fdWrapper2D.hh

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/* This file is part of the Palabos library.
 *
 * Copyright (C) 2011 FlowKit Sarl
 * Avenue de Chailly 23
 * 1012 Lausanne, Switzerland
 * E-mail contact: contact@flowkit.com
 *
 * The most recent release of Palabos can be downloaded at 
 * <http://www.palabos.org/>
 *
 * The library Palabos is free software: you can redistribute it and/or
 * modify it under the terms of the GNU Affero General Public License as
 * published by the Free Software Foundation, either version 3 of the
 * License, or (at your option) any later version.
 *
 * The library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef FINITE_DIFFERENCE_WRAPPER_2D_HH
#define FINITE_DIFFERENCE_WRAPPER_2D_HH

#include "finiteDifference/fdWrapper2D.h"
#include "finiteDifference/fdFunctional2D.h"
#include "atomicBlock/reductiveDataProcessorWrapper2D.h"
#include "atomicBlock/dataProcessorWrapper2D.h"
#include "multiBlock/reductiveMultiDataProcessorWrapper2D.h"
#include "multiBlock/multiDataProcessorWrapper2D.h"
#include "multiGrid/gridConversion2D.h"


namespace plb {

template<typename T>
void computeXderivative(MultiScalarField2D<T>& value, MultiScalarField2D<T>& derivative, Box2D const& domain) {
    plint boundaryWidth = 1;
    applyProcessingFunctional (
            new BoxXderivativeFunctional2D<T>, domain, value, derivative, boundaryWidth );
}

template<typename T>
std::auto_ptr<MultiScalarField2D<T> > computeXderivative(MultiScalarField2D<T>& value, Box2D const& domain) {
    MultiScalarField2D<T>* derivative = new MultiScalarField2D<T>(value, domain);
    computeXderivative(value, *derivative, domain);
    return std::auto_ptr<MultiScalarField2D<T> >(derivative);
}

template<typename T>
std::auto_ptr<MultiScalarField2D<T> > computeXderivative(MultiScalarField2D<T>& value) {
    return computeXderivative(value, value.getBoundingBox());
}


template<typename T>
void computeYderivative(MultiScalarField2D<T>& value, MultiScalarField2D<T>& derivative, Box2D const& domain) {
    plint boundaryWidth = 1;
    applyProcessingFunctional (
            new BoxYderivativeFunctional2D<T>, domain, value, derivative, boundaryWidth );
}

template<typename T>
std::auto_ptr<MultiScalarField2D<T> > computeYderivative(MultiScalarField2D<T>& value, Box2D const& domain) {
    MultiScalarField2D<T>* derivative = new MultiScalarField2D<T>(value, domain);
    computeYderivative(value, *derivative, domain);
    return std::auto_ptr<MultiScalarField2D<T> >(derivative);
}

template<typename T>
std::auto_ptr<MultiScalarField2D<T> > computeYderivative(MultiScalarField2D<T>& value) {
    return computeYderivative(value, value.getBoundingBox());
}

template<typename T>
void computeGradientNorm(MultiScalarField2D<T>& value, MultiScalarField2D<T>& derivative, Box2D const& domain) {
    plint boundaryWidth = 1;
    applyProcessingFunctional (
            new BoxGradientNormFunctional2D<T>, domain, value, derivative, boundaryWidth );
}

template<typename T>
std::auto_ptr<MultiScalarField2D<T> > computeGradientNorm(MultiScalarField2D<T>& value, Box2D const& domain) {
    MultiScalarField2D<T>* derivative = new MultiScalarField2D<T>(value, domain);
    computeGradientNorm(value, *derivative, domain);
    return std::auto_ptr<MultiScalarField2D<T> >(derivative);
}

template<typename T>
std::auto_ptr<MultiScalarField2D<T> > computeGradientNorm(MultiScalarField2D<T>& value) {
    return computeGradientNorm(value, value.getBoundingBox());
}


template<typename T>
std::auto_ptr<MultiScalarField2D<T> > computePoissonRHS(MultiTensorField2D<T,2>& velocity, Box2D const& domain)
{
    std::auto_ptr<MultiScalarField2D<T> > ux = extractComponent(velocity, domain, 0);
    std::auto_ptr<MultiScalarField2D<T> > uy = extractComponent(velocity, domain, 1);

    std::auto_ptr<MultiScalarField2D<T> > dx_ux = computeXderivative(*ux, domain);
    std::auto_ptr<MultiScalarField2D<T> > dy_ux = computeYderivative(*ux, domain);
    std::auto_ptr<MultiScalarField2D<T> > dx_uy = computeXderivative(*uy, domain);
    std::auto_ptr<MultiScalarField2D<T> > dy_uy = computeYderivative(*uy, domain);

