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343 lines
12 KiB
C++
343 lines
12 KiB
C++
/*
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Copyright 2013 SINTEF ICT, Applied Mathematics.
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "config.h"
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#include <opm/core/tof/DGBasis.hpp>
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#include <opm/core/grid.h>
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#include <opm/core/utility/ErrorMacros.hpp>
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#include <numeric>
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namespace Opm
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{
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// ---------------- Methods for class DGBasisInterface ----------------
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/// Virtual destructor.
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DGBasisInterface::~DGBasisInterface()
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{
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}
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/// Evaluate function f = sum_i c_i b_i at the point x.
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/// Note that this function is not virtual, but implemented in
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/// terms of the virtual functions of the class.
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/// \param[in] cell Cell index
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/// \param[in] coefficients Coefficients {c_i} for a single cell.
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/// \param[in] x Point at which to compute f(x).
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double DGBasisInterface::evalFunc(const int cell,
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const double* coefficients,
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const double* x) const
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{
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bvals_.resize(numBasisFunc());
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eval(cell, x, &bvals_[0]);
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return std::inner_product(bvals_.begin(), bvals_.end(), coefficients, 0.0);
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}
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// ---------------- Methods for class DGBasisBoundedTotalDegree ----------------
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/// Constructor.
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/// \param[in] grid grid on which basis is used (cell-wise)
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/// \param[in] degree polynomial degree of basis
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DGBasisBoundedTotalDegree::DGBasisBoundedTotalDegree(const UnstructuredGrid& grid,
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const int degree_arg)
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: grid_(grid),
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degree_(degree_arg)
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{
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if (grid_.dimensions > 3) {
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OPM_THROW(std::runtime_error, "Grid dimension must be 1, 2 or 3.");
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}
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if (degree_ > 1 || degree_ < 0) {
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OPM_THROW(std::runtime_error, "Degree must be 0 or 1.");
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}
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}
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/// Destructor.
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DGBasisBoundedTotalDegree::~DGBasisBoundedTotalDegree()
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{
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}
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/// The number of basis functions per cell.
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int DGBasisBoundedTotalDegree::numBasisFunc() const
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{
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switch (dimensions()) {
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case 1:
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return degree_ + 1;
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case 2:
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return (degree_ + 2)*(degree_ + 1)/2;
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case 3:
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return (degree_ + 3)*(degree_ + 2)*(degree_ + 1)/6;
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default:
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OPM_THROW(std::runtime_error, "Dimensions must be 1, 2 or 3.");
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}
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}
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/// The number of space dimensions.
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int DGBasisBoundedTotalDegree::dimensions() const
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{
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return grid_.dimensions;
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}
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/// The polynomial degree of the basis functions.
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int DGBasisBoundedTotalDegree::degree() const
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{
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return degree_;
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}
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/// Evaluate all basis functions associated with cell at x,
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/// writing to f_x. The array f_x must have size equal to
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/// numBasisFunc().
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void DGBasisBoundedTotalDegree::eval(const int cell,
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const double* x,
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double* f_x) const
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{
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const int dim = dimensions();
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const double* cc = grid_.cell_centroids + dim*cell;
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// Note intentional fallthrough in this switch statement!
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switch (degree_) {
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case 1:
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for (int ix = 0; ix < dim; ++ix) {
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f_x[1 + ix] = x[ix] - cc[ix];
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}
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case 0:
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f_x[0] = 1;
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break;
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default:
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OPM_THROW(std::runtime_error, "Maximum degree is 1 for now.");
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}
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}
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/// Evaluate gradients of all basis functions associated with
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/// cell at x, writing to grad_f_x. The array grad_f_x must
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/// have size numBasisFunc() * dimensions(). The dimensions()
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/// components of the first basis function gradient come
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/// before the components of the second etc.
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void DGBasisBoundedTotalDegree::evalGrad(const int /*cell*/,
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const double* /*x*/,
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double* grad_f_x) const
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{
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const int dim = dimensions();
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const int num_basis = numBasisFunc();
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std::fill(grad_f_x, grad_f_x + num_basis*dim, 0.0);
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if (degree_ == 1) {
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for (int ix = 0; ix < dim; ++ix) {
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grad_f_x[dim*(ix + 1) + ix] = 1.0;
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}
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}
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}
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/// Modify basis coefficients to add to the function value.
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/// A function f = sum_i c_i b_i is assumed, and we change
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/// it to (f + increment) by modifying the c_i. This is done without
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/// modifying its gradient.
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/// \param[in] increment Add this value to the function.
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/// \param[out] coefficients Coefficients {c_i} for a single cell.
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void DGBasisBoundedTotalDegree::addConstant(const double increment,
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double* coefficients) const
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{
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coefficients[0] += increment;
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}
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/// Modify basis coefficients to change the function's slope.
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/// A function f = sum_i c_i b_i is assumed, and we change
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/// it to a function g with the property that grad g = factor * grad f
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/// by modifying the c_i. This is done without modifying the average,
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/// i.e. the integrals of g and f over the cell are the same.
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/// \param[in] factor Multiply gradient by this factor.
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/// \param[out] coefficients Coefficients {c_i} for a single cell.
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void DGBasisBoundedTotalDegree::multiplyGradient(const double factor,
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double* coefficients) const
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{
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const int nb = numBasisFunc();
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for (int ix = 1; ix < nb; ++ix) {
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coefficients[ix] *= factor;
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}
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}
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/// Compute the average of the function f = sum_i c_i b_i.
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/// \param[in] coefficients Coefficients {c_i} for a single cell.
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double DGBasisBoundedTotalDegree::functionAverage(const double* coefficients) const
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{
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return coefficients[0];
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}
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// ---------------- Methods for class DGBasisMultilin ----------------
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/// Constructor.
