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DynamicsDiagonalSemiPeriodic.h
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rGOOSEFEM GooseFEM
DynamicsDiagonalSemiPeriodic.h
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/* ========================================== DESCRIPTION ==========================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_DYNAMICS_DIAGONAL_SEMIPERIODIC_H
#define GOOSEFEM_DYNAMICS_DIAGONAL_SEMIPERIODIC_H
#include "Macros.h"
#include <cppmat/cppmat.h>
// -------------------------------------------------------------------------------------------------
namespace
GooseFEM
{
namespace
Dynamics
{
namespace
Diagonal
{
// =========================================== OVERVIEW ============================================
template
<
class
Element
>
class
SemiPeriodic
{
public:
// variables
// ---------
// element/quadrature/material definition
std
::
unique_ptr
<
Element
>
elem
;
// mesh: nodal position/displacement/velocity/acceleration, DOF-numbers, connectivity, dimensions
size_t
nnode
,
nelem
,
nne
,
ndim
,
ndof
;
MatS
conn
,
dofs
;
MatD
x
,
u
,
v
,
a
;
// fixed DOFs: prescribed velocity/acceleration, DOF-numbers, dimensions
size_t
nfixed
;
ColS
fixedDofs
;
ColD
fixedV
,
fixedA
;
// linear system: columns (also "M" and "D" which are diagonal)
ColD
M
,
Minv
,
D
,
F
,
V
,
V_n
,
A
,
A_n
;
// time integration
double
dt
,
t
=
0.0
;
// constructor
// -----------
SemiPeriodic
(){};
SemiPeriodic
(
std
::
unique_ptr
<
Element
>
elem
,
const
MatD
&
x
,
const
MatS
&
conn
,
const
MatS
&
dofs
,
const
ColS
&
fixedDofs
,
double
dt
);
// functions
// ---------
void
velocityVerlet
();
// one time step of time integrator
void
Verlet
();
// one time step of time integrator (no velocity dependence)
void
updated_x
();
// process update in "x"
void
updated_u
(
bool
init
=
false
);
// process update in "u", if init all possible updates are made
void
updated_v
(
bool
init
=
false
);
// process update in "v", if init all possible updates are made
void
assemble_M
();
// assemble the mass matrix from the element mass matrices
void
assemble_D
();
// assemble the damping matrix from the element damping matrices
void
assemble_F
();
// assemble the force from the element forces
};
// ========================================== SOURCE CODE ==========================================
template
<
class
Element
>
SemiPeriodic
<
Element
>::
SemiPeriodic
(
std
::
unique_ptr
<
Element
>
_elem
,
const
MatD
&
_x
,
const
MatS
&
_conn
,
const
MatS
&
_dofs
,
const
ColS
&
_fixedDofs
,
double
_dt
)
{
// copy input
elem
=
std
::
move
(
_elem
);
x
=
_x
;
conn
=
_conn
;
dofs
=
_dofs
;
dt
=
_dt
;
fixedDofs
=
_fixedDofs
;
// compute sizes
nfixed
=
static_cast
<
size_t
>
(
fixedDofs
.
size
());
nnode
=
static_cast
<
size_t
>
(
x
.
rows
());
ndim
=
static_cast
<
size_t
>
(
x
.
cols
());
nelem
=
static_cast
<
size_t
>
(
conn
.
rows
());
nne
=
static_cast
<
size_t
>
(
conn
.
cols
());
ndof
=
dofs
.
maxCoeff
()
+
1
;
// basic checks (mostly the user is 'trusted')
assert
(
dofs
.
size
()
==
nnode
*
ndim
);
assert
(
ndof
<
nnode
*
ndim
);
#ifndef NDEBUG
for
(
size_t
i
=
0
;
i
<
nfixed
;
++
i
)
assert
(
fixedDofs
(
i
)
<
ndof
);
#endif
// allocate and zero-initialize nodal quantities
u
.
