Cantera  2.2.1
solveSP Class Reference

Method to solve a pseudo steady state surface problem. More...

#include <solveSP.h>

Collaboration diagram for solveSP:
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## Public Member Functions

solveSP (ImplicitSurfChem *surfChemPtr, int bulkFunc=BULK_ETCH)
Constructor for the object. More...

~solveSP ()
Destructor. Deletes the integrator. More...

int solveSurfProb (int ifunc, doublereal time_scale, doublereal TKelvin, doublereal PGas, doublereal reltol, doublereal abstol)
Main routine that actually calculates the pseudo steady state of the surface problem. More...

int m_ioflag

## Private Member Functions

solveSP (const solveSP &right)
Unimplemented private copy constructor. More...

solveSPoperator= (const solveSP &right)
Unimplemented private assignment operator. More...

void print_header (int ioflag, int ifunc, doublereal time_scale, int damping, doublereal reltol, doublereal abstol)
Printing routine that optionally gets called at the start of every invocation. More...

void printIteration (int ioflag, doublereal damp, int label_d, int label_t, doublereal inv_t, doublereal t_real, size_t iter, doublereal update_norm, doublereal resid_norm, bool do_time, bool final=false)
Printing routine that gets called after every iteration. More...

doublereal calc_t (doublereal netProdRateSolnSP[], doublereal XMolSolnSP[], int *label, int *label_old, doublereal *label_factor, int ioflag)
Calculate a conservative delta T to use in a pseudo-steady state algorithm. More...

void calcWeights (doublereal wtSpecies[], doublereal wtResid[], const Array2D &Jac, const doublereal CSolnSP[], const doublereal abstol, const doublereal reltol)
Calculate the solution and residual weights. More...

Update the surface states of the surface phases. More...

void updateMFSolnSP (doublereal *XMolSolnSP)
Update mole fraction vector consisting of unknowns in surface problem. More...

void updateMFKinSpecies (doublereal *XMolKinSp, int isp)
Update the mole fraction vector for a specific kinetic species vector corresponding to one InterfaceKinetics object. More...

void evalSurfLarge (const doublereal *CSolnSP)
Update the vector that keeps track of the largest species in each surface phase. More...

void fun_eval (doublereal *resid, const doublereal *CSolnSP, const doublereal *CSolnOldSP, const bool do_time, const doublereal deltaT)
Main Function evaluation. More...

void resjac_eval (SquareMatrix &jac, doublereal *resid, doublereal *CSolnSP, const doublereal *CSolnSPOld, const bool do_time, const doublereal deltaT)
Main routine that calculates the current residual and Jacobian. More...

## Private Attributes

ImplicitSurfChemm_SurfChemPtr
Pointer to the manager of the implicit surface chemistry problem. More...

std::vector< InterfaceKinetics * > & m_objects
Vector of interface kinetics objects. More...

size_t m_neq
Total number of equations to solve in the implicit problem. More...

int m_bulkFunc
This variable determines how the bulk phases are to be handled. More...

size_t m_numSurfPhases
Number of surface phases in the surface problem. More...

size_t m_numTotSurfSpecies
Total number of surface species in all surface phases. More...

std::vector< size_t > m_indexKinObjSurfPhase
Mapping between the surface phases and the InterfaceKinetics objects. More...

std::vector< size_t > m_nSpeciesSurfPhase
Vector of length number of surface phases containing the number of surface species in each phase. More...

