GMLS_Tutorial.hpp

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// @HEADER
// *****************************************************************************
//     Compadre: COMpatible PArticle Discretization and REmap Toolkit
//
// Copyright 2018 NTESS and the Compadre contributors.
// SPDX-License-Identifier: BSD-2-Clause
// *****************************************************************************
// @HEADER
#ifndef _GMLS_TUTORIAL_HPP_
#define _GMLS_TUTORIAL_HPP_
 
#include <Kokkos_Core.hpp>
#include <basis/Compadre_DivergenceFreePolynomial.hpp>
#include <Compadre_GMLS.hpp>
 
KOKKOS_INLINE_FUNCTION
double device_max(double d1, double d2) {
    return (d1 > d2) ? d1 : d2;
}
 
KOKKOS_INLINE_FUNCTION
double trueSolution(double x, double y, double z, int order, int dimension) {
    double ans = 0;
    for (int i=0; i<order+1; i++) {
        for (int j=0; j<order+1; j++) {
            for (int k=0; k<order+1; k++) {
                if (i+j+k <= order) {
                    ans += std::pow(x,i)*std::pow(y,j)*std::pow(z,k);
                }
            }
        }
    }
    return ans;
}
 
KOKKOS_INLINE_FUNCTION
double trueLaplacian(double x, double y, double z, int order, int dimension) {
    double ans = 0;
    for (int i=0; i<order+1; i++) {
        for (int j=0; j<order+1; j++) {
            for (int k=0; k<order+1; k++) {
                if (i+j+k <= order) {
                    ans += device_max(0,i-1)*device_max(0,i)*
                            std::pow(x,device_max(0,i-2))*std::pow(y,j)*std::pow(z,k);
                }
            }
        }
    }
    if (dimension>1) {
        for (int i=0; i<order+1; i++) {
            for (int j=0; j<order+1; j++) {
                for (int k=0; k<order+1; k++) {
                    if (i+j+k <= order) {
                        ans += device_max(0,j-1)*device_max(0,j)*
                                std::pow(x,i)*std::pow(y,device_max(0,j-2))*std::pow(z,k);
                    }
                }
            }
        }
    }
    if (dimension>2) {
        for (int i=0; i<order+1; i++) {
            for (int j=0; j<order+1; j++) {
                for (int k=0; k<order+1; k++) {
                    if (i+j+k <= order) {
                        ans += device_max(0,k-1)*device_max(0,k)*
                                std::pow(x,i)*std::pow(y,j)*std::pow(z,device_max(0,k-2));
                    }
                }
            }
        }
    }
    return ans;
}
 
KOKKOS_INLINE_FUNCTION
void trueGradient(double* ans, double x, double y, double z, int order, int dimension) {
 
    for (int i=0; i<order+1; i++) {
        for (int j=0; j<order+1; j++) {
            for (int k=0; k<order+1; k++) {
                if (i+j+k <= order) {
                    ans[0] += device_max(0,i)*
                               std::pow(x,device_max(0,i-1))*std::pow(y,j)*std::pow(z,k);
                }
            }
        }
    }
    if (dimension>1) {
        for (int i=0; i<order+1; i++) {
            for (int j=0; j<order+1; j++) {
                for (int k=0; k<order+1; k++) {
                    if (i+j+k <= order) {
                        ans[1] += device_max(0,j)*
                                   std::pow(x,i)*std::pow(y,device_max(0,j-1))*std::pow(z,k);
                    }
                }
            }
        }
    }
    if (dimension>2) {
        for (int i=0; i<order+1; i++) {
            for (int j=0; j<order+1; j++) {
                for (int k=0; k<order+1; k++) {
                    if (i+j+k <= order) {
                        ans[2] += device_max(0,k)*
                                   std::pow(x,i)*std::pow(y,j)*std::pow(z,device_max(0,k-1));
                    }
                }
            }
        }
    }
}
 