conservativeResize
(
nnode
,
ndim
);
u
.
setZero
();
v
.
conservativeResize
(
nnode
,
ndim
);
v
.
setZero
();
a
.
conservativeResize
(
nnode
,
ndim
);
a
.
setZero
();
// allocate and zero-initialize linear system (DOFs)
Minv
.
conservativeResize
(
ndof
);
M
.
conservativeResize
(
ndof
);
D
.
conservativeResize
(
ndof
);
F
.
conservativeResize
(
ndof
);
V
.
conservativeResize
(
ndof
);
V_n
.
conservativeResize
(
ndof
);
V_n
.
setZero
();
A
.
conservativeResize
(
ndof
);
A_n
.
conservativeResize
(
ndof
);
A_n
.
setZero
();
// fixed DOFs : default zero velocity and acceleration
fixedV
.
conservativeResize
(
nfixed
);
fixedV
.
setZero
();
fixedA
.
conservativeResize
(
nfixed
);
fixedA
.
setZero
();
// initialize all fields
updated_x
();
updated_u
(
true
);
updated_v
(
true
);
}
// =================================================================================================
template
<
class
Element
>
void
SemiPeriodic
<
Element
>::
velocityVerlet
()
{
// (1) new positions (displacements)
// - apply update (nodal) : x_{n+1} = x_n + dt * v_n + .5 * dt^2 * a_n"
u
+=
dt
*
v
+
(
.5
*
std
::
pow
(
dt
,
2.
)
)
*
a
;
// - process update in displacements
updated_u
();
// (2a) estimate new velocities
// - update velocities (DOFs)
V
.
noalias
()
=
V_n
+
dt
*
A
;
// - apply the fixed velocities
for
(
size_t
i
=
0
;
i
<
nfixed
;
++
i
)
V
(
fixedDofs
(
i
))
=
fixedV
(
i
);
// - convert to nodal velocities (periodicity implies that several nodes depend on the same DOF)
for
(
size_t
i
=
0
;
i
<
nnode
*
ndim
;
++
i
)
v
(
i
)
=
V
(
dofs
(
i
));
// - process update in velocities
updated_v
();
// - solve for accelerations (DOFs)
A
.
noalias
()
=
Minv
.
cwiseProduct
(
-
F
-
D
.
cwiseProduct
(
V
)
);
// - update velocities (DOFs)
V
.
noalias
()
=
V_n
+
(
.5
*
dt
)
*
(
A_n
+
A
);
// - apply the fixed velocities
for
(
size_t
i
=
0
;
i
<
nfixed
;
++
i
)
V
(
fixedDofs
(
i
))
=
fixedV
(
i
);
// - convert to nodal velocities (periodicity implies that several nodes depend on the same DOF)
for
(
size_t
i
=
0
;
i
<
nnode
*
ndim
;
++
i
)
v
(
i
)
=
V
(
dofs
(
i
));
// - process update in velocities
updated_v
();
// (2b) new velocities
// - solve for accelerations (DOFs)
A
.
noalias
()
=
Minv
.
cwiseProduct
(
-
F
-
D
.
cwiseProduct
(
V
)
);
// - update velocities (DOFs)
V
.
noalias
()
=
V_n
+
(
.5
*
dt
)
*
(
A_n
+
A
);
// - apply the fixed velocities
for
(
size_t
i
=
0
;
i
<
nfixed
;
++
i
)
V
(
fixedDofs
(
i
))
=
fixedV
(
i
);
// - convert to nodal velocities (periodicity implies that several nodes depend on the same DOF)
for
(
size_t
i
=
0
;
i
<
nnode
*
ndim
;
++
i
)
v
(
i
)
=
V
(
dofs
(
i
));
// - process update in velocities
updated_v
();
// (3) new accelerations
// - solve for accelerations (DOFs)
A
.
noalias
()
=
Minv
.
cwiseProduct
(
-
F
-
D
.
