BSSNMetricUtils.hpp

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#pragma once
 
#include "../../Core/Tensor.hpp"
#include "../../Core/Vector.hpp"
#include "../Metric.hpp"
#include <cassert>
#include <cstddef>
 
namespace tensorium_RG {
 
template <typename T>
tensorium::Tensor<T, 5> generate_conformal_metric_field(const tensorium_RG::Metric<T> &metric,
                                                        size_t Nx, size_t Ny, size_t Nz, T dx, T dy,
                                                        T dz) {
    tensorium::Tensor<T, 5> gamma_tilde_field({Nx, Ny, Nz, 3, 3});
 
    tensorium::Vector<T> X(4); 
    X(0) = T(0);               
 
    for (size_t i = 0; i < Nx; ++i) {
        T x = i * dx;
        for (size_t j = 0; j < Ny; ++j) {
            T y = j * dy;
            for (size_t k = 0; k < Nz; ++k) {
                T z = k * dz;
 
                X(1) = x;
                X(2) = y;
                X(3) = z;
 
                tensorium::Tensor<T, 2> gamma(3, 3), gamma_tilde(3, 3);
                tensorium::Vector<T>    beta(3);
                T                       alpha, chi;
 
                metric.BSSN(X, alpha, beta, gamma);
                chi = metric.compute_conformal_factor(gamma);
                metric.compute_conformal_metric(gamma, chi, gamma_tilde);
 
                for (size_t a = 0; a < 3; ++a)
                    for (size_t b = 0; b < 3; ++b)
                        gamma_tilde_field(i, j, k, a, b) = gamma_tilde(a, b);
            }
        }
    }
 
    return gamma_tilde_field;
}
 
} // namespace tensorium_RG