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/// \param[in] grid grid on which basis is used (cell-wise)
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/// \param[in] degree polynomial degree of basis
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DGBasisMultilin::DGBasisMultilin(const UnstructuredGrid& grid,
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const int degree_arg)
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: grid_(grid),
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degree_(degree_arg)
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{
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if (grid_.dimensions > 3) {
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OPM_THROW(std::runtime_error, "Grid dimension must be 1, 2 or 3.");
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}
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if (degree_ > 1 || degree_ < 0) {
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OPM_THROW(std::runtime_error, "Degree must be 0 or 1.");
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}
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}
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/// Destructor.
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DGBasisMultilin::~DGBasisMultilin()
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{
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}
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/// The number of basis functions per cell.
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int DGBasisMultilin::numBasisFunc() const
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{
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switch (dimensions()) {
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case 1:
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return degree_ + 1;
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case 2:
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return (degree_ + 1)*(degree_ + 1);
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case 3:
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return (degree_ + 1)*(degree_ + 1)*(degree_ + 1);
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default:
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OPM_THROW(std::runtime_error, "Dimensions must be 1, 2 or 3.");
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}
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}
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/// The number of space dimensions.
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int DGBasisMultilin::dimensions() const
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{
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return grid_.dimensions;
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}
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/// The polynomial degree of the basis functions.
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int DGBasisMultilin::degree() const
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{
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return degree_;
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}
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/// Evaluate all basis functions associated with cell at x,
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/// writing to f_x. The array f_x must have size equal to
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/// numBasisFunc().
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void DGBasisMultilin::eval(const int cell,
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const double* x,
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double* f_x) const
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{
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const int dim = dimensions();
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const int num_basis = numBasisFunc();
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const double* cc = grid_.cell_centroids + dim*cell;
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switch (degree_) {
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case 0:
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f_x[0] = 1;
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break;
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case 1:
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std::fill(f_x, f_x + num_basis, 1.0);
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for (int dd = 0; dd < dim; ++dd) {
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const double f[2] = { 0.5 - x[dd] + cc[dd], 0.5 + x[dd] - cc[dd] };
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const int divi = 1 << (dim - dd - 1); // { 4, 2, 1 } for 3d, for example.
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for (int ix = 0; ix < num_basis; ++ix) {
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f_x[ix] *= f[(ix/divi) % 2];
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}
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}
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break;
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default:
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OPM_THROW(std::runtime_error, "Maximum degree is 1 for now.");
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}
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}
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/// Evaluate gradients of all basis functions associated with
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/// cell at x, writing to grad_f_x. The array grad_f_x must
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/// have size numBasisFunc() * dimensions(). The dimensions()
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/// components of the first basis function gradient come
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/// before the components of the second etc.
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void DGBasisMultilin::evalGrad(const int cell,
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const double* x,
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double* grad_f_x) const
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{
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const int dim = dimensions();
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const int num_basis = numBasisFunc();
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const double* cc = grid_.cell_centroids + dim*cell;
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switch (degree_) {
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case 0:
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std::fill(grad_f_x, grad_f_x + num_basis*dim, 0.0);
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break;
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case 1:
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std::fill(grad_f_x, grad_f_x + num_basis*dim, 1.0);
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for (int dd = 0; dd < dim; ++dd) {
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const double f[2] = { 0.5 - x[dd] + cc[dd], 0.5 + x[dd] - cc[dd] };
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const double fder[2] = { -1.0, 1.0 };
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const int divi = 1 << (dim - dd - 1); // { 4, 2, 1 } for 3d, for example.
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for (int ix = 0; ix < num_basis; ++ix) {
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const int ind = (ix/divi) % 2;
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for (int dder = 0; dder < dim; ++dder) {
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grad_f_x[ix*dim + dder] *= (dder == dd ? fder[ind] : f[ind]);
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}
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}
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}
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break;
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default:
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OPM_THROW(std::runtime_error, "Maximum degree is 1 for now.");
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}
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}
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/// Modify basis coefficients to add to the function value.
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/// A function f = sum_i c_i b_i is assumed, and we change
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/// it to (f + increment) by modifying the c_i. This is done without
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/// modifying its gradient.
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/// \param[in] increment Add this value to the function.
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/// \param[out] coefficients Coefficients {c_i} for a single cell.
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void DGBasisMultilin::addConstant(const double increment,
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double* coefficients) const
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{
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const int nb = numBasisFunc();
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const double term = increment/double(nb);
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for (int ix = 0; ix < nb; ++ix) {
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coefficients[ix] += term;
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}
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}
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/// Modify basis coefficients to change the function's slope.
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/// A function f = sum_i c_i b_i is assumed, and we change
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/// it to a function g with the property that grad g = factor * grad f
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/// by modifying the c_i. This is done without modifying the average,
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/// i.e. the integrals of g and f over the cell are the same.
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/// \param[in] factor Multiply gradient by this factor.
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/// \param[out] coefficients Coefficients {c_i} for a single cell.
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void DGBasisMultilin::multiplyGradient(const double factor,
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double* coefficients) const
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{
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const int nb = numBasisFunc();
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const double aver = functionAverage(coefficients);
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for (int ix = 0; ix < nb; ++ix) {
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coefficients[ix] = factor*(coefficients[ix] - aver) + aver;
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}
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}
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/// Compute the average of the function f = sum_i c_i b_i.
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/// \param[in] coefficients Coefficients {c_i} for a single cell.
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double DGBasisMultilin::functionAverage(const double* coefficients) const
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{
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const int nb = numBasisFunc();
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return std::accumulate(coefficients, coefficients + nb, 0.0)/double(nb);
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}
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} // namespace Opm
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