    std::auto_ptr<MultiScalarField2D<T> > term1 = multiply(*dx_ux, *dx_ux, domain);
    std::auto_ptr<MultiScalarField2D<T> > term2 = multiply((T)2, *multiply(*dx_uy, *dy_ux, domain), domain);
    std::auto_ptr<MultiScalarField2D<T> > term3 = multiply(*dy_uy, *dy_uy, domain);

    std::auto_ptr<MultiScalarField2D<T> > rhs = add(*term1, *add(*term2, *term3));
    return rhs;
}

template<typename T>
std::auto_ptr<MultiScalarField2D<T> > computePoissonRHS(MultiTensorField2D<T,2>& velocity) {
    return computePoissonRHS(velocity, velocity.getBoundingBox());
}

template<typename T>
void poissonIterate(MultiScalarField2D<T>& oldPressure, MultiScalarField2D<T>& newPressure,
                    MultiScalarField2D<T>& rhs, T beta, Box2D const& domain)
{
    std::vector<MultiScalarField2D<T>* > fields;
    fields.push_back(&oldPressure);
    fields.push_back(&newPressure);
    fields.push_back(&rhs);
    plint boundaryWidth=1;
    applyProcessingFunctional (
            new BoxPoissonIteration2D<T>(beta), domain, fields, boundaryWidth );
}

template<typename T>
T computePoissonResidue(MultiScalarField2D<T>& pressure, MultiScalarField2D<T>& rhs, Box2D const& domain) {
    BoxPoissonResidueFunctional2D<T> functional;
    applyProcessingFunctional(functional, domain, pressure, rhs);
    return functional.getMaxResidue();
}

/* ************ Wrapper for one Jacobi iteration *************** */
template<typename T> 
void JacobiIteration( MultiScalarField2D<T>& u_h, MultiScalarField2D<T>& new_u_h,
                      MultiScalarField2D<T>& rhs, Box2D const& domain ){
    
    std::vector<MultiScalarField2D<T>* > fields;
    fields.push_back(&u_h);
    fields.push_back(&new_u_h);
    fields.push_back(&rhs);
    plint boundaryWidth=1;
    applyProcessingFunctional (
            new JacobiIteration2D<T>(), domain, fields, boundaryWidth );

}

/* ************ Wrapper for one Gauss-Seidel iteration *************** */
template<typename T> 
void GaussSeidelIteration( MultiScalarField2D<T>& u_h, MultiScalarField2D<T>& jacobi_u_h,
                           MultiScalarField2D<T>& new_u_h, MultiScalarField2D<T>& rhs, Box2D const& domain )
{
    std::vector<MultiScalarField2D<T>* > fields;
    fields.push_back(&u_h);
    fields.push_back(&jacobi_u_h);
    fields.push_back(&new_u_h);
    fields.push_back(&rhs);
    plint boundaryWidth=1;
    applyProcessingFunctional (
            new GaussSeidelIteration2D<T>(), domain, fields, boundaryWidth );
}

/* ************ Wrapper for Gauss-Seidel defect computation *************** */
template<typename T> 
MultiScalarField2D<T>* computeGaussSeidelDefect(MultiScalarField2D<T>& u_h, MultiScalarField2D<T>& rhs, 
                                                Box2D const& domain)
{
    MultiScalarField2D<T>* residual = new MultiScalarField2D<T>(u_h);
    std::vector<MultiScalarField2D<T>* > fields;
    fields.push_back(&u_h);
    fields.push_back(residual);
    fields.push_back(&rhs);
    plint boundaryWidth=1;
    applyProcessingFunctional (
            new GaussSeidelDefect2D<T>(), domain, fields,boundaryWidth);
            
    return residual;
} 

template<typename T>
T computeEuclidianNorm(MultiScalarField2D<T>& matrix, Box2D const& domain){
    T av = computeAverage( *multiply(matrix,matrix),domain);
    return sqrt(av);
}


/* ************ Gauss-Seidel Solver *************** */
template<typename T>
void GaussSeidelSolver( MultiScalarField2D<T>& initialValue,
                        MultiScalarField2D<T>& result,
                        MultiScalarField2D<T>& rhs, Box2D const& domain, T tolerance, plint maxIter )
{
    T originalNorm;
    T newNorm;
    plint infoIt=100;
    
    // to contain the Jacobi result
    MultiScalarField2D<T> jacobiValue(initialValue); 
    jacobiValue.reset();
    
