integrand_oscillation

type, public, extends(integrand_tester_object) :: integrand_oscillation

The oscillation equations field.

It is a FOODIE integrand class concrete extension.

Oscillation ODEs system

The (inertial) Oscillation equations system is a non linear system of pure ODEs and it can be written as:

$$\begin{matrix} U_t = R(U) \\ U = \begin{bmatrix} v_1 \\ v_2 \end{bmatrix}\;\;\; R(U) = \begin{bmatrix} -f v_2 \\ f v_1 \end{bmatrix} \end{matrix}$$

The frequency f is constant and it is here selected as f=10^-4.

In the space v1-v2 the path of the oscillation must be a circle, but for the frequency selected some ODE solvers are not stable leading to a wrong path, see [1].

Bibliography

[1] Numerical Methods for Fluid Dynamics With Applications to Geophysics, Dale R. Durran, Springer, 2010.

State variables organization

State variables are organized as an array (rank 1) of reals of n=2 elements.

Inherited By

Help

Variables

U U0 f

Type-Bound Procedures

add_fast amplitude_phase assign_integrand assign_real assignment(=) description error exact_solution export_tecplot initialize integrand_add_integrand integrand_add_integrand_fast integrand_add_real integrand_dimension integrand_multiply_integrand integrand_multiply_integrand_fast integrand_multiply_real integrand_multiply_real_scalar integrand_multiply_real_scalar_fast integrand_sub_integrand integrand_sub_real integrand_subtract_integrand_fast local_error multiply_fast operator(*) operator(+) operator(-) operator(.lterror.) output parse_cli real_add_integrand real_multiply_integrand real_scalar_multiply_integrand real_sub_integrand set_cli subtract_fast t t_fast

Source Code

integrand_oscillation

Components

Type	Visibility		Name		Initial
real(kind=R_P),	private	::	U(1:2)	=	[0._R_P, 0._R_P]	Integrand (state) variables.
real(kind=R_P),	private	::	U0(1:2)	=	[0._R_P, 0._R_P]	Initial state.
real(kind=R_P),	private	::	f	=	0._R_P	Oscillation frequency (Hz).

Type-Bound Procedures

generic, public :: add_fast => integrand_add_integrand_fast

Overloading add_fast method.

private pure subroutine integrand_add_integrand_fast(opr, lhs, rhs)

+ fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(self) :: amplitude_phase

Return amplitude and phase of the oscillation.

private function amplitude_phase(self) result(ap)

Compute amplitude and phase of the oscillation.

Arguments

Type Intent Optional Attributes Name

class(integrand_oscillation), intent(in) :: self
Advection field.

Return Value real(kind=R_P) (1:2)

Amplitude and phase.

procedure, public, pass(lhs) :: assign_integrand

= operator.

private pure subroutine assign_integrand(lhs, rhs)

= operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

procedure, public, pass(lhs) :: assign_real

= real operator.

private pure subroutine assign_real(lhs, rhs)

= real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

generic, public :: assignment(=) => assign_integrand, assign_real

Overloading = assignament.

private pure subroutine assign_integrand(lhs, rhs)

= operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

private pure subroutine assign_real(lhs, rhs)

= real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

procedure, public, pass(self) :: description

Return an informative description of the test.

private pure function description(self, prefix) result(desc)

Return informative integrator description.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	self	Integrand.
character(len=*),	intent(in),	optional		::	prefix	Prefixing string.

Return Value character(len=:), allocatable

Description.

procedure, public, pass(self) :: error

Return error.

private pure function error(self, t, t0, U0)

Return error.

Arguments

Type	Intent	Optional		Name
class(integrand_oscillation),	intent(in)		::	self	Integrand.
real(kind=R_P),	intent(in)		::	t	Time.
real(kind=R_P),	intent(in),	optional	::	t0	Initial time.
class(integrand_object),	intent(in),	optional	::	U0	Initial conditions.

Return Value real(kind=R_P), allocatable, (:)

Error.

procedure, public, pass(self) :: exact_solution

Return exact solution.

private pure function exact_solution(self, t, t0, U0) result(exact)

Return exact solution.

Arguments

Type	Intent	Optional		Name
class(integrand_oscillation),	intent(in)		::	self	Integrand.
real(kind=R_P),	intent(in)		::	t	Time.
real(kind=R_P),	intent(in),	optional	::	t0	Initial time.
class(integrand_object),	intent(in),	optional	::	U0	Initial conditions.

Return Value real(kind=R_P), allocatable, (:)

Exact solution.

procedure, public, pass(self) :: export_tecplot

Export integrand to Tecplot file.

private subroutine export_tecplot(self, file_name, t, scheme, close_file, with_exact_solution, U0)

Export integrand to Tecplot file.

Arguments

Type	Intent	Optional		Name
class(integrand_oscillation),	intent(in)		::	self	Advection field.
character(len=*),	intent(in),	optional	::	file_name	File name.
real(kind=R_P),	intent(in),	optional	::	t	Time.
character(len=*),	intent(in),	optional	::	scheme	Scheme used to integrate integrand.
logical,	intent(in),	optional	::	close_file	Flag for closing file.
logical,	intent(in),	optional	::	with_exact_solution	Flag for export also exact solution.
class(integrand_object),	intent(in),	optional	::	U0	Initial conditions.

procedure, public, pass(self) :: initialize

Initialize field.

private pure subroutine initialize(self, Dt)

Initialize integrand.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	self	Integrand.
real(kind=R_P),	intent(in)			::	Dt	Time step.

procedure, public, pass(