cwiseProduct
(
V
)
);
// - apply the fixed accelerations
for
(
size_t
i
=
0
;
i
<
nfixed
;
++
i
)
A
(
fixedDofs
(
i
))
=
fixedA
(
i
);
// - convert to nodal acceleration (periodicity implies that several nodes depend on the same DOF)
for
(
size_t
i
=
0
;
i
<
nnode
*
ndim
;
++
i
)
a
(
i
)
=
A
(
dofs
(
i
));
// store history
A_n
=
A
;
// accelerations (DOFs)
V_n
=
V
;
// nodal velocities
t
+=
dt
;
// current time instance
// N.B. at this point:
// "a" == "A" == "A_n" -> new nodal accelerations, their DOF equivalents, and a 'back-up'
// "v" == "V_n" -> new nodal velocities, and a 'back-up'
// "u" -> new nodal displacements
// The forces "F" correspond to this state of the system
}
// =================================================================================================
template
<
class
Element
>
void
SemiPeriodic
<
Element
>::
Verlet
()
{
// (1) new nodal positions (displacements)
// - apply update (nodal) : x_{n+1} = x_n + dt * v_n + .5 * dt^2 * a_n"
u
+=
dt
*
v
+
(
.5
*
std
::
pow
(
dt
,
2.
)
)
*
a
;
// - process update in displacements
updated_u
();
// - solve for accelerations (DOFs)
A
.
noalias
()
=
Minv
.
cwiseProduct
(
-
F
);
// - apply the fixed accelerations
for
(
size_t
i
=
0
;
i
<
nfixed
;
++
i
)
A
(
fixedDofs
(
i
))
=
fixedA
(
i
);
// - convert to nodal acceleration (periodicity implies that several nodes depend on the same DOF)
for
(
size_t
i
=
0
;
i
<
nnode
*
ndim
;
++
i
)
a
(
i
)
=
A
(
dofs
(
i
));
// (2) propagate velocities
// - update velocities (DOFs)
V
.
noalias
()
=
V_n
+
(
.5
*
dt
)
*
(
A_n
+
A
);
// - apply the fixed velocities
for
(
size_t
i
=
0
;
i
<
nfixed
;
++
i
)
V
(
fixedDofs
(
i
))
=
fixedV
(
i
);
// - convert to nodal velocities (periodicity implies that several nodes depend on the same DOF)
for
(
size_t
i
=
0
;
i
<
nnode
*
ndim
;
++
i
)
v
(
i
)
=
V
(
dofs
(
i
));
// store history
A_n
=
A
;
// accelerations (DOFs)
V_n
=
V
;
// nodal velocities
t
+=
dt
;
// current time instance
// N.B. at this point:
// "a" == "A" == "A_n" -> new nodal accelerations, their DOF equivalents, and a 'back-up'
// "v" == "V_n" -> new nodal velocities, and a 'back-up'
// "u" -> new nodal displacements
// The forces "F" correspond to this state of the system
}
// =================================================================================================
template
<
class
Element
>
void
SemiPeriodic
<
Element
>::
updated_x
()
{
// set the nodal positions of all elements (in parallel)
#pragma omp parallel for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
for
(
size_t
i
=
0
;
i
<
ndim
;
++
i
)
elem
->
x
(
e
,
m
,
i
)
=
x
(
conn
(
e
,
m
),
i
);
// signal update
elem
->
updated_x
();
}
// =================================================================================================
template
<
class
Element
>
void
SemiPeriodic
<
Element
>::
updated_u
(
bool
init
)
{
// set the nodal displacements of all elements (in parallel)
#pragma omp parallel for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
for
(
size_t
i
=
0
;
i
<
ndim
;
++
i
)
elem
->
u
(
e
,
m
,
i
)
=
u
(
conn
(
e
,
m
),
i
);
// signal update
elem
->
updated_u
();
// update
if
(
elem
->
changed_M
or
init
)
assemble_M
();
if
(
elem
->
changed_D
or
init
)
assemble_D
();
if
(
elem
->
changed_f
or
init
)
assemble_F
();
}
// =================================================================================================
template
<
class
Element
>
void
SemiPeriodic
<
Element
>::
updated_v
(
bool
init
)
{
// set the nodal displacements of all elements (in parallel)
#pragma omp parallel for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
for
(
size_t
i
=
0
;
i
<
ndim
;
++
i
)
elem
->
v
(
e
,
m
,
i
)
=
v
(
conn
(
e
,
m
),
i
);
// signal update
elem
->
updated_v
();
// update
if
(
elem
->
changed_M
or
init
)
assemble_M
();
if
(
elem
->
changed_D
or
init
)
assemble_D
();
if
(
elem
->
changed_f
or
init
)
assemble_F
();
}
// =================================================================================================
template
<
class
Element
>
void
SemiPeriodic
<
Element
>::
assemble_M
()
{
// zero-initialize
M
.
