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#define _RHEOLEF_FIELD_EXPR_V2_VARIATIONAL_TERMINAL_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
//
// terminals variational expressions are used for field assembly
// e.g. for right-hand-side of linear systems
//
// author: Pierre.Saramito@imag.fr
//
// date: 21 september 2015
//
// Notes: use template expressions and SFINAE techniques
//
// SUMMARY:
// 1. concept
// 2. grad, grad_s, D, etc
// 3. div, div_s
// 4. curl
// 5. jump, average, inner, outer
//
#include "rheolef/field_expr_v2_nonlinear.h"
#include "rheolef/test.h" // for grad_option_type
namespace rheolef {
// -------------------------------------------------------------------
// 1. concept
// -------------------------------------------------------------------
namespace details {
// Define a trait type for detecting field expression valid arguments
template<class T> struct is_field_expr_v2_variational_arg : std::false_type {};
template<class T, class M, class VfTag> struct is_field_expr_v2_variational_arg<test_basic<T,M,VfTag> > : std::true_type {};
} // namespace details
// ---------------------------------------------------------------------------
// 2. grad, grad_s, D, etc
// ---------------------------------------------------------------------------
namespace details {
template<class Expr>
class field_expr_v2_variational_grad {
public:
// typedefs:
typedef geo_element::size_type size_type;
typedef typename Expr::memory_type memory_type;
typedef typename scalar_traits<typename Expr::value_type>::type
scalar_type;
typedef typename space_constant::rank_up<typename Expr::value_type>::type
value_type;
typedef typename float_traits<scalar_type>::type float_type;
typedef space_basic<scalar_type,memory_type> space_type;
typedef typename Expr::vf_tag_type vf_tag_type;
typedef typename details::dual_vf_tag<vf_tag_type>::type
vf_dual_tag_type;
typedef field_expr_v2_variational_grad<Expr> self_type;
typedef field_expr_v2_variational_grad<typename Expr::dual_self_type>
dual_self_type;
// alocators:
field_expr_v2_variational_grad (const Expr& expr, const grad_option_type& opt = grad_option_type())
: _expr(expr),
_opt(opt)
{
check_macro (opt.broken
|| get_vf_space().get_numbering().is_continuous()
|| get_vf_space().get_numbering().name() == "bubble",
"grad(.): unexpected " << get_vf_space().get_numbering().name()
<< " discontinuous approximation (HINT: consider grad_h(.))");
}
field_expr_v2_variational_grad (const field_expr_v2_variational_grad<Expr>& x)
: _expr(x._expr),
_opt(x._opt)
{}
// accessors:
const space_type& get_vf_space() const { return _expr.get_vf_space(); }
static const space_constant::valued_type valued_hint = space_constant::valued_tag_traits<value_type>::value;
space_constant::valued_type valued_tag() const {
space_constant::valued_type v = _expr.valued_tag();
switch (v) {
case space_constant::scalar: return space_constant::vector;
case space_constant::vector: return space_constant::unsymmetric_tensor;
case space_constant::tensor: return space_constant::tensor3;
default:
fatal_macro ("unexpected " << space_constant::valued_name(v) << "-valued argument for grad() operator");
return space_constant::last_valued;
}
}
size_type n_derivative() const { return _expr.n_derivative() + 1; }
// mutable modifiers:
void initialize (const geo_basic<float_type,memory_type>& dom, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr.initialize (dom, quad, ignore_sys_coord);
}
void initialize (const band_basic<float_type,memory_type>& gh, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr.initialize (gh, quad, ignore_sys_coord);
}
void element_initialize (const geo_element& K) const {
_expr.element_initialize (K);
}
void element_initialize_on_side (const geo_element& K, const side_information_type& sid) {
_expr.element_initialize_on_side (K, sid);
}
template<class ValueType>
void basis_evaluate (const reference_element& hat_K, size_type q, std::vector<ValueType>& value) const {
_expr.grad_basis_evaluate (hat_K, q, _opt, value);
}
template<class ValueType>
void valued_check() const {
typedef typename space_constant::rank_down<ValueType>::type A1; // may be defined when ValueType is
_expr.template valued_check<A1>();
}
protected:
// data:
Expr _expr;
grad_option_type _opt;
};
template<class Expr> struct is_field_expr_v2_variational_arg <field_expr_v2_variational_grad<Expr> > : std::true_type {};
} // namespace details
// grad(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_grad<Expr>
>::type
grad (const Expr& expr)
{
return details::field_expr_v2_variational_grad <Expr> (expr);
}
// grad_s(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_grad<Expr>
>::type
grad_s (const Expr& expr)
{
details::grad_option_type opt;
opt.surfacic = true;
return details::field_expr_v2_variational_grad <Expr> (expr, opt);
