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Semi-Lagrangian Library
Modular library for kinetic and gyrokinetic simulations of plasmas in fusion energy devices.
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Semi-Lagrangian Library
Modular library for kinetic and gyrokinetic simulations of plasmas in fusion energy devices.
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Interpolator 1d using cubic splines on regular mesh with halo cells.
The module provides an optimized implementation of the interpolator function interpolate_array_disp for a domain with halo cells, i.e. we do not have explicit boundary conditions but compute the Lagrange interpolation for a number of cells provided that enough cells around this domain are present such that no boundary conditions need to be imposed. The module also provides a version for periodic boundary conditions. The implementation is based on the algorithms described in Section 5.4.4 (Fast local spline interpolation) of Sonnendrücker, Numerical Methods for the Vlasov-Maxwell equations, to appear.
Functions/Subroutines | |
| subroutine, public | sll_s_cubic_spline_halo_1d_prepare_exchange (fdata, si, num_points, d_0, c_np2) |
| Compute the part of d(0) and c(num_points+2) that need to be send to neighboring processors. More... | |
| subroutine, public | sll_s_cubic_spline_halo_1d_finish_boundary_conditions (fdata, si, num_points, d_0, c_np2) |
| Complete d(0) and c(num_points+2) with local data after their values have been received from the neighboring processors. More... | |
| subroutine, public | sll_s_cubic_spline_halo_1d_compute_interpolant (f, num_points, d, coeffs) |
| Compute the coefficients of the local interpolating spline (after d(0) and c(num_points+2) have been computed. More... | |
| subroutine, public | sll_s_cubic_spline_halo_1d_eval_disp (coeffs, alpha, num_points, fout) |
| This function corresponds to the interpolate_array_disp function of the interpolators but the displacement is normalized and between [0,1]. More... | |
| subroutine, public | sll_s_cubic_spline_halo_1d_periodic (fin, alpha, num_cells, fout) |
| subroutine | sll_s_cubic_spline_halo_1d_compute_periodic (num_points, d, f_coeffs) |
| Compute the coefficients of the local interpolating spline (after d(0) and c(num_points+2) have been computed. More... | |
Variables | |
| real(kind=f64), parameter | p_a = sqrt((2.0_f64 + sqrt(3.0_f64))/6.0_f64) |
| real(kind=f64), parameter | p_r_a = 1.0_f64/p_a |
| real(kind=f64), parameter | p_b = sqrt((2.0_f64 - sqrt(3.0_f64))/6.0_f64) |
| real(kind=f64), parameter | p_b_a = p_b/p_a |
| real(kind=f64), parameter | p_sqrt3 = sqrt(3.0_f64) |
| real(kind=f64), parameter | p_inv_6 = 1._f64/6._f64 |
| real(kind=f64), dimension(0:27), parameter | pba_pow = [ (-p_b_a)**0, (-p_b_a)**1, (-p_b_a)**2, (-p_b_a)**3, (-p_b_a)**4, (-p_b_a)**5, (-p_b_a)**6, (-p_b_a)**7, (-p_b_a)**8, (-p_b_a)**9, (-p_b_a)**10, (-p_b_a)**11, (-p_b_a)**12, (-p_b_a)**13, (-p_b_a)**14, (-p_b_a)**15, (-p_b_a)**16, (-p_b_a)**17, (-p_b_a)**18, (-p_b_a)**19, (-p_b_a)**20, (-p_b_a)**21, (-p_b_a)**22, (-p_b_a)**23, (-p_b_a)**24, (-p_b_a)**25, (-p_b_a)**26, (-p_b_a)**27 ] |
| subroutine, public sll_m_cubic_spline_halo_1d::sll_s_cubic_spline_halo_1d_compute_interpolant | ( | real(kind=f64), dimension(0:), intent(in) | f, |
| integer(kind=i32), intent(in) | num_points, | ||
| real(kind=f64), dimension(0:), intent(out) | d, | ||
| real(kind=f64), dimension(0:), intent(out) | coeffs | ||
| ) |
Compute the coefficients of the local interpolating spline (after d(0) and c(num_points+2) have been computed.
| [in] | f | data values including all points to be interpolated at |
| [in] | num_points | number of local data points |
| [out] | d | helper variable for spline coefficients (vales from forward recursion) |
| [out] | coeffs | spline coefficients |
Definition at line 143 of file sll_m_cubic_spline_halo_1d.F90.