    // computation of the initial residual. We will stop when currentResidual=tolerance*initialResidual
    // or when we have made maxIter iterations
    MultiScalarField2D<T>* defect = computeGaussSeidelDefect<T>(initialValue, rhs, domain);
    originalNorm = computeEuclidianNorm<T>(*defect, domain);
    delete defect;

    // MAIN LOOP
    for (plint iT=0; iT<maxIter; ++iT){
        // use one Jacobi iteration
        JacobiIteration<T>(initialValue, jacobiValue, rhs, domain);
        
        // with this jacobiValue, make one gauss-sidel iteration (eliminate the asynchronie for parallelism)
        GaussSeidelIteration<T>(initialValue, jacobiValue, result, rhs, domain);
        
        // compute the new residual norm to know if we continue
        defect = computeGaussSeidelDefect<T>(result, rhs, domain);
        newNorm = computeEuclidianNorm<T>(*defect, domain);
        delete defect;
        
        if (newNorm < tolerance*originalNorm) 
        {
            pcout << "Gauss-Seidel iterations: " << iT << std::endl;
            break;
        }
        
        // result becomes the new initial value
        result.swap(initialValue);
        
        if (iT%infoIt==0 && iT>0){
            pcout << "Gauss-Seidel iteration " << iT << " : error=" << newNorm/originalNorm 
                  << " : NORM=" << newNorm << std::endl;
        }
    }
    pcout << "Gauss-Seidel iterations: " << maxIter << std::endl;
}

/* ************ MultiGrid method *************** */
template<typename T>
MultiScalarField2D<T>* smooth( MultiScalarField2D<T>& initialValue, 
                               MultiScalarField2D<T>& rhs, Box2D const& domain,
                               plint smoothIters){
    // create the solution for Jacobi
    MultiScalarField2D<T> jacobiValue(initialValue); 
    jacobiValue.reset();
    
    // copy initialValue
    MultiScalarField2D<T> initialCopy(initialValue);
    // the result holder
    MultiScalarField2D<T>* newValue = new MultiScalarField2D<T>(initialValue);
    
    // iteration over the original system: one Jacobi + one Gauss-Seidel
    plint v1 = smoothIters;
    for (plint iV1=0; iV1< v1; ++iV1){
        newValue->swap(initialCopy);
        JacobiIteration<T>(initialCopy, jacobiValue, rhs, domain);
        GaussSeidelIteration<T>(initialCopy, jacobiValue, *newValue, rhs, domain);
    }
   
    return newValue;
}

template<typename T>
MultiScalarField2D<T>* smoothAndInterpolate( MultiScalarField2D<T>& initialValue, 
                                             MultiScalarField2D<T>& rhs, Box2D const& domain,
                                             plint smoothIters )
{
    // smooth
    MultiScalarField2D<T>* coarseNewValue = smooth(initialValue,rhs,domain,smoothIters);
    // interpolate
    MultiScalarField2D<T>* fineNewValue = new MultiScalarField2D<T>(*refine<T>(*coarseNewValue,1,-1,-1,-1));
    delete coarseNewValue;
    
    return fineNewValue;
}

template<typename T>
MultiScalarField2D<T>* smoothAndComputeError( MultiScalarField2D<T>& initialValue, MultiScalarField2D<T>& rhs, 
                         Box2D const& domain, T& newError, plint smoothIters ){
    
    MultiScalarField2D<T>* newValue = smooth(initialValue,rhs,domain,smoothIters);
    // compute the new defect norm
    MultiScalarField2D<T>* newDefect = computeGaussSeidelDefect<T>(*newValue, rhs, domain);
    newError = computeEuclidianNorm<T>(*newDefect, domain);
    delete newDefect;
    
    return newValue;
}

template<typename T>
MultiScalarField2D<T>* smoothAndComputeCoarseDefect( MultiScalarField2D<T>& initialValue, 
                                               MultiScalarField2D<T>& rhs, Box2D const& domain,
                                               plint smoothIters ){
    