}
// grad_h(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_grad<Expr>
>::type
grad_h (const Expr& expr)
{
details::grad_option_type opt;
opt.broken = true;
return details::field_expr_v2_variational_grad <Expr> (expr, opt);
}
// D(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_grad<Expr>
>::type
D (const Expr& expr)
{
details::grad_option_type opt;
opt.symmetrized = true;
return details::field_expr_v2_variational_grad <Expr> (expr, opt);
}
// Ds(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_grad<Expr>
>::type
Ds (const Expr& expr)
{
details::grad_option_type opt;
opt.symmetrized = true;
opt.surfacic = true;
return details::field_expr_v2_variational_grad <Expr> (expr, opt);
}
// Dh(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_grad<Expr>
>::type
Dh (const Expr& expr)
{
details::grad_option_type opt;
opt.symmetrized = true;
opt.broken = true;
return details::field_expr_v2_variational_grad <Expr> (expr, opt);
}
// ---------------------------------------------------------------------------
// 3. div, div_s
// ---------------------------------------------------------------------------
namespace details {
template<class Expr>
class field_expr_v2_variational_div {
public:
// typedefs:
typedef geo_element::size_type size_type;
typedef typename Expr::memory_type memory_type;
typedef typename space_constant::rank_down<typename Expr::value_type>::type
value_type;
typedef typename scalar_traits<typename Expr::value_type>::type
scalar_type;
typedef typename float_traits<scalar_type>::type float_type;
typedef space_basic<scalar_type,memory_type> space_type;
typedef typename Expr::vf_tag_type vf_tag_type;
typedef typename details::dual_vf_tag<vf_tag_type>::type
vf_dual_tag_type;
typedef field_expr_v2_variational_div<Expr> self_type;
typedef field_expr_v2_variational_div<typename Expr::dual_self_type>
dual_self_type;
// alocators:
field_expr_v2_variational_div (const Expr& expr, const grad_option_type& opt = grad_option_type())
: _expr(expr),
_opt(opt)
{
check_macro (opt.broken
|| get_vf_space().get_numbering().is_continuous()
|| get_vf_space().get_numbering().name() == "bubble",
"div(.): unexpected " << get_vf_space().get_numbering().name()
<< " discontinuous approximation (HINT: consider div_h(.))");
}
// accessors:
const space_type& get_vf_space() const { return _expr.get_vf_space(); }
static const space_constant::valued_type valued_hint = space_constant::valued_tag_traits<value_type>::value;
space_constant::valued_type valued_tag() const {
space_constant::valued_type v = _expr.valued_tag();
switch (v) {
case space_constant::vector: return space_constant::scalar;
case space_constant::tensor:
case space_constant::unsymmetric_tensor: return space_constant::vector;
default:
fatal_macro ("unexpected " << space_constant::valued_name(v) << "-valued argument for div() operator");
return space_constant::last_valued;
}
}
size_type n_derivative() const { return _expr.n_derivative() + 1; }
// mutable modifiers:
void initialize (const geo_basic<float_type,memory_type>& dom, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr.initialize (dom, quad, ignore_sys_coord);
}
void initialize (const band_basic<float_type,memory_type>& gh, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr.initialize (gh, quad, ignore_sys_coord);
}
void element_initialize (const geo_element& K) const {
_expr.element_initialize (K);
}
void element_initialize_on_side (const geo_element& K, const side_information_type& sid) {
_expr.element_initialize_on_side (K, sid);
}
template<class ValueType>
void basis_evaluate (const reference_element& hat_K, size_type q, std::vector<ValueType>& value) const {
_expr.div_basis_evaluate (hat_K, q, _opt, value);
}
template<class ValueType>
void valued_check() const {
_expr.template div_valued_check<ValueType>();
}
protected:
// data:
Expr _expr;
grad_option_type _opt;
};
template<class Expr> struct is_field_expr_v2_variational_arg <field_expr_v2_variational_div<Expr> > : std::true_type {};
} // namespace details
// div(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_div<Expr>
>::type
div (const Expr& expr)
{
return details::field_expr_v2_variational_div <Expr> (expr);
}
// div_s(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_div<Expr>
>::type
div_s (const Expr& expr)
{
details::grad_option_type opt;
opt.surfacic = true;
return details::field_expr_v2_variational_div <Expr> (expr, opt);
}
// div_h(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_div<Expr>
>::type
div_h (const Expr& expr)
{
details::grad_option_type opt;
opt.broken = true;
return details::field_expr_v2_variational_div <Expr> (expr, opt);
}
// ---------------------------------------------------------------------------
// 4. curl
// ---------------------------------------------------------------------------