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private |
Compute the coefficients of the local interpolating spline (after d(0) and c(num_points+2) have been computed.
| [in] | num_points | number of local data points |
| [out] | d | helper variable for spline coefficients (vales from forward recursion) |
| [in,out] | f_coeffs | on input: data values including all points to be interpolated at; on output: spline coefficients |
Definition at line 216 of file sll_m_cubic_spline_halo_1d.F90.
| subroutine, public sll_m_cubic_spline_halo_1d::sll_s_cubic_spline_halo_1d_eval_disp | ( | real(kind=f64), dimension(0:), intent(in) | coeffs, |
| real(kind=f64), intent(in) | alpha, | ||
| integer(kind=i32), intent(in) | num_points, | ||
| real(kind=f64), dimension(:), intent(out) | fout | ||
| ) |
This function corresponds to the interpolate_array_disp function of the interpolators but the displacement is normalized and between [0,1].
| [in] | coeffs | Spline coefficients (centered around the cell into which we displace, i.e. integer part of displacement is already build in here) |
| [in] | alpha | Displacement normalized by dx and only remainder of modulo 1 (in [0,1]) |
| [in] | num_points | Number of local data points |
| [out] | fout | Interpolated values |
Definition at line 179 of file sll_m_cubic_spline_halo_1d.F90.
| subroutine, public sll_m_cubic_spline_halo_1d::sll_s_cubic_spline_halo_1d_finish_boundary_conditions | ( | real(kind=f64), dimension(:), intent(in) | fdata, |
| integer(kind=i32), intent(in) | si, | ||
| integer(kind=i32), intent(in) | num_points, | ||
| intent(out) | d_0, | ||
| intent(inout) | c_np2 | ||
| ) |
Complete d(0) and c(num_points+2) with local data after their values have been received from the neighboring processors.
| [in] | fdata | Local data values |
| [in] | si | Integer part of the shift |
| [in] | num_points | number of local data values |
Definition at line 110 of file sll_m_cubic_spline_halo_1d.F90.
| subroutine, public sll_m_cubic_spline_halo_1d::sll_s_cubic_spline_halo_1d_periodic | ( | real(kind=f64), dimension(0:), intent(inout) | fin, |
| real(kind=f64), intent(in) | alpha, | ||
| integer(kind=i32), intent(in) | num_cells, | ||
| real(kind=f64), dimension(:), intent(out) | fout | ||
| ) |
Definition at line 204 of file sll_m_cubic_spline_halo_1d.F90.
| subroutine, public sll_m_cubic_spline_halo_1d::sll_s_cubic_spline_halo_1d_prepare_exchange | ( | real(kind=f64), dimension(:), intent(in) | fdata, |
| integer(kind=i32), intent(in) | si, | ||
| integer(kind=i32), intent(in) | num_points, | ||
| intent(out) | d_0, | ||
| intent(out) | c_np2 | ||
| ) |
Compute the part of d(0) and c(num_points+2) that need to be send to neighboring processors.
| [in] | fdata | Local data values |
| [in] | si | Integer part of the shift |
| [in] | num_points | number of local data values |
Definition at line 71 of file sll_m_cubic_spline_halo_1d.F90.
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Definition at line 51 of file sll_m_cubic_spline_halo_1d.F90.
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Definition at line 53 of file sll_m_cubic_spline_halo_1d.F90.
Definition at line 54 of file sll_m_cubic_spline_halo_1d.F90.
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Definition at line 56 of file sll_m_cubic_spline_halo_1d.F90.
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Definition at line 52 of file sll_m_cubic_spline_halo_1d.F90.
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Definition at line 55 of file sll_m_cubic_spline_halo_1d.F90.
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Definition at line 60 of file sll_m_cubic_spline_halo_1d.F90.
1.9.1