    MultiScalarField2D<T>* newValue = smooth(initialValue,rhs,domain,smoothIters);
    // compute the new defect norm
    MultiScalarField2D<T>* newDefect = computeGaussSeidelDefect<T>(*newValue, rhs, domain);
    MultiScalarField2D<T>* coarseDefect = new MultiScalarField2D<T>(*coarsen<T>(*newDefect, 1, -1,1,1));
    delete newDefect;
    
    return coarseDefect;
}

template<typename T> 
void generateRHS(MultiScalarField2D<T>& originalRHS, std::vector<MultiScalarField2D<T>* >& rhs){
    plint vectorSize = (plint) rhs.size();
    rhs[vectorSize-1] = new MultiScalarField2D<T>(originalRHS);
    for (plint iLevel=vectorSize-2; iLevel>=0; iLevel--){
        rhs[iLevel] = new MultiScalarField2D<T>( *coarsen<T>(*rhs[iLevel+1],1,-1,1,1));
    }
}

template<typename T>
T multiGridVCycle( MultiScalarField2D<T>& initialValue, MultiScalarField2D<T>& newValue,
                   MultiScalarField2D<T>& rhs, Box2D const& domain, plint depth ){
    
    
    PLB_PRECONDITION(depth>=1);
        
    // containers of the values to not lose anything
    std::vector<MultiScalarField2D<T>* > newValues(depth+1);
    std::vector<MultiScalarField2D<T>* > defects(depth+1);
    
    plint smoothIters1 = 5;
    plint smoothIters2 = 5;
    // we go down until the level before the coarsest
    newValues[depth] = smooth<T>(initialValue,rhs,initialValue.getBoundingBox(), smoothIters1);
    defects[depth]  = computeGaussSeidelDefect<T>(*newValues[depth],rhs,initialValue.getBoundingBox());
    defects[depth-1] = new MultiScalarField2D<T>(*coarsen<T>(*defects[depth],1,-1,1,1));
    *defects[depth-1] = *plb::multiply(-1.0,*defects[depth-1]);
    
    for (plint iLevel=depth-1; iLevel>=1; iLevel--){
        
        // create initial solution = 0
        MultiScalarField2D<T> initialSolution(*defects[iLevel]);
        initialSolution.reset();
        // smooth the new system
        newValues[iLevel] = smooth<T>( initialSolution,*defects[iLevel],
                                         initialSolution.getBoundingBox(), smoothIters1);
        MultiScalarField2D<T>* tempDefect =
            computeGaussSeidelDefect<T>(*newValues[iLevel],*defects[iLevel],newValues[iLevel]->getBoundingBox());
        defects[iLevel-1] = new 
                    MultiScalarField2D<T>(*coarsen<T>(*tempDefect,1,-1,1,1));
        *defects[iLevel-1] = *plb::multiply(-1.0,*defects[iLevel-1]); // change the sign
        delete tempDefect;
    }
    
    // resolve the system exactly for the coarse system
    MultiScalarField2D<T> initialValueCoarse(*defects[0]);
    MultiScalarField2D<T> resultCoarse(*defects[0]); // container for the coarse solution to the correction scheme
    initialValueCoarse.reset(); // for the correction 0 is a good first approximation
    
    T tolerance = 1e-5;
    plint maxIter = 100;
    GaussSeidelSolver<T>( initialValueCoarse, resultCoarse,
                          *defects[0],resultCoarse.getBoundingBox(),tolerance, maxIter );

    newValues[0] = new MultiScalarField2D<T>(resultCoarse);
    // we interpolate the error computed in the coarse grid and add it to the original result from level 1
    MultiScalarField2D<T>* v_h = new MultiScalarField2D<T>(*refine<T>( *newValues[0], 1, -1 ,-1,-1));
    // compute new approximation as newValue = u_h + v_h
    *newValues[1] = *plb::add(*newValues[1],*v_h);
    delete v_h;
    
    // go up interpolating and smoothing up to the level before the finest
    for (plint iLevel=1; iLevel<depth; ++iLevel){
        MultiScalarField2D<T>* tempNewVal = smoothAndInterpolate<T>( *newValues[iLevel], *defects[iLevel], 
                                                                    newValues[iLevel]->getBoundingBox(), smoothIters2);
        *newValues[iLevel+1] = *plb::add(*newValues[iLevel+1],*tempNewVal);
        delete tempNewVal;

    }
    
    // we smooth and compute the new error in the finest level
    T newError = 0.0;
    MultiScalarField2D<T>* result = smoothAndComputeError( *newValues[depth], rhs,
                                                           newValues[depth]->getBoundingBox(),
                                                           newError, smoothIters2 );
    // copy new initial value
    newValue = *result;
    delete result;
    