Vector of surface phase pointers. More...

std::vector< size_t > m_eqnIndexStartSolnPhase
Index of the start of the unknowns for each solution phase. More...

std::vector< size_t > m_kinObjPhaseIDSurfPhase
Phase ID in the InterfaceKinetics object of the surface phase. More...

size_t m_numBulkPhasesSS
Total number of volumetric condensed phases included in the steady state problem handled by this routine. More...

std::vector< size_t > m_numBulkSpecies
Vector of number of species in the m_numBulkPhases phases. More...

size_t m_numTotBulkSpeciesSS
Total number of species in all bulk phases. More...

std::vector< ThermoPhase * > m_bulkPhasePtrs
Vector of bulk phase pointers, length is equal to m_numBulkPhases. More...

std::vector< size_t > m_kinSpecIndex
Index between the equation index and the position in the kinetic species array for the appropriate kinetics operator. More...

std::vector< size_t > m_kinObjIndex
Index between the equation index and the index of the InterfaceKinetics object. More...

std::vector< size_t > m_spSurfLarge
Vector containing the indices of the largest species in each surface phase. More...

doublereal m_atol
The absolute tolerance in real units. units are (kmol/m2) More...

doublereal m_rtol
The relative error tolerance. More...

doublereal m_maxstep
maximum value of the time step. units = seconds More...

size_t m_maxTotSpecies
Maximum number of species in any single kinetics operator -> also maxed wrt the total # of solution species. More...

vector_fp m_netProductionRatesSave
Temporary vector with length equal to max m_maxTotSpecies. More...

vector_fp m_numEqn1
Temporary vector with length equal to max m_maxTotSpecies. More...

vector_fp m_numEqn2
Temporary vector with length equal to max m_maxTotSpecies. More...

vector_fp m_CSolnSave
Temporary vector with length equal to max m_maxTotSpecies. More...

vector_fp m_CSolnSP
Solution vector. length MAX(1, m_neq) More...

vector_fp m_CSolnSPInit
Saved initial solution vector. length MAX(1, m_neq) More...

vector_fp m_CSolnSPOld
Saved solution vector at the old time step. length MAX(1, m_neq) More...

vector_fp m_wtResid
Weights for the residual norm calculation. length MAX(1, m_neq) More...

vector_fp m_wtSpecies
Weights for the species concentrations norm calculation. More...

vector_fp m_resid
Residual for the surface problem. More...

vector_fp m_XMolKinSpecies
Vector of mole fractions. length m_maxTotSpecies. More...

SquareMatrix m_Jac
Jacobian. More...

## Detailed Description

Method to solve a pseudo steady state surface problem.

The following class handles solving the surface problem. The calculation uses Newton's method to obtain the surface fractions of the surface and bulk species by requiring that the surface species production rate = 0 and that the either the bulk fractions are proportional to their production rates or they are constants.

Currently, the bulk mole fractions are treated as constants. Implementation of their being added to the unknown solution vector is delayed.

Lets introduce the unknown vector for the "surface problem". The surface problem is defined as the evaluation of the surface site fractions for multiple surface phases. The unknown vector will consist of the vector of surface concentrations for each species in each surface vector. Species are grouped first by their surface phases

• C_i_j = Concentration of the ith species in the jth surface phase
• Nj = number of surface species in the jth surface phase

The unknown solution vector is defined as follows:

C_i_j kindexSP
C_0_0 0
C_1_0 1
C_2_0 2
. . . ...
C_N0-1_0 N0-1
C_0_1 N0
C_1_1 N0+1
C_2_1 N0+2
. . . ...
C_N1-1_1 NO+N1-1

Note there are a couple of different types of species indices floating around in the formulation of this object.

kindexSP: This is the species index in the contiguous vector of unknowns for the surface problem.

Note, in the future, BULK_DEPOSITION systems will be added, and the solveSP unknown vector will get more complicated. It will include the mole fraction and growth rates of specified bulk phases

Indices which relate to individual kinetics objects use the suffix KSI (kinetics species index).

## Solution Method

This routine is typically used within a residual calculation in a large code. It's typically invoked millions of times for large calculations, and it must work every time. Therefore, requirements demand that it be robust but also efficient.

The solution methodology is largely determined by the ifunc parameter, that is input to the solution object. This parameter may have one of the values defined in Surface Problem Solver Methods.

### Pseudo time stepping algorithm:

The time step is determined from sdot[], so so that the time step doesn't ever change the value of a variable by more than 100%.