namespace details {
template<class Expr>
class field_expr_v2_variational_curl {
public:
// typedefs:
typedef geo_element::size_type size_type;
typedef typename Expr::memory_type memory_type;
typedef typename scalar_traits<typename Expr::value_type>::type
scalar_type;
// value_type = vctor when d=2 and Expr is scalar or when d=3
// = scalar when d=2 and Expr is vector
// thus is undeterminated at compile-time
typedef undeterminated_basic<scalar_type> value_type;
typedef typename float_traits<scalar_type>::type float_type;
typedef space_basic<scalar_type,memory_type> space_type;
typedef typename Expr::vf_tag_type vf_tag_type;
typedef typename details::dual_vf_tag<vf_tag_type>::type
vf_dual_tag_type;
typedef field_expr_v2_variational_curl<Expr> self_type;
typedef field_expr_v2_variational_curl<typename Expr::dual_self_type>
dual_self_type;
// alocators:
field_expr_v2_variational_curl (const Expr& expr, const grad_option_type& opt = grad_option_type())
: _expr(expr),
_opt(opt)
{
check_macro (opt.broken
|| get_vf_space().get_numbering().is_continuous()
|| get_vf_space().get_numbering().name() == "bubble",
"curl(.): unexpected " << get_vf_space().get_numbering().name()
<< " discontinuous approximation (HINT: consider curl_h(.))");
}
// accessors:
const space_type& get_vf_space() const { return _expr.get_vf_space(); }
static const space_constant::valued_type valued_hint = space_constant::valued_tag_traits<value_type>::value;
space_constant::valued_type valued_tag() const {
space_constant::valued_type arg_v = _expr.valued_tag();
switch (arg_v) {
case space_constant::scalar: return space_constant::vector;
case space_constant::vector: {
size_type d = get_vf_space().get_geo().dimension();
return (d==2) ? space_constant::scalar : space_constant::vector;
}
default:
fatal_macro ("unexpected " << space_constant::valued_name(arg_v) << "-valued argument for curl() operator");
return space_constant::last_valued;
}
}
size_type n_derivative() const { return _expr.n_derivative() + 1; }
// mutable modifiers:
void initialize (const geo_basic<float_type,memory_type>& dom, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr.initialize (dom, quad, ignore_sys_coord);
}
void initialize (const band_basic<float_type,memory_type>& gh, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr.initialize (gh, quad, ignore_sys_coord);
}
void element_initialize (const geo_element& K) const {
_expr.element_initialize (K);
}
void element_initialize_on_side (const geo_element& K, const side_information_type& sid) {
_expr.element_initialize_on_side (K, sid);
}
template<class ValueType>
void basis_evaluate (const reference_element& hat_K, size_type q, std::vector<ValueType>& value) const {
_expr.curl_basis_evaluate (hat_K, q, _opt, value);
}
void _valued_check_internal(const scalar_type&) const {
_expr.template valued_check<point_basic<scalar_type> >();
size_type d = get_vf_space().get_geo().dimension();
check_macro (d==2, "unexpected "<<d<<"D physical dimension for the scalar-valued curl() operator");
}
void _valued_check_internal(const point_basic<scalar_type>&) const {
size_type d = get_vf_space().get_geo().dimension();
check_macro (d==2 || d==3, "unexpected "<<d<<"D physical dimension for the vector-valued curl() operator");
if (d == 2) {
_expr.template valued_check<scalar_type>();
} else {
_expr.template valued_check<point_basic<scalar_type> >();
}
}
void _valued_check_internal(const tensor_basic<scalar_type>&) const {
fatal_macro ("unexpected tensor-valued result for the curl() operator");
}
template<class ValueType>
void valued_check() const {
_valued_check_internal(ValueType());
}
protected:
// data:
Expr _expr;
grad_option_type _opt;
};
template<class Expr> struct is_field_expr_v2_variational_arg <field_expr_v2_variational_curl<Expr> > : std::true_type {};
} // namespace details
// curl(v)
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_curl<Expr>
>::type
curl (const Expr& expr)
{
return details::field_expr_v2_variational_curl <Expr> (expr);
}
// bcurl(v) = Batchelor curl
template<class Expr>
inline
typename
std::enable_if<
details::is_field_expr_v2_variational_arg<Expr>::value
,details::field_expr_v2_variational_curl<Expr>
>::type
bcurl (const Expr& expr)
{
details::grad_option_type opt;
opt.batchelor_curl = true;
return details::field_expr_v2_variational_curl <Expr> (expr, opt);
}
// ---------------------------------------------------------------------------
// 5. jump, average, inner, outer
// ---------------------------------------------------------------------------
// discontinuous Galerkin operators
// in expressions templates for variationnal formulations
//
/*
SPECIFICATION: a first example
Let v be a function defined over Omega
and discontinuous accross internal sides (e.g. Pkd).