    // CLEAN-UP
    for (plint iLevel = 0; iLevel <= depth; ++iLevel){
        delete newValues[iLevel];
        delete defects[iLevel];
    }
    
    return newError;
}

template<typename T>
std::vector<MultiScalarField2D<T>* > fullMultiGrid( MultiScalarField2D<T>& initialValue, 
                                                    MultiScalarField2D<T>& originalRhs, Box2D const& domain,         
                                                    plint gridLevels, plint ncycles )
{
    PLB_PRECONDITION( gridLevels>=2 && ncycles>=1 );
    
    std::vector<MultiScalarField2D<T>* > rhs(gridLevels);
    std::vector<MultiScalarField2D<T>* > solutions(gridLevels);
    
    // create all the right-hand sides from restriction over rhs
    generateRHS(originalRhs, rhs);
    
    // Initial solution computed exactly on the coarsest grid
    MultiScalarField2D<T> initialSolution(*rhs[0]);
    MultiScalarField2D<T> initialValueCoarse(*rhs[0]);
    initialValueCoarse.reset();
    GaussSeidelSolver<T>(initialValueCoarse, initialSolution, *rhs[0],initialSolution.getBoundingBox());
    solutions[0] = new MultiScalarField2D<T>(initialSolution);
    
    // MAIN LOOP (at each time we add one more level)
    for (plint iLevel=1; iLevel<gridLevels; ++iLevel){
        pcout << "Level: " << iLevel << std::endl;
        // interpolate the iLevel-1 solution
        MultiScalarField2D<T>* initialSolutionLevel = new
                MultiScalarField2D<T>( *refine<T>(*solutions[iLevel-1],1,-1,-1,-1) );
        MultiScalarField2D<T> newValue(*initialSolutionLevel);
        // for each level we itere ncycles
        for (plint iNcycle=0; iNcycle<ncycles*iLevel; ++iNcycle){
            // we use a V cycle with the current number of grids
            T error;
            error = multiGridVCycle<T>( *initialSolutionLevel, newValue, *rhs[iLevel], domain, iLevel);
            pcout << "\tError=" << error << std::endl;
            newValue.swap(*initialSolutionLevel);
        }
        
        // save the current level solution
        solutions[iLevel] = new MultiScalarField2D<T>(*initialSolutionLevel);
        delete initialSolutionLevel;        
    }
    
    // CLEAN-UP
    for (plint iLevel=0; iLevel<gridLevels; ++iLevel){
        delete rhs[iLevel];
    }
    
    return solutions;
}

template<typename T>
std::vector<MultiScalarField2D<T>* > simpleMultiGrid( MultiScalarField2D<T>& initialValue, 
                                                    MultiScalarField2D<T>& originalRhs, Box2D const& domain,         
                                                    plint gridLevels )
{
    PLB_PRECONDITION( gridLevels>=2 );
    
    std::vector<MultiScalarField2D<T>* > rhs(gridLevels);
    std::vector<MultiScalarField2D<T>* > solutions(gridLevels);
    
    // create all the right-hand sides from restriction over rhs
    generateRHS(originalRhs, rhs);
    
    // Initial solution computed exactly on the coarsest grid
    pcout << "Level: 0" << std::endl;
    pcout << "Size of the field : " << rhs[0]->getNx() << " x " << rhs[0]->getNy() << std::endl;
    MultiScalarField2D<T> initialSolution(*rhs[0]);
    MultiScalarField2D<T> initialValueCoarse(*rhs[0]);
    initialValueCoarse.reset();
    GaussSeidelSolver<T>(initialValueCoarse, initialSolution, *rhs[0],initialSolution.getBoundingBox());
    solutions[0] = new MultiScalarField2D<T>(initialSolution);
    
    // MAIN LOOP (at each time we add one more level)
    for (plint iLevel=1; iLevel<gridLevels; ++iLevel){
        pcout << "Level: " << iLevel << std::endl;
        
        // interpolate the iLevel-1 solution
        MultiScalarField2D<T>* initialSolutionLevel = new
                MultiScalarField2D<T>( *refine<T>(*solutions[iLevel-1],1,-1,-1,-1) );
        MultiScalarField2D<T> newValue(*initialSolutionLevel);
        pcout << "Size of the field : " << newValue.getNx() << " x " << newValue.getNy() << std::endl;
        GaussSeidelSolver<T>(*initialSolutionLevel, newValue, *rhs[iLevel],initialSolutionLevel->getBoundingBox());
        
        // save the current level solution
        solutions[iLevel] = new MultiScalarField2D<T>(*initialSolutionLevel);
        delete initialSolutionLevel;
    }
    
    // CLEAN-UP
    for (plint iLevel=0; iLevel<gridLevels; ++iLevel){
        delete rhs[iLevel];
    }
    
    return solutions;
}




}  // namespace plb

#endif  // FINITE_DIFFERENCE_WRAPPER_2D_HH