This algorithm does use a damped Newton's method to relax the equations. Damping is based on a "delta damping" technique. The solution unknowns are not allowed to vary too much between iterations.

EXTRA_ACCURACY: A constant that is the ratio of the required update norm in this Newton iteration compared to that in the nonlinear solver. A value of 0.1 is used so surface species are safely overconverged.

Functions called:

• ct_dgetrf – First half of LAPACK direct solve of a full Matrix
• ct_dgetrs – Second half of LAPACK direct solve of a full matrix. Returns solution vector in the right-hand-side vector, resid.

Definition at line 142 of file solveSP.h.

## Constructor & Destructor Documentation

 solveSP ( ImplicitSurfChem * surfChemPtr, int bulkFunc = BULK_ETCH )

Constructor for the object.

Parameters
 surfChemPtr Pointer to the ImplicitSurfChem object that defines the surface problem to be solved. bulkFunc Integer representing how the bulk phases should be handled. See Surface Problem Bulk Phase Mode. Currently, only the default value of BULK_ETCH is supported.

Definition at line 32 of file solveSP.cpp.

 ~solveSP ( )
inline

Destructor. Deletes the integrator.

Definition at line 157 of file solveSP.h.

 solveSP ( const solveSP & right )
private

Unimplemented private copy constructor.

## Member Function Documentation

 solveSP& operator= ( const solveSP & right )
private

Unimplemented private assignment operator.

 int solveSurfProb ( int ifunc, doublereal time_scale, doublereal TKelvin, doublereal PGas, doublereal reltol, doublereal abstol )

Main routine that actually calculates the pseudo steady state of the surface problem.

The actual converged solution is returned as part of the internal state of the InterfaceKinetics objects.

Uses Newton's method to get the surface fractions of the surface and bulk species by requiring that the surface species production rate = 0 and that the bulk fractions are proportional to their production rates.

Parameters
 ifunc Determines the type of solution algorithm to be used. See Surface Problem Solver Methods for possible values. time_scale Time over which to integrate the surface equations, where applicable TKelvin Temperature (kelvin) PGas Pressure (pascals) reltol Relative tolerance to use abstol absolute tolerance.
Returns
Returns 1 if the surface problem is successfully solved. Returns -1 if the surface problem wasn't solved successfully. Note the actual converged solution is returned as part of the internal state of the InterfaceKinetics objects.

Definition at line 131 of file solveSP.cpp.

 void print_header ( int ioflag, int ifunc, doublereal time_scale, int damping, doublereal reltol, doublereal abstol )
private

Printing routine that optionally gets called at the start of every invocation.

Definition at line 791 of file solveSP.cpp.

Referenced by solveSP::solveSurfProb().

 void printIteration ( int ioflag, doublereal damp, int label_d, int label_t, doublereal inv_t, doublereal t_real, size_t iter, doublereal update_norm, doublereal resid_norm, bool do_time, bool final = false )
private

Printing routine that gets called after every iteration.

Definition at line 840 of file solveSP.cpp.

Referenced by solveSP::solveSurfProb().

 doublereal calc_t ( doublereal netProdRateSolnSP[], doublereal XMolSolnSP[], int * label, int * label_old, doublereal * label_factor, int ioflag )
private

Calculate a conservative delta T to use in a pseudo-steady state algorithm.

This routine calculates a pretty conservative 1/del_t based on MAX_i(sdot_i/(X_i*SDen0)). This probably guarantees diagonal dominance.

Small surface fractions are allowed to intervene in the del_t determination, no matter how small. This may be changed. Now minimum changed to 1.0e-12,

Maximum time step set to time_scale.

Parameters
 netProdRateSolnSP Output variable. Net production rate of all of the species in the solution vector. XMolSolnSP output variable. Mole fraction of all of the species in the solution vector label Output variable. Pointer to the value of the species index (kindexSP) that is controlling the time step label_old Output variable. Pointer to the value of the species index (kindexSP) that controlled the time step at the previous iteration label_factor Output variable. Pointer to the current factor that is used to indicate the same species is controlling the time step. ioflag Level of the output requested.
Returns
Returns the 1. / delta T to be used on the next step

Definition at line 732 of file solveSP.cpp.