KOKKOS_INLINE_FUNCTION
double trueDivergence(double x, double y, double z, int order, int dimension) {
    double ans = 0;
    for (int i=0; i<order+1; i++) {
        for (int j=0; j<order+1; j++) {
            for (int k=0; k<order+1; k++) {
                if (i+j+k <= order) {
                    ans += device_max(0,i)*
                            std::pow(x,device_max(0,i-1))*std::pow(y,j)*std::pow(z,k);
                }
            }
        }
    }
    if (dimension>1) {
        for (int i=0; i<order+1; i++) {
            for (int j=0; j<order+1; j++) {
                for (int k=0; k<order+1; k++) {
                    if (i+j+k <= order) {
                        ans += device_max(0,j)*
                                std::pow(x,i)*std::pow(y,device_max(0,j-1))*std::pow(z,k);
                    }
                }
            }
        }
    }
    if (dimension>2) {
        for (int i=0; i<order+1; i++) {
            for (int j=0; j<order+1; j++) {
                for (int k=0; k<order+1; k++) {
                    if (i+j+k <= order) {
                        ans += device_max(0,k)*
                                std::pow(x,i)*std::pow(y,j)*std::pow(z,device_max(0,k-1));
                    }
                }
            }
        }
    }
    return ans;
}
 
KOKKOS_INLINE_FUNCTION
void trueHessian(double* ans, double x, double y, double z, int order, int dimension) {
    for (int i=0; i<order+1; i++) {
        for (int j=0; j<order+1; j++) {
            for (int k=0; k<order+1; k++) {
                if (i+j+k <= order) {
                    // XX
                    ans[0] += device_max(0,i)*device_max(0,i-1)*
                               std::pow(x,device_max(0,i-2))*std::pow(y,j)*std::pow(z,k);
                    if (dimension>1) {
                        // XY
                        ans[1] += device_max(0,i)*device_max(0,j)*
                               std::pow(x,device_max(0,i-1))*std::pow(y,device_max(0,j-1))*std::pow(z,k);
                        // YX = XY
                        ans[1*dimension+0] = ans[1];
                        // YY
                        ans[1*dimension+1] += device_max(0,j)*device_max(0,j-1)*
                               std::pow(x,i)*std::pow(y,device_max(0,j-2))*std::pow(z,k);
                    }
                    if (dimension>2) {
                        // XZ
                        ans[2] += device_max(0,i)*device_max(0,k)*
                               std::pow(x,device_max(0,i-1))*std::pow(y,j)*std::pow(z,device_max(0,k-1));
                        // YZ
                        ans[1*dimension+2] += device_max(0,j)*device_max(0,k)*
                               std::pow(x,i)*std::pow(y,device_max(0,j-1))*std::pow(z,device_max(0,k-1));
                        // ZX = XZ
                        ans[2*dimension+0] = ans[2];
                        // ZY = YZ
                        ans[2*dimension+1] = ans[1*dimension+2];
                        // ZZ
                        ans[2*dimension+2] += device_max(0,k)*device_max(0,k-1)*
                               std::pow(x,i)*std::pow(y,j)*std::pow(z,device_max(0,k-2));
                    }
                }
            }
        }
    }
}
 
KOKKOS_INLINE_FUNCTION
double divergenceTestSamples(double x, double y, double z, int component, int dimension) {
    // solution can be captured exactly by at least 2rd order
    switch (component) {
    case 0:
        return x*x + y*y - z*z;
    case 1:
        return 2*x +3*y + 4*z;
    default:
        return -21*x*y + 3*z*x*y + 4*z;
    }
}
 
KOKKOS_INLINE_FUNCTION
double divergenceTestSolution(double x, double y, double z, int dimension) {
    switch (dimension) {
    case 1:
        // returns divergence of divergenceTestSamples
        return 2*x;
    case 2:
        return 2*x + 3;
    default:
        return 2*x + 3 + 3*x*y + 4;
    }
}
 
KOKKOS_INLINE_FUNCTION
double curlTestSolution(double x, double y, double z, int component, int dimension) {
    if (dimension==3) {
        // returns curl of divergenceTestSamples
        switch (component) {
        case 0:
            // u3,y- u2,z
            return (-21*x + 3*z*x) - 4;
        case 1:
            // -u3,x + u1,z
            return (21*y - 3*z*y) - 2*z;
        default:
            // u2,x - u1,y
            return 2 - 2*y;
        }
    } else if (dimension==2) {
        switch (component) {
        case 0:
            // u2,y
            return 3;
        default:
            // -u1,x
            return -2*x;
        }
    } else {
        return 0;
    }
}
 