Let f be a function defined on Oemga.
We want to assembly
l(v) = int_{internal sides} f(x) [v](x) ds
where [v] is the jump of v accross internal sides.
=> l(v) = sum_{K is internal sides} int_K f(x) [v](x) ds
Let K be an internal side of the mesh of Omega.
int_K f(x) [v](x) ds
= int_{hat_K} f(F(hat_x))
[v](F(hat_x))
det(DF(hat_x)) d hat_s
where F is the piola transformation from the reference element hat_K to K:
F : hat_K ---> K
hat_x |--> x = F(hat_x)
The fonction v is not defined on a basis over internal sides K but over
elements L of the mesh of Omega.
Let L0 and L1 the two elements such that K is the common side of L0 and L1
and K is oriented from L0 to L1:
[v] = v0 - v1 on K, where v0=v/L0 and v1=v/L1.
Let G0 the piola transformation from the reference element tilde_L to L0:
G0 : tilde_L ---> L0
tilde_x |--> x = G0(tilde_x)
Conversely, let G1 the piola transformation from the reference element tilde_L to L1.
int_K f(x) [v](x) ds
= int_{hat_K} f(F(hat_x))
(v0-v1)(F(hat_x))
det(DF(hat_x)) d hat_s
The the basis fonction v0 and v1 are defined by using tilde_v, on the reference element tilde_L:
v0(x) = tilde_v (G0^{-1}(x))
v1(x) = tilde_v (G1^{-1}(x))
and with x=F(hat_x):
v0(F(hat_x)) = tilde_v (G0^{-1}(F(hat_x)))
v1(F(hat_x)) = tilde_v (G1^{-1}(F(hat_x)))
Thus:
int_K f(x) [v](x) ds
= int_{hat_K} f(F(hat_x))
( tilde_v (G0^{-1}(F(hat_x)))
- tilde_v (G1^{-1}(F(hat_x))) )
det(DF(hat_x)) ds
Observe that H0=G0^{-1}oF is linear:
H0 : hat_K ---> tilde0_K subset tilde_L
hat_x ---> tilde0_x = H0(hat_x)
Conversely:
H1 : hat_K ---> tilde1_K subset tilde_L
hat_x ---> tilde1_x = H1(hat_x)
Thus, K linearly transforms by H0 into a side tilde0_K of the reference element tilde_L
and, by H1, into another side tilde1_K of tilde_L.
int_K f(x) [v](x) ds
= int_{hat_K} f(F(hat_x))
( tilde_v (H0(hat_x))
- tilde_v (H1(hat_x)) )
det(DF(hat_x)) ds
Let (hat_xq, hat_wq)_{q=0...} a quadrature formulae over hat_K.
The integral becomes:
int_K f(x) [v](x) ds
= sum_q f(F(hat_xq))
( tilde_v (H0(hat_xq))
- tilde_v (H1(hat_xq)) )
det(DF(hat_xq)) hat_wq
Then, the basis functions tilde_v can be computed one time for all
over all the sides tilde(i)_K of the reference element tilde_L, i=0..nsides(tilde_L)
at the quadratures nodes tilde(i)_xq = Hi(hat_xq):
tilde_v (Hi(hat_xq)), i=0..nsides(tilde_L), q=0..nq(hat_K)
SPECIFICATION: a second example
We want to assembly
l(v) = int_{internal sides} f(x) [grad(v).n](x) ds
where [grad(v).n] is the jump of the normal derivative of v accross internal sides.