Referenced by solveSP::solveSurfProb().

 void calcWeights ( doublereal wtSpecies[], doublereal wtResid[], const Array2D & Jac, const doublereal CSolnSP[], const doublereal abstol, const doublereal reltol )
private

Calculate the solution and residual weights.

Parameters
 wtSpecies Weights to use for the soln unknowns. These are in concentration units wtResid Weights to sue for the residual unknowns. Jac Jacobian. Row sum scaling is used for the Jacobian CSolnSP Solution vector for the surface problem abstol Absolute error tolerance reltol Relative error tolerance

Definition at line 691 of file solveSP.cpp.

Referenced by solveSP::solveSurfProb().

 void updateState ( const doublereal * cSurfSpec )
private

Update the surface states of the surface phases.

Definition at line 400 of file solveSP.cpp.

Referenced by solveSP::fun_eval(), and solveSP::solveSurfProb().

 void updateMFSolnSP ( doublereal * XMolSolnSP )
private

Update mole fraction vector consisting of unknowns in surface problem.

Parameters
 XMolSolnSP Vector of mole fractions for the unknowns in the surface problem.

Definition at line 409 of file solveSP.cpp.

Referenced by solveSP::calc_t().

 void updateMFKinSpecies ( doublereal * XMolKinSp, int isp )
private

Update the mole fraction vector for a specific kinetic species vector corresponding to one InterfaceKinetics object.

Parameters
 XMolKinSp Mole fraction vector corresponding to a particular kinetic species for a single InterfaceKinetics Object This is a vector over all the species in all of the phases in the InterfaceKinetics object isp ID of the InterfaceKinetics Object.

Definition at line 417 of file solveSP.cpp.

 void evalSurfLarge ( const doublereal * CSolnSP )
private

Update the vector that keeps track of the largest species in each surface phase.

Parameters
 CSolnSP Vector of the current values of the surface concentrations in all of the surface species.

Definition at line 428 of file solveSP.cpp.

Referenced by solveSP::solveSurfProb().

 void fun_eval ( doublereal * resid, const doublereal * CSolnSP, const doublereal * CSolnOldSP, const bool do_time, const doublereal deltaT )
private

Main Function evaluation.

Parameters
 resid output Vector of residuals, length = m_neq CSolnSP Vector of species concentrations, unknowns in the problem, length = m_neq CSolnOldSP Old Vector of species concentrations, unknowns in the problem, length = m_neq do_time Calculate a time dependent residual deltaT Delta time for time dependent problem.

Definition at line 445 of file solveSP.cpp.

Referenced by solveSP::resjac_eval(), and solveSP::solveSurfProb().

 void resjac_eval ( SquareMatrix & jac, doublereal * resid, doublereal * CSolnSP, const doublereal * CSolnSPOld, const bool do_time, const doublereal deltaT )
private

Main routine that calculates the current residual and Jacobian.

Parameters
 jac Jacobian to be evaluated. resid output Vector of residuals, length = m_neq CSolnSP Vector of species concentrations, unknowns in the problem, length = m_neq. These are tweaked in order to derive the columns of the Jacobian. CSolnSPOld Old Vector of species concentrations, unknowns in the problem, length = m_neq do_time Calculate a time dependent residual deltaT Delta time for time dependent problem.

Definition at line 557 of file solveSP.cpp.

Referenced by solveSP::solveSurfProb().

## Member Data Documentation

 ImplicitSurfChem* m_SurfChemPtr
private

Pointer to the manager of the implicit surface chemistry problem.

This object actually calls the current object. Thus, we are providing a loop-back functionality here.

Definition at line 322 of file solveSP.h.

 std::vector& m_objects
private

Vector of interface kinetics objects.

Each of these is associated with one and only one surface phase.