KOKKOS_INLINE_FUNCTION
double divfreeTestSolution_single_polynomial(double x, double y, double z, int component, int dimension) {
    if (dimension==3) {
        // returns divfreeTestSamples
        switch (component) {
        case 0:
            return 6.0*x*x*y - 9.0*x*y + 7.0*x*z*z + 6.0*y*y*z;
        case 1:
            return 10.0*x*x*z - 7.0*y*z*z - 6.0*x*y*y;
        default:
            return -2.0*x*x*x + 9.0*x*y*y + 9.0*y*z;
        }
    } else if (dimension==2) {
        switch (component) {
        case 0:
            return 6.0*x*x*y;
        default:
            return -6.0*x*y*y;
        }
    } else {
        return 0.0;
    }
}
 
KOKKOS_INLINE_FUNCTION
double divfreeTestSolution_span_basis(double x, double y, double z, int component, int dimension, int exact_order) {
    double val = 0.0;
    const int NP = Compadre::GMLS::getNP(exact_order, dimension, Compadre::ReconstructionSpace::DivergenceFreeVectorTaylorPolynomial);
    if (dimension==3) {
        for (int i=0; i<NP; ++i) {
            Compadre::XYZ basis_i = Compadre::DivergenceFreePolynomialBasis::evaluate(i, x, y, z);
            val += basis_i[component];
        }
    } else {
        for (int i=0; i<NP; ++i) {
            Compadre::XYZ basis_i = Compadre::DivergenceFreePolynomialBasis::evaluate(i, x, y);
            val += basis_i[component];
        }
    }
    return val;
}
 
KOKKOS_INLINE_FUNCTION
double curldivfreeTestSolution_single_polynomial(double x, double y, double z, int component, int dimension) {
    if (dimension==3) {
        // returns curl of divergenceTestSamples
        switch (component) {
        case 0:
            return -10.0*x*x + 18.0*x*y + 14.0*y*z + 9.0*z;
        case 1:
            return 6.0*x*x + 14.0*x*z - 3.0*y*y;
        default:
            return -6.0*x*x + 20.0*x*z + 9.0*x - 6.0*y*y - 12.0*y*z;
        }
    } else {
        return 0;
    }
}
 
KOKKOS_INLINE_FUNCTION
double curldivfreeTestSolution_span_basis(double x, double y, double z, int component, int dimension, int exact_order) {
    double val = 0.0;
    const int NP = Compadre::GMLS::getNP(exact_order, dimension, Compadre::ReconstructionSpace::DivergenceFreeVectorTaylorPolynomial);
    if (dimension==3) {
        if (component==0) {
            for (int i=0; i<NP; ++i) {
                Compadre::XYZ grad_y = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, 1, 1, x, y, z);
                Compadre::XYZ grad_z = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, 2, 1, x, y, z);
                val += grad_y[2] - grad_z[1];
            }
        } else if (component==1) {
            for (int i=0; i<NP; ++i) {
                Compadre::XYZ grad_x = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, 0, 1, x, y, z);
                Compadre::XYZ grad_z = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, 2, 1, x, y, z);
                val += -grad_x[2] + grad_z[0];
            }
        } else if (component==2) {
            for (int i=0; i<NP; ++i) {
                Compadre::XYZ grad_x = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, 0, 1, x, y, z);
                Compadre::XYZ grad_y = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, 1, 1, x, y, z);
                val += grad_x[1] - grad_y[0];
            }
        }
        return val;
    } else if (dimension==2) {
        if (component==0) {
            for (int i=0; i<NP; ++i) {
                Compadre::XYZ grad_x = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, 0, 1, x, y);
                Compadre::XYZ grad_y = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, 1, 1, x, y);
                val += grad_x[1] - grad_y[0];
            }
            return val;
        } else return 0;
    } else {
        return 0;
    }
}
 