Let K be an internal side of the mesh of Omega.
int_K f(x) [grad(v).n](x) ds
= int_{hat_K} f(F(hat_x))
[grad(v).n](F(hat_x))
det(DF(hat_x)) d hat_s
= int_{hat_K} f(F(hat_x))
(grad(v0).n)(F(hat_x))
det(DF(hat_x)) d hat_s
- int_{hat_K} f(F(hat_x))
(grad(v1).n)(F(hat_x))
det(DF(hat_x)) d hat_s
where v0=v/L0 and v1=v/L1 and Li are the two elements containing the side K.
Let us fix one of the Li and omits the i subscript.
The computation reduces to evaluate:
int_K f(x) grad(v).n(x) ds
= sum_q f(F(hat_xq))
(grad(v).n)(F(hat_xq))
det(DF(hat_xq)) hat_wq
From the gradient transformation:
grad(v)(F(hat_xq)) = DG^{-T}(H(hat_xq)) * tilde_grad(tilde_v)(H(hat_xq))
where H = G^{-1}oF is linear from hat_K to tilde_K subset tilde_L.
int_K f(x) grad(v).n(x) ds
= sum_q f(F(hat_xq))
DG^{-T}(H(hat_xq))*tilde_grad(tilde_v)(H(hat_xq))
.n(F(hat_xq))
det(DF(hat_xq)) hat_wq
We can evaluate one time for all the gradients of basis functions tilde_v
on the quadrature nodes of each sides tilde_K of tilde_L :
tilde_grad(tilde_v)(H(hat_xq))
The piola basis functions and their derivatives are also evaluated one time for all on these nodes :
DG^{-T}(H(hat_xq))
The normal vector
n(xq), xq=F(hat_xq), q=...
should be evaluated on K, not on L that has no normal vector.
IMPLEMENTATION: bassis evaluation => test.cc
The basis_on_pointset class extends to the case of an integration over a side of
test_rep<T,M>::initialize (const geo_basic<float_type,M>& dom, const quadrature<T>& quad, bool ignore_sys_coord) const {
_basis_on_quad.set (quad, get_vf_space().get_numbering().get_basis());
_piola_on_quad.set (quad, get_vf_space().get_geo().get_piola_basis());
=> inchange'
}
test_rep<T,M>::element_initialize (const geo_element& L, size_type loc_isid=-1) const {
if (loc_isid != -1) {
basis_on_quad.restrict_on_side (tilde_L, loc_isid);
piola_on_quad.restrict_on_side (tilde_L, loc_isid);
}
}
test_rep<T,M>::basis_evaluate (...) {
// Then, a subsequent call to
basis_on_quad.evaluate (tilde_L, q);
// will restrict to the loc_isid part.
}
IMPLEMENTATION: normal vector => field_vf_expr.h & field_nl_expr_terminal.h
on propage des vf_expr aux nl_expr le fait qu'on travaille sur une face :
class nl_helper {
void element_initialize (const This& obj, const geo_element& L, size_type loc_isid=-1) const {
obj._nl_expr.evaluate (L, isid, obj._vector_nl_value_quad);
}
};
pour la classe normal :
field_expr_terminal_normal::evaluate (L, loc_isid, value) {
if (loc_isid != -1) K=side(L,loc_isid); else K=L;
puis inchange.
}
pour la classe terminal_field: si on evalue un field uh qui est discontinu :
on sait sur quelle face il se restreint :
field_expr_terminal_field::evaluate (L, loc_isid, value) {
if (loc_isid != -1) {
_basis_on_quad.restrict_on_side (tilde_L, loc_isid);
}
for (q..) {
general_field_evaluate (_uh, _basis_on_quad, tilde_L, _dis_idof, q, value[q]);
}
}
IMPLEMENTATION: bassis evaluation => basis_on_pointset.cc
c'est la que se fait le coeur du travail :
basis_on_pointset::restrict_on_side (tilde_L, loc_isid)
=> initialise
a l'initialisation, on evalue une fois pour tte
sur toutes les faces en transformant la quadrature via
tilde(i)_xq = Hi(hat_xq)
tilde(i)_wq = ci*hat_wq
avec
ci = meas(tilde(i)_K)/meas(hat_K)
puis :
basis_on_pointset::evaluate (tilde_L, q)
on se baladera dans la tranche [loc_isid*nq, (loc_isid+1)*nq[
du coup, on positionne un pointeur de debut q_start = loc_isid*nq
et une taille q_size = nq
si les faces sont differentes (tri,qua) dans un prisme, il faudra
un tableau de pointeurs pour gerer cela :
q_start [loc_nsid+1]
q_size [loc_isid] = q_start[loc_isid+1] - q_start[loc_isid]
basis_on_pointset::begin() { return _val[_curr_K_variant][_curr_q].begin() + q_start[_curr_K_variant][loc_isid]; }
basis_on_pointset::begin() { return _val[_curr_K_variant][_curr_q].begin() + q_start[_curr_K_variant][loc_isid+1]; }
et le tour est joue' !
