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ImplicitSolveOperator.cpp
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Mon, Sep 30, 21:26
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rLAMMPS lammps
ImplicitSolveOperator.cpp
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// Header file for this class
#include "ImplicitSolveOperator.h"
// Other ATC includes
#include "ATC_Coupling.h"
#include "FE_Engine.h"
#include "PhysicsModel.h"
#include "PrescribedDataManager.h"
using
std
::
set
;
using
std
::
vector
;
namespace
ATC
{
// --------------------------------------------------------------------
// --------------------------------------------------------------------
// ImplicitSolveOperator
// --------------------------------------------------------------------
// --------------------------------------------------------------------
ImplicitSolveOperator
::
ImplicitSolveOperator
(
double
alpha
,
double
dt
)
:
n_
(
0
),
dof_
(
0
),
dt_
(
dt
),
alpha_
(
alpha
),
epsilon0_
(
1.0e-8
)
{
// Nothing else to do here
}
// --------------------------------------------------------------------
// operator *
// --------------------------------------------------------------------
DENS_VEC
ImplicitSolveOperator
::
operator
*
(
const
DENS_VEC
&
x
)
const
{
// This method uses a matrix-free approach to approximate the
// multiplication by matrix A in the matrix equation Ax=b, where the
// matrix equation results from an implicit treatment of the
// fast field. In brief, if the ODE for the fast field can be written:
//
// dx/dt = R(x)
//
// A generalized discretization can be written:
//
// 1/dt * (x^n+1 - x^n) = alpha * R(x^n+1) + (1-alpha) * R(x^n)
//
// Taylor expanding the R(x^n+1) term and rearranging gives the
// equation to be solved for dx at each timestep:
//
// [1 - dt * alpha * dR/dx] * dx = dt * R(x^n)
//
// The operator defined in this method computes the left-hand side,
// given a vector dx. It uses a finite difference, matrix-free
// approximation of dR/dx * dx, giving:
//
// [1 - dt * alpha * dR/dx] * dx = dt * R(x^n)
// ~= dx - dt*alpha/epsilon * ( R(x^n + epsilon*dx) - R(x^n) )
//
// Compute epsilon
double
epsilon
=
(
x
.
norm
()
>
0.0
)
?
epsilon0_
*
x0_
.
norm
()
/
x
.
norm
()
:
epsilon0_
;
// Compute incremented vector x^n+1 = x^n + epsilon*dx
x_
=
x0_
+
epsilon
*
x
;
// Evaluate R(x)
this
->
R
(
x_
,
R_
);
// Compute full left hand side and return it
DENS_VEC
Ax
=
x
-
dt_
*
alpha_
/
epsilon
*
(
R_
-
R0_
);
return
Ax
;
}
// --------------------------------------------------------------------
// rhs of Ax = r
// --------------------------------------------------------------------
DENS_VEC
ImplicitSolveOperator
::
r
()
const
{
return
dt_
*
R0_
;
// dt * R(T^n)
}
// --------------------------------------------------------------------
// preconditioner
// --------------------------------------------------------------------
DIAG_MAT
ImplicitSolveOperator
::
preconditioner
()
const
{
DENS_VEC
diag
(
n_
);
diag
=
1.0
;
DIAG_MAT
preconditioner
(
diag
);
return
preconditioner
;
}
// --------------------------------------------------------------------
// --------------------------------------------------------------------
// FieldImplicitSolveOperator
// --------------------------------------------------------------------
// --------------------------------------------------------------------
FieldImplicitSolveOperator
::
FieldImplicitSolveOperator
(
ATC_Coupling
*
atc
,
FIELDS
&
fields
,
const
FieldName
fieldName
,
const
Array2D
<
bool
>
&
rhsMask
,
const
PhysicsModel
*
physicsModel
,
double
simTime
,
double
dt
,
double
alpha
)
:
ImplicitSolveOperator
(
alpha
,
dt
),
fieldName_
(
fieldName
),
atc_
(
atc
),
physicsModel_
(
physicsModel
),
fields0_
(
fields
),
// ref to fields
fields_
(
fields
),
// copy of fields
rhsMask_
(
rhsMask
),
time_
(
simTime
)
{
const
DENS_MAT
&
f
=
fields0_
[
fieldName_
].
quantity
();
dof_
=
f
.
nCols
();
if
(
dof_
>
1
)
throw
ATC_Error
(
"Implicit solver operator can only handle scalar fields"
);
// create all to free map
int
nNodes
=
f
.
nRows
();
set
<
int
>
fixedNodes_
=
atc_
->
prescribed_data_manager
()
->
fixed_nodes
(
fieldName_
);
n_
=
nNodes
;
vector
<
bool
>
tag
(
nNodes
);
set
<
int
>::
const_iterator
it
;
int
i
=
0
;
for
(
i
=
0
;
i
<
nNodes
;
++
i
)
{
tag
[
i
]
=
true
;
}
for
(
it
=
fixedNodes_
.
begin
();
it
!=
fixedNodes_
.
end
();
++
it
)
{
tag
[
*
it
]
=
false
;}
int
m
=
0
;
for
(
i
=
0
;
i
<
nNodes
;
++
i
)
{
if
(
tag
[
i
])
freeNodes_
[
i
]
=
m
++
;
}
//std::cout << " nodes " << n_ << " " << nNodes << "\n";
// Save current field
x0_
.
reset
(
n_
);
to_free
(
f
,
x0_
);
x_
=
x0_
;
// initialize
// righthand side/forcing vector
rhsMask_
.
reset
(
NUM_FIELDS
,
NUM_FLUX
);
rhsMask_
=
false
;
for
(
int
i
=
0
;
i
<
rhsMask
.
nCols
();
i
++
)
{
rhsMask_
(
fieldName_
,
i
)
=
rhsMask
(
fieldName_
,
i
);
}
//std::cout << print_mask(rhsMask_) << "\n";
massMask_
.
reset
(
1
);
massMask_
(
0
)
=
fieldName_
;
rhs_
[
fieldName_
].
reset
(
nNodes
,
dof_
);
// Compute the RHS vector R(T^n)
R0_
.
reset
(
n_
);
R_
.
reset
(
n_
);
R
(
x0_
,
R0_
);
}
void
FieldImplicitSolveOperator
::
to_all
(
const
VECTOR
&
x
,
MATRIX
&
f
)
const
{
f
.
reset
(
x
.
nRows
(),
1
);
for
(
int
i
=
0
;
i
<
x
.
nRows
();
++
i
)
{
f
(
i
,
0
)
=
x
(
i
);
}
}
void
FieldImplicitSolveOperator
::
to_free
(
const
MATRIX
&
r
,
VECTOR
&
v
)
const
{
v
.
reset
(
r
.
nRows
());
for
(
int
i
=
0
;
i
<
r
.
nRows
();
++
i
)
{
v
(
i
)
=
r
(
i
,
0
);
}
}
void
FieldImplicitSolveOperator
::
R
(
const
DENS_VEC
&
x
,
DENS_VEC
&
v
)
const
{
DENS_MAT
&
f
=
fields_
[
fieldName_
].
set_quantity
();
atc_
->
prescribed_data_manager
()
->
set_fixed_field
(
time_
,
fieldName_
,
f
);
to_all
(
x
,
f
);
atc_
->
compute_rhs_vector
(
rhsMask_
,
fields_
,
rhs_
,
FULL_DOMAIN
,
physicsModel_
);
DENS_MAT
&
r
=
rhs_
[
fieldName_
].
set_quantity
();
atc_
->
prescribed_data_manager
()
->
set_fixed_dfield
(
time_
,
fieldName_
,
r
);
atc_
->
apply_inverse_mass_matrix
(
r
,
fieldName_
);
to_free
(
r
,
v
);
#if 0
int n = 6;
//std::cout << "# x "; for (int i = 0; i < n_; ++i) std::cout << x(i) << " "; std::cout << "\n";
//std::cout << "# f "; for (int i = 0; i < n; ++i) std::cout << f(i,0) << " "; std::cout << "\n";
std::cout << "# r "; for (int i = 0; i < n; ++i) std::cout << r(i,0) << " "; std::cout << "\n";
//std::cout << "# v "; for (int i = 0; i < n; ++i) std::cout << v(i) << " "; std::cout << "\n";
#endif
}
void
FieldImplicitSolveOperator
::
solution
(
const
DENS_MAT
&
dx
,
DENS_MAT
&
f
)
const
{
DENS_MAT
&
df
=
fields_
[
fieldName_
].
set_quantity
();
to_all
(
column
(
dx
,
0
),
df
);
atc_
->
prescribed_data_manager
()
->
set_fixed_dfield
(
time_
,
fieldName_
,
df
);
f
+=
df
;
}
void
FieldImplicitSolveOperator
::
rhs
(
const
DENS_MAT
&
r
,
DENS_MAT
&
rhs
)
const
{
to_all
(
column
(
r
,
0
),
rhs
);
}
}
// namespace ATC
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