KOKKOS_INLINE_FUNCTION
double curlcurldivfreeTestSolution_single_polynomial(double x, double y, double z, int component, int dimension) {
    if (dimension==3) {
        // returns curl of divergenceTestSamples
        switch (component) {
        case 0:
            return -14.0*x - 12.0*y - 12.0*z;
        case 1:
            return 12.0*x + 14.0*y - 20.0*z;
        default:
            return -6.0*x;
        }
    } else if (dimension==2) {
        switch (component) {
        case 0:
            return -12.0*y;
        default:
            return 12.0*x;
        }
    } else {
        return 0;
    }
}
 
KOKKOS_INLINE_FUNCTION
double gradientdivfreeTestSolution_single_polynomial(double x, double y, double z, int component, int dimension) {
    if (dimension==3) {
        switch (component) {
            case 0:
                return 12.0*x*y - 9.0*y + 7.0*z*z;
            case 1:
                return 6.0*x*x - 9.0*x + 12.0*y*z;
            case 2:
                return 14.0*x*z + 6.0*y*y;
            case 3:
                return 20.0*x*z - 6.0*y*y;
            case 4:
                return -7.0*z*z - 12.0*x*y;
            case 5:
                return 10.0*x*x - 14.0*y*z;
            case 6:
                return -6.0*x*x + 9.0*y*y;
            case 7:
                return 18.0*x*y + 9.0*z;
            case 8:
                return 9.0*y;
        }
    }
    if (dimension==2) {
        switch (component) {
            case 0:
                return 12.0*x*y ;
            case 1:
                return 6.0*x*x;
            case 2:
                return -6.0*y*y;
            case 3:
                return -12.0*x*y;
        }
    }
    return 0.0;
}
 
KOKKOS_INLINE_FUNCTION
double gradientdivfreeTestSolution_span_basis(double x, double y, double z, int input_component, int output_component, int dimension, int exact_order) {
    double val = 0.0;
    const int NP = Compadre::GMLS::getNP(exact_order, dimension, Compadre::ReconstructionSpace::DivergenceFreeVectorTaylorPolynomial);
    if (dimension==3) {
        for (int i=0; i<NP; ++i) {
            Compadre::XYZ basis_i = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, output_component, 1.0, x, y, z);
            val += basis_i[input_component];
        }
    } else {
        for (int i=0; i<NP; ++i) {
            Compadre::XYZ basis_i = Compadre::DivergenceFreePolynomialBasis::evaluatePartialDerivative(i, output_component, 1.0, x, y);
            val += basis_i[input_component];
        }
    }
    return val;
}
 
/** Standard GMLS Example 
 *
 *  Exercises GMLS operator evaluation with data over various orders and numbers of targets for targets including point evaluation, Laplacian, divergence, curl, and gradient.
 */
int main (int argc, char* args[]);
 
/**
 * \example "GMLS Tutorial" based on GMLS_Device.cpp
 * \section ex GMLS Example with Device Views
 *
 * This tutorial sets up a batch of GMLS problems, solves the minimization problems, and applies the coefficients produced to data.
 * 
 * \section ex1a Parse Command Line Arguments
 * \snippet GMLS_Device.cpp Parse Command Line Arguments
 *
 * \section ex1b Setting Up The Point Cloud
 * \snippet GMLS_Device.cpp Setting Up The Point Cloud
 *
 * \section ex1c Performing Neighbor Search
 * \snippet GMLS_Device.cpp Performing Neighbor Search
 *
 * \section ex2 Creating The Data
 * \snippet GMLS_Device.cpp Creating The Data
 *
 * \section ex3 Setting Up The GMLS Object
 * \snippet GMLS_Device.cpp Setting Up The GMLS Object
 * 
 * \section ex4 Apply GMLS Alphas To Data
 * \snippet GMLS_Device.cpp Apply GMLS Alphas To Data
 *
 * \section ex5 Check That Solutions Are Correct
 * \snippet GMLS_Device.cpp Check That Solutions Are Correct
 *
 * \section ex6 Finalize Program
 * \snippet GMLS_Device.cpp Finalize Program
 */ 
 
#endif