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rTAMAAS tamaas
integrator.hh
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/**
* @file
* @section LICENSE
*
* Copyright (©) 2016-2020 EPFL (École Polytechnique Fédérale de Lausanne),
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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 Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef INTEGRATOR_HH
#define INTEGRATOR_HH
/* -------------------------------------------------------------------------- */
#include "element.hh"
#include <expolit/expolit>
/* -------------------------------------------------------------------------- */
namespace
tamaas
{
template
<
UInt
interpolation_order
>
class
Integrator
{
using
element
=
ExponentialElement
<
interpolation_order
>
;
static
constexpr
std
::
pair
<
Real
,
Real
>
bounds
{
-
1
,
1
};
public
:
/// Standard integral of \f$\exp(\pm qy) \phi(y)\f$ over an element of radius
/// \f$r\f$ and center \f$x_c\f$
template
<
bool
upper
,
UInt
shape
>
static
Real
G0
(
Real
q
,
Real
r
,
Real
xc
)
{
const
auto
F
=
element
::
template
g0
<
upper
,
shape
>
(
q
*
r
);
return
r
*
std
::
exp
(
element
::
sign
(
upper
)
*
q
*
xc
)
*
expolit
::
definite_integral
(
bounds
,
F
);
}
/// Standard integral of \f$qy\exp(\pm qy) \phi(y)\f$ over an element of
/// radius \f$r\f$ and center \f$x_c\f$
template
<
bool
upper
,
UInt
shape
>
static
Real
G1
(
Real
q
,
Real
r
,
Real
xc
)
{
const
auto
c
=
q
*
r
;
const
auto
integrals
=
std
::
make_pair
(
element
::
template
g0
<
upper
,
shape
>
(
c
),
element
::
template
g1
<
upper
,
shape
>
(
c
));
return
r
*
std
::
exp
(
element
::
sign
(
upper
)
*
q
*
xc
)
*
(
q
*
xc
*
expolit
::
definite_integral
(
bounds
,
integrals
.
first
)
+
expolit
::
definite_integral
(
bounds
,
integrals
.
second
));
}
/// Standard integral of \f$\phi(y)\f$ over an element of radius
/// \f$r\f$ and center \f$x_c\f$. Used for fundamental mode
template
<
UInt
shape
>
constexpr
static
Real
F
(
Real
r
)
{
return
r
*
expolit
::
definite_integral
(
bounds
,
element
::
shapes
[
shape
]);
}
};
// static member declare
template
<
UInt
interpolation_order
>
constexpr
std
::
pair
<
Real
,
Real
>
Integrator
<
interpolation_order
>::
bounds
;
}
// namespace tamaas
#endif
// INTEGRATOR_HH
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