PLAN DE DEVELOPPEMENT:
1) DG transport
basis_on_pointset.cc
test.cc
essais :
lh = integrate(jump(v)*f);
convect_dg2.cc
2) DG diffusion : avec normale et gradient
field_vf_expr.h
class nl_helper
field_nl_expr_terminal.h
field_expr_terminal_normal::evaluate (L, loc_isid, value)
field_expr_terminal_field ::evaluate (L, loc_isid, value)
*/
namespace details {
// ---------------------------------------------------------------------------
// 5.1 class dg
// ---------------------------------------------------------------------------
template<class Expr>
class field_expr_v2_variational_dg {
public:
// typedefs:
typedef typename Expr::size_type size_type;
typedef typename Expr::memory_type memory_type;
typedef typename Expr::value_type value_type;
typedef typename Expr::scalar_type scalar_type;
typedef typename Expr::float_type float_type;
typedef typename Expr::space_type space_type;
typedef typename Expr::vf_tag_type vf_tag_type;
typedef typename details::dual_vf_tag<vf_tag_type>::type
vf_dual_tag_type;
typedef field_expr_v2_variational_dg<Expr> self_type;
typedef field_expr_v2_variational_dg<typename Expr::dual_self_type>
dual_self_type;
// alocators:
field_expr_v2_variational_dg (const Expr& expr, const float_type& c0, const float_type& c1)
: _expr0(expr),
_expr1(expr),
_c0(c0),
_c1(c1),
_tilde0_L0(),
_tilde1_L1(),
_bgd_omega()
{
}
// accessors:
const space_type& get_vf_space() const { return _expr0.get_vf_space(); }
static const space_constant::valued_type valued_hint = Expr::valued_hint;
space_constant::valued_type valued_tag() const { return _expr0.valued_tag(); }
size_type n_derivative() const { return _expr0.n_derivative(); }
// mutable modifiers:
void initialize (const geo_basic<float_type,memory_type>& dom, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr0.initialize (dom, quad, ignore_sys_coord);
_expr1.initialize (dom, quad, ignore_sys_coord);
_bgd_omega = get_vf_space().get_geo().get_background_geo();
check_macro (_bgd_omega == dom.get_background_geo(),
"discontinuous Galerkin: incompatible integration domain "<<dom.name() << " and test function based domain "
<< get_vf_space().get_geo().name());
}
void initialize (const band_basic<float_type,memory_type>& gh, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr0.initialize (gh, quad, ignore_sys_coord);
_expr1.initialize (gh, quad, ignore_sys_coord);
fatal_macro ("unsupported discontinuous Galerkin on a band"); // how to define background mesh _bgd_omega ?
}
void element_initialize (const geo_element& K) const;
template<class ValueType>
void basis_evaluate (const reference_element& hat_K, size_type q, std::vector<ValueType>& value) const;
template<class ValueType>
void valued_check() const {
check_macro (get_vf_space().get_numbering().is_discontinuous(),
"unexpected continuous test-function in space " << get_vf_space().stamp()
<< " for jump or average operator (HINT: omit jump or average)");
_expr0.template valued_check<ValueType>();
}
protected:
// data:
mutable Expr _expr0;
mutable Expr _expr1;
scalar_type _c0;
scalar_type _c1;
mutable reference_element _tilde0_L0;
mutable reference_element _tilde1_L1;
mutable geo_basic<float_type,memory_type> _bgd_omega;
};
template<class Expr> struct is_field_expr_v2_variational_arg <field_expr_v2_variational_dg<Expr> > : std::true_type {};
// ---------------------------------------------------------------------------
// 5.2. basis_evaluate
// ---------------------------------------------------------------------------
template<class Expr>
template<class ValueType>
void
field_expr_v2_variational_dg<Expr>::basis_evaluate (
const reference_element& hat_K,
size_type q,
std::vector<ValueType>& value) const
{
size_type loc_ndof0 = _expr0.get_vf_space().get_constitution().loc_ndof (_tilde0_L0),
loc_ndof1 = 0;
if (_tilde1_L1.variant() != reference_element::max_variant) {
loc_ndof1 = _expr1.get_vf_space().get_constitution().loc_ndof (_tilde1_L1);
}
check_macro (loc_ndof0+loc_ndof1 == value.size(),
"unexpected value.size="<<value.size()<<": expect size="<<loc_ndof0+loc_ndof1
<< " for ValueType="<<typename_macro(ValueType)<<" and valued=" << _expr1.get_vf_space().valued());
std::vector<ValueType> value0 (loc_ndof0),
value1 (loc_ndof1);
_expr0.basis_evaluate (_tilde0_L0, q, value0);
// average (i.e. _c0==0.5): fix it on the boundary where c0=1 : average(v)=v on the boundary
Float c0 = (_tilde1_L1.variant() != reference_element::max_variant || _c0 != 0.5) ? _c0 : 1;
for (size_type loc_idof = 0; loc_idof < loc_ndof0; ++loc_idof) {
value[loc_idof] = c0*value0 [loc_idof];
}
if (_tilde1_L1.variant() != reference_element::max_variant) {
_expr1.basis_evaluate (_tilde1_L1, q, value1);
for (size_type loc_idof = 0; loc_idof < loc_ndof1; ++loc_idof) {
value[loc_idof+loc_ndof0] = _c1*value1 [loc_idof];
}
}
}
// ---------------------------------------------------------------------------
// 5.3. element_initialize
// ---------------------------------------------------------------------------
template<class Expr>
void
field_expr_v2_variational_dg<Expr>::element_initialize (const geo_element& K) const
{
size_type L_map_d = K.dimension() + 1;
size_type L_dis_ie0, L_dis_ie1;
side_information_type sid0, sid1;
L_dis_ie0 = K.master(0);
L_dis_ie1 = K.master(1);
check_macro (L_dis_ie0 != std::numeric_limits<size_type>::max(),
"unexpected isolated mesh side K.dis_ie="<<K.dis_ie());
if (L_dis_ie1 != std::numeric_limits<size_type>::max()) {
// K is an internal side
const geo_element& L0 = _bgd_omega.dis_get_geo_element (L_map_d, L_dis_ie0);
const geo_element& L1 = _bgd_omega.dis_get_geo_element (L_map_d, L_dis_ie1);
L0.get_side_informations (K, sid0);
L1.get_side_informations (K, sid1);
_tilde0_L0 = L0;
_tilde1_L1 = L1;
// methode "non-const": provoque une copie physique au 1er appel (c'est ce qu'il faut)
_expr0.element_initialize_on_side (L0, sid0);
_expr1.element_initialize_on_side (L1, sid1);
} else {
// K is a boundary side
const geo_element& L0 = _bgd_omega.dis_get_geo_element (L_map_d, L_dis_ie0);
L0.get_side_informations (K, sid0);
_tilde0_L0 = L0;
_tilde1_L1 = reference_element::max_variant;
_expr0.element_initialize_on_side (L0, sid0);
}
}
} // namespace details
// ---------------------------------------------------------------------------
// 5.4. user-level interface
// ---------------------------------------------------------------------------
#define _RHEOLEF_make_field_expr_v2_variational_dg(op,c0,c1) \
template<class Expr> \
inline \
typename \
std::enable_if< \
details::is_field_expr_v2_variational_arg<Expr>::value \
,details::field_expr_v2_variational_dg<Expr> \
>::type \
op (const Expr& expr) \
{ \
return details::field_expr_v2_variational_dg <Expr> (expr, c0, c1); \
}
_RHEOLEF_make_field_expr_v2_variational_dg (jump, 1, -1)
_RHEOLEF_make_field_expr_v2_variational_dg (average, 0.5, 0.5)
_RHEOLEF_make_field_expr_v2_variational_dg (inner, 1, 0)
_RHEOLEF_make_field_expr_v2_variational_dg (outer, 0, 1)
#undef _RHEOLEF_make_field_expr_v2_variational_dg
#ifdef TODO
#endif // TODO
} // namespace rheolef
#endif // _RHEOLEF_FIELD_EXPR_V2_VARIATIONAL_TERMINAL_H
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