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/* Copyright 2019 Maxence Thevenet, Michael Rowan
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#ifndef SHAPEFACTORS_H_
#define SHAPEFACTORS_H_
/**
* Compute shape factor and return index of leftmost cell where
* particle writes.
* Specialized templates are defined below for orders 0 to 3.
* Shape factor functors may be evaluated with double arguments
* in current deposition to ensure that current deposited by
* particles that move only a small distance is still resolved.
* Without this safeguard, single and double precision versions
* can give disagreeing results in the time evolution for some
* problem setups.
*/
template <int depos_order>
struct Compute_shape_factor
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, T xint) const { return 0; };
};
/**
* Compute shape factor and return index of leftmost cell where
* particle writes.
* Specialization for order 0
*/
template <>
struct Compute_shape_factor< 0 >
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, T xmid) const
{
const auto j = static_cast<int>(xmid + T(0.5));
sx[0] = T(1.0);
return j;
};
};
/**
* Compute shape factor and return index of leftmost cell where
* particle writes.
* Specialization for order 1
*/
template <>
struct Compute_shape_factor< 1 >
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, T xmid) const
{
const auto j = static_cast<int>(xmid);
const T xint = xmid - T(j);
sx[0] = T(1.0) - xint;
sx[1] = xint;
return j;
};
};
/**
* Compute shape factor and return index of leftmost cell where
* particle writes.
* Specialization for order 2
*/
template <>
struct Compute_shape_factor< 2 >
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, T xmid) const
{
const auto j = static_cast<int>(xmid + T(0.5));
const T xint = xmid - T(j);
sx[0] = T(0.5)*(T(0.5) - xint)*(T(0.5) - xint);
sx[1] = T(0.75) - xint*xint;
sx[2] = T(0.5)*(T(0.5) + xint)*(T(0.5) + xint);
// index of the leftmost cell where particle deposits
return j-1;
};
};
/**
* Compute shape factor and return index of leftmost cell where
* particle writes.
* Specialization for order 3
*/
template <>
struct Compute_shape_factor< 3 >
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, T xmid) const
{
const auto j = static_cast<int>(xmid);
const T xint = xmid - T(j);
sx[0] = (T(1.0))/(T(6.0))*(T(1.0) - xint)*(T(1.0) - xint)*(T(1.0) - xint);
sx[1] = (T(2.0))/(T(3.0)) - xint*xint*(T(1.0) - xint/(T(2.0)));
sx[2] = (T(2.0))/(T(3.0)) - (T(1.0) - xint)*(T(1.0) - xint)*(T(1.0) - T(0.5)*(T(1.0) - xint));
sx[3] = (T(1.0))/(T(6.0))*xint*xint*xint;
// index of the leftmost cell where particle deposits
return j-1;
};
};
/**
* Compute shifted shape factor and return index of leftmost cell where
* particle writes, for Esirkepov algorithm.
* Specialized templates are defined below for orders 1, 2 and 3.
*/
template <int depos_order>
struct Compute_shifted_shape_factor
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, const T x_old, const int i_new) const;
};
/**
* Compute shifted shape factor and return index of leftmost cell where
* particle writes, for Esirkepov algorithm.
* Specialization for order 1
*/
template <>
struct Compute_shifted_shape_factor< 1 >
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, const T x_old, const int i_new) const
{
const auto i = static_cast<int>(x_old);
const int i_shift = i - i_new;
const T xint = x_old - T(i);
sx[1+i_shift] = T(1.0) - xint;
sx[2+i_shift] = xint;
return i;
};
};
/**
* Compute shifted shape factor and return index of leftmost cell where
* particle writes, for Esirkepov algorithm.
* Specialization for order 2
*/
template <>
struct Compute_shifted_shape_factor< 2 >
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, const T x_old, const int i_new) const
{
const auto i = static_cast<int>(x_old + T(0.5));
const int i_shift = i - (i_new + 1);
const T xint = x_old - T(i);
sx[1+i_shift] = T(0.5)*(T(0.5) - xint)*(T(0.5) - xint);
sx[2+i_shift] = T(0.75) - xint*xint;
sx[3+i_shift] = T(0.5)*(T(0.5) + xint)*(T(0.5) + xint);
// index of the leftmost cell where particle deposits
return i - 1;
};
};
/**
* Compute shifted shape factor and return index of leftmost cell where
* particle writes, for Esirkepov algorithm.
* Specialization for order 3
*/
template <>
struct Compute_shifted_shape_factor< 3 >
{
template< typename T >
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
int operator()(T* const sx, const T x_old, const int i_new) const
{
const auto i = static_cast<int>(x_old);
const int i_shift = i - (i_new + 1);
const T xint = x_old - i;
sx[1+i_shift] = (T(1.0))/(T(6.0))*(T(1.0) - xint)*(T(1.0) - xint)*(T(1.0) - xint);
sx[2+i_shift] = (T(2.0))/(T(3.0)) - xint*xint*(T(1.0) - xint/(T(2.0)));
sx[3+i_shift] = (T(2.0))/(T(3.0)) - (T(1.0) - xint)*(T(1.0) - xint)*(T(1.0) - T(0.5)*(T(1.0) - xint));
sx[4+i_shift] = (T(1.0))/(T(6.0))*xint*xint*xint;
// index of the leftmost cell where particle deposits
return i - 1;
};
};
#endif // SHAPEFACTORS_H_
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