \vdots & \vdots & \ddots & \vdots\\
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n} \partial \boldsymbol{x}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n}\partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n}^{2}}
* \end{bmatrix} =
* \begin{bmatrix}
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) \\
* \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) \\
* \vdots & \vdots & \ddots & \vdots\\
* \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)
* \end{bmatrix},
* \f]
* where \f$\boldsymbol{x}\f$ is the solution vector, \f$\boldsymbol{p}_1\f$ is a first parameter, \f$\ldots\f$, and \f$\boldsymbol{p}_n\f$ is the \f$n\f$-th
* parameter, this function computes the contribution:
* \f[
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{x}}.
* \f]
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param v [in] Direction vector on which the Hessian is applied: \f$\boldsymbol{v}_{\boldsymbol{x}}\f$.
*
* \param z [in] Lagrange multiplier vector: \f$\boldsymbol{z}\f$.
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$.
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param Hv_f_xx [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{x}}\f$.
*
* This implementation relies on:
* <ul>
* <li> PHAL::GatherSolution<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarExtruded2DNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::ScatterResidual<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::ScatterResidualWithExtrudedParams<PHAL::AlbanyTraits::HessianVec,Traits>.
* </ul>
*/
void
evaluateResidual_HessVecProd_xx(
const double current_time,
const Teuchos::RCP<const Thyra_MultiVector>& v,
const Teuchos::RCP<const Thyra_Vector>& z,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const Teuchos::RCP<Thyra_MultiVector>& Hv_f_xx);
/**
* \brief evaluateResidual_HessVecProd_xp function
*
* This function is used to compute contributions of the application of the Hessian \f$\boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\f$ of the inner product of the residual vector \f$\boldsymbol{f}\f$
* and a Lagrange multiplier vector \f$\boldsymbol{z}\f$ to a direction vector \f$\boldsymbol{v}\f$.
*
* Representing the Hessian \f$\boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\f$ as a block matrix:
* \f[
* \boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) :=
* \begin{bmatrix}
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x}^{2}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{n}} \\
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{x}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1}^{2}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{p}_{n}} \\
* \vdots & \vdots & \ddots & \vdots\\
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n} \partial \boldsymbol{x}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n}\partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n}^{2}}
* \end{bmatrix} =
* \begin{bmatrix}
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) \\
* \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) \\
* \vdots & \vdots & \ddots & \vdots\\
* \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)
* \end{bmatrix},
* \f]
* where \f$\boldsymbol{x}\f$ is the solution vector, \f$\boldsymbol{p}_1\f$ is a first parameter, \f$\ldots\f$, and \f$\boldsymbol{p}_n\f$ is the \f$n\f$-th
* parameter, this function computes the contribution:
* \f[
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_j}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{p}_j},
* \f]
* where \f$j\f$ is an index included in the range \f$\left[1,n\right]\f$.
*
* This function can currently compute only one block contribution at a time; for one function call \f$\boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_j}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{p}_j}\f$
* can be computed for only one fixed \f$j\f$ at a time.
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param v [in] Direction vector on which the Hessian is applied: \f$\boldsymbol{v}_{\boldsymbol{p}_j}\f$.
*
* \param z [in] Lagrange multiplier vector: \f$\boldsymbol{z}\f$.
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$.
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param param_direction_name [in] Name of the parameter used for the second differentiation: \f$\boldsymbol{p}_j\f$.
*
* \param Hv_f_xp [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_j}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{p}_j}\f$.
*
* This implementation relies on:
* <ul>
* <li> PHAL::GatherSolution<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarExtruded2DNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::ScatterResidual<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::ScatterResidualWithExtrudedParams<PHAL::AlbanyTraits::HessianVec,Traits>.
* </ul>
*/
void
evaluateResidual_HessVecProd_xp(
const double current_time,
const Teuchos::RCP<const Thyra_MultiVector>& v,
const Teuchos::RCP<const Thyra_Vector>& z,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const std::string& param_direction_name,
const Teuchos::RCP<Thyra_MultiVector>& Hv_f_xp);
/**
* \brief evaluateResidual_HessVecProd_px function
*
* This function is used to compute contributions of the application of the Hessian \f$\boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\f$ of the inner product of the residual vector \f$\boldsymbol{f}\f$
* and a Lagrange multiplier vector \f$\boldsymbol{z}\f$ to a direction vector \f$\boldsymbol{v}\f$.
*
* Representing the Hessian \f$\boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\f$ as a block matrix:
* \f[
* \boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) :=
* \begin{bmatrix}
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x}^{2}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{n}} \\
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{x}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1}^{2}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{p}_{n}} \\
* \vdots & \vdots & \ddots & \vdots\\
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n} \partial \boldsymbol{x}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n}\partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n}^{2}}
* \end{bmatrix} =
* \begin{bmatrix}
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) \\
* \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) \\
* \vdots & \vdots & \ddots & \vdots\\
* \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)
* \end{bmatrix},
* \f]
* where \f$\boldsymbol{x}\f$ is the solution vector, \f$\boldsymbol{p}_1\f$ is a first parameter, \f$\ldots\f$, and \f$\boldsymbol{p}_n\f$ is the \f$n\f$-th
* parameter, this function computes the contribution:
* \f[
* \boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{x}},
* \f]
* where \f$i\f$ is an index included in the range \f$\left[1,n\right]\f$.
*
* This function can currently compute only one block contribution at a time; for one function call \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{x}}\f$
* can be computed for only one fixed \f$i\f$ at a time.
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param v [in] Direction vector on which the Hessian is applied: \f$\boldsymbol{v}_{\boldsymbol{x}}\f$.
*
* \param z [in] Lagrange multiplier vector: \f$\boldsymbol{z}\f$.
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$.
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param param_name [in] Name of the parameter used for the first differentiation: \f$\boldsymbol{p}_i\f$.
*
* \param Hv_f_px [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{x}}\f$.
*
* This implementation relies on:
* <ul>
* <li> PHAL::GatherSolution<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarExtruded2DNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::ScatterResidual<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::ScatterResidualWithExtrudedParams<PHAL::AlbanyTraits::HessianVec,Traits>.
* </ul>
*/
void
evaluateResidual_HessVecProd_px(
const double current_time,
const Teuchos::RCP<const Thyra_MultiVector>& v,
const Teuchos::RCP<const Thyra_Vector>& z,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const std::string& param_name,
const Teuchos::RCP<Thyra_MultiVector>& Hv_f_px);
/**
* \brief evaluateResidual_HessVecProd_pp function
*
* This function is used to compute contributions of the application of the Hessian \f$\boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\f$ of the inner product of the residual vector \f$\boldsymbol{f}\f$
* and a Lagrange multiplier vector \f$\boldsymbol{z}\f$ to a direction vector \f$\boldsymbol{v}\f$.
*
* Representing the Hessian \f$\boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\f$ as a block matrix:
* \f[
* \boldsymbol{H}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) :=
* \begin{bmatrix}
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x}^{2}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{x} \partial \boldsymbol{p}_{n}} \\
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{x}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1}^{2}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{1} \partial \boldsymbol{p}_{n}} \\
* \vdots & \vdots & \ddots & \vdots\\
* \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n} \partial \boldsymbol{x}} & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n}\partial \boldsymbol{p}_{1}} & \cdots & \frac{\partial^{2} \left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle}{\partial \boldsymbol{p}_{n}^{2}}
* \end{bmatrix} =
* \begin{bmatrix}
* \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{x}\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) \\
* \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_1\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) \\
* \vdots & \vdots & \ddots & \vdots\\
* \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{x}}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_1}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle) & \cdots & \boldsymbol{H}_{\boldsymbol{p}_n\boldsymbol{p}_n}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)
* \end{bmatrix},
* \f]
* where \f$\boldsymbol{x}\f$ is the solution vector, \f$\boldsymbol{p}_1\f$ is a first parameter, \f$\ldots\f$, and \f$\boldsymbol{p}_n\f$ is the \f$n\f$-th
* parameter, this function computes the contribution:
* \f[
* \boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{p}_j}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{p}_j},
* \f]
* where \f$i\f$ and \f$j\f$ are 2 (potentially different) indices included in the range \f$\left[1,n\right]\f$.
*
* This function can currently compute only one block contribution at a time; for one function call \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{p}_j}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{p}_j}\f$
* can be computed for only one fixed \f$i\f$ and one fixed \f$j\f$ at a time.
*
* \param current_time [in] Current time at which the Hessian is computed for transient simulations.
*
* \param v [in] Direction vector on which the Hessian is applied: \f$\boldsymbol{v}_{\boldsymbol{p}_j}\f$.
*
* \param z [in] Lagrange multiplier vector: \f$\boldsymbol{z}\f$.
*
* \param x [in] Solution vector for the current time step: \f$\boldsymbol{x}\f$.
*
* \param xdot [in] Velocity vector for the current time step.
*
* \param xdotdot [in] Acceleration vector for the current time step.
*
* \param param_array [in] Array of the parameters vectors.
*
* \param param_name [in] Name of the parameter used for the first differentiation: \f$\boldsymbol{p}_i\f$.
*
* \param param_direction_name [in] Name of the parameter used for the second differentiation: \f$\boldsymbol{p}_j\f$.
*
* \param Hv_f_pp [out] the output of the computation: \f$\boldsymbol{H}_{\boldsymbol{p}_i\boldsymbol{p}_j}(\left\langle \boldsymbol{f},\boldsymbol{z}\right\rangle)\boldsymbol{v}_{\boldsymbol{p}_j}\f$.
*
* This implementation relies on:
* <ul>
* <li> PHAL::GatherSolution<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::GatherScalarExtruded2DNodalParameter<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::ScatterResidual<PHAL::AlbanyTraits::HessianVec,Traits>,
* <li> PHAL::ScatterResidualWithExtrudedParams<PHAL::AlbanyTraits::HessianVec,Traits>.
* </ul>
*/
void
evaluateResidual_HessVecProd_pp(
const double current_time,
const Teuchos::RCP<const Thyra_MultiVector>& v,
const Teuchos::RCP<const Thyra_Vector>& z,
const Teuchos::RCP<const Thyra_Vector>& x,
const Teuchos::RCP<const Thyra_Vector>& xdot,
const Teuchos::RCP<const Thyra_Vector>& xdotdot,
const Teuchos::Array<ParamVec>& param_array,
const std::string& param_name,
const std::string& param_direction_name,
const Teuchos::RCP<Thyra_MultiVector>& Hv_f_pp);
//! Class to manage state variables (a.k.a. history)
StateManager&
getStateMgr()
{
return stateMgr;
}
//! Evaluate state field manager
void
evaluateStateFieldManager(
const double current_time,
const Thyra_Vector& x,
Teuchos::Ptr<const Thyra_Vector> xdot,
Teuchos::Ptr<const Thyra_Vector> xdotdot,
Teuchos::Ptr<const Thyra_MultiVector> dxdp = Teuchos::null);
void
evaluateStateFieldManager(
const double current_time,
const Thyra_MultiVector& x,
Teuchos::Ptr<const Thyra_MultiVector> dxdp = Teuchos::null);
//! Access to number of worksets - needed for working with StateManager
int getNumWorksets() const { return disc->getNumWorksets(); }