Definition at line 328 of file solveSP.h.

 size_t m_neq
private

Total number of equations to solve in the implicit problem.

Note, this can be zero, and frequently is

Definition at line 334 of file solveSP.h.

 int m_bulkFunc
private

This variable determines how the bulk phases are to be handled.

Possible values are given in Surface Problem Bulk Phase Mode.

Definition at line 340 of file solveSP.h.

 size_t m_numSurfPhases
private

Number of surface phases in the surface problem.

This number is equal to the number of InterfaceKinetics objects in the problem. (until further noted)

Definition at line 347 of file solveSP.h.

 size_t m_numTotSurfSpecies
private

Total number of surface species in all surface phases.

This is also the number of equations to solve for m_mode=0 system It's equal to the sum of the number of species in each of the m_numSurfPhases.

Definition at line 355 of file solveSP.h.

Referenced by solveSP::fun_eval(), and solveSP::solveSP().

 std::vector m_indexKinObjSurfPhase
private

Mapping between the surface phases and the InterfaceKinetics objects.

Currently this is defined to be a 1-1 mapping (and probably assumed in some places) m_surfKinObjID[i] = i

Definition at line 363 of file solveSP.h.

Referenced by solveSP::fun_eval(), and solveSP::solveSP().

 std::vector m_nSpeciesSurfPhase
private

Vector of length number of surface phases containing the number of surface species in each phase.

Length is equal to the number of surface phases, m_numSurfPhases

Definition at line 370 of file solveSP.h.

private

Vector of surface phase pointers.

This is created during the constructor Length is equal to the number of surface phases, m_numSurfPhases

Definition at line 377 of file solveSP.h.

 std::vector m_eqnIndexStartSolnPhase
private

Index of the start of the unknowns for each solution phase.

i_eqn = m_eqnIndexStartPhase[isp]

isp is the phase id in the list of phases solved by the surface problem.

i_eqn is the equation number of the first unknown in the solution vector corresponding to isp'th phase.

Definition at line 389 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::updateMFSolnSP().

 std::vector m_kinObjPhaseIDSurfPhase
private

Phase ID in the InterfaceKinetics object of the surface phase.

For each surface phase, this lists the PhaseId of the surface phase in the corresponding InterfaceKinetics object

Length is equal to m_numSurfPhases

Definition at line 398 of file solveSP.h.

Referenced by solveSP::solveSP().

 size_t m_numBulkPhasesSS
private

Total number of volumetric condensed phases included in the steady state problem handled by this routine.

This is equal to or less than the total number of volumetric phases in all of the InterfaceKinetics objects. We usually do not include bulk phases. Bulk phases are only included in the calculation when their domain isn't included in the underlying continuum model conservation equation system.

This is equal to 0, for the time being

Definition at line 411 of file solveSP.h.

Referenced by solveSP::calcWeights(), solveSP::fun_eval(), solveSP::resjac_eval(), and solveSP::solveSP().

 std::vector m_numBulkSpecies
private

Vector of number of species in the m_numBulkPhases phases.

Length is number of bulk phases

Definition at line 417 of file solveSP.h.

Referenced by solveSP::calcWeights(), and solveSP::resjac_eval().

 size_t m_numTotBulkSpeciesSS
private

Total number of species in all bulk phases.

This is also the number of bulk equations to solve when bulk equation solving is turned on.

Definition at line 428 of file solveSP.h.

Referenced by solveSP::solveSP().

 std::vector m_bulkPhasePtrs
private

Vector of bulk phase pointers, length is equal to m_numBulkPhases.

Definition at line 431 of file solveSP.h.

Referenced by solveSP::calcWeights(), solveSP::fun_eval(), and solveSP::resjac_eval().

 std::vector m_kinSpecIndex
private

Index between the equation index and the position in the kinetic species array for the appropriate kinetics operator.

Length = m_neq.

ksp = m_kinSpecIndex[ieq] ksp is the kinetic species index for the ieq'th equation.

Definition at line 441 of file solveSP.h.