setZero
();
// temporarily disable parallelization by Eigen
Eigen
::
setNbThreads
(
1
);
// assemble
#pragma omp parallel
{
// - mass matrix, per thread
ColD
M_
(
ndof
);
M_
.
setZero
();
// - assemble diagonal mass matrix, per thread
#pragma omp for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
for
(
size_t
i
=
0
;
i
<
ndim
;
++
i
)
M_
(
dofs
(
conn
(
e
,
m
),
i
))
+=
elem
->
M
(
e
,
m
*
ndim
+
i
,
m
*
ndim
+
i
);
// - reduce "M_" per thread to total "M"
#pragma omp critical
M
+=
M_
;
}
// automatic parallelization by Eigen
Eigen
::
setNbThreads
(
0
);
// compute inverse of the mass matrix
Minv
=
M
.
cwiseInverse
();
}
// =================================================================================================
template
<
class
Element
>
void
SemiPeriodic
<
Element
>::
assemble_D
()
{
// zero-initialize
D
.
setZero
();
// temporarily disable parallelization by Eigen
Eigen
::
setNbThreads
(
1
);
// assemble
#pragma omp parallel
{
// - damping matrix, per thread
ColD
D_
(
ndof
);
D_
.
setZero
();
// - assemble diagonal damping matrix, per thread
#pragma omp for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
for
(
size_t
i
=
0
;
i
<
ndim
;
++
i
)
D_
(
dofs
(
conn
(
e
,
m
),
i
))
+=
elem
->
D
(
e
,
m
*
ndim
+
i
,
m
*
ndim
+
i
);
// - reduce "D_" per thread to total "D"
#pragma omp critical
D
+=
D_
;
}
// automatic parallelization by Eigen
Eigen
::
setNbThreads
(
0
);
}
// =================================================================================================
template
<
class
Element
>
void
SemiPeriodic
<
Element
>::
assemble_F
()
{
// zero-initialize
F
.
setZero
();
// temporarily disable parallelization by Eigen
Eigen
::
setNbThreads
(
1
);
// assemble
#pragma omp parallel
{
// - force, per thread
ColD
F_
(
ndof
);
F_
.
setZero
();
// - assemble force, per thread
#pragma omp for
for
(
size_t
e
=
0
;
e
<
nelem
;
++
e
)
for
(
size_t
m
=
0
;
m
<
nne
;
++
m
)
for
(
size_t
i
=
0
;
i
<
ndim
;
++
i
)
F_
(
dofs
(
conn
(
e
,
m
),
i
))
+=
elem
->
f
(
e
,
m
,
i
);
// - reduce "F_" per thread to total "F"
#pragma omp critical
F
+=
F_
;
}
// automatic parallelization by Eigen
Eigen
::
setNbThreads
(
0
);
}
// =================================================================================================
}}}
// namespace GooseFEM::Dynamics::Diagonal
#endif
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