Referenced by solveSP::printIteration(), solveSP::solveSP(), and solveSP::solveSurfProb().

 std::vector m_kinObjIndex
private

Index between the equation index and the index of the InterfaceKinetics object.

Length m_neq

Definition at line 448 of file solveSP.h.

Referenced by solveSP::printIteration(), and solveSP::solveSP().

 std::vector m_spSurfLarge
private

Vector containing the indices of the largest species in each surface phase.

k = m_spSurfLarge[i] where k is the local species index, i.e., it varies from 0 to (num species in phase - 1) and i is the surface phase index in the problem. Length is equal to m_numSurfPhases.

Definition at line 457 of file solveSP.h.

Referenced by solveSP::evalSurfLarge(), solveSP::fun_eval(), and solveSP::solveSP().

 doublereal m_atol
private

The absolute tolerance in real units. units are (kmol/m2)

Definition at line 460 of file solveSP.h.

 doublereal m_rtol
private

The relative error tolerance.

Definition at line 463 of file solveSP.h.

 doublereal m_maxstep
private

maximum value of the time step. units = seconds

Definition at line 466 of file solveSP.h.

 size_t m_maxTotSpecies
private

Maximum number of species in any single kinetics operator -> also maxed wrt the total # of solution species.

Definition at line 470 of file solveSP.h.

Referenced by solveSP::solveSP().

 vector_fp m_netProductionRatesSave
private

Temporary vector with length equal to max m_maxTotSpecies.

Definition at line 473 of file solveSP.h.

Referenced by solveSP::fun_eval(), solveSP::solveSP(), and solveSP::solveSurfProb().

 vector_fp m_numEqn1
private

Temporary vector with length equal to max m_maxTotSpecies.

Definition at line 476 of file solveSP.h.

Referenced by solveSP::calc_t(), solveSP::fun_eval(), solveSP::solveSP(), and solveSP::solveSurfProb().

 vector_fp m_numEqn2
private

Temporary vector with length equal to max m_maxTotSpecies.

Definition at line 479 of file solveSP.h.

Referenced by solveSP::resjac_eval(), and solveSP::solveSP().

 vector_fp m_CSolnSave
private

Temporary vector with length equal to max m_maxTotSpecies.

Definition at line 482 of file solveSP.h.

Referenced by solveSP::solveSP().

 vector_fp m_CSolnSP
private

Solution vector. length MAX(1, m_neq)

Definition at line 485 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::solveSurfProb().

 vector_fp m_CSolnSPInit
private

Saved initial solution vector. length MAX(1, m_neq)

Definition at line 488 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::solveSurfProb().

 vector_fp m_CSolnSPOld
private

Saved solution vector at the old time step. length MAX(1, m_neq)

Definition at line 491 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::solveSurfProb().

 vector_fp m_wtResid
private

Weights for the residual norm calculation. length MAX(1, m_neq)

Definition at line 494 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::solveSurfProb().

 vector_fp m_wtSpecies
private

Weights for the species concentrations norm calculation.

length MAX(1, m_neq)

Definition at line 500 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::solveSurfProb().

 vector_fp m_resid
private

Residual for the surface problem.

The residual vector of length "dim" that, that has the value of "sdot" for surface species. The residuals for the bulk species are a function of the sdots for all species in the bulk phase. The last residual of each phase enforces {Sum(fractions) = 1}. After linear solve (dgetrf_ & dgetrs_), resid holds the update vector.

length MAX(1, m_neq)

Definition at line 513 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::solveSurfProb().

 vector_fp m_XMolKinSpecies
private

Vector of mole fractions. length m_maxTotSpecies.

Definition at line 516 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::solveSurfProb().

 SquareMatrix m_Jac
private

Jacobian.

m_neq by m_neq computed Jacobian matrix for the local Newton's method.

Definition at line 520 of file solveSP.h.

Referenced by solveSP::solveSP(), and solveSP::solveSurfProb().

The documentation for this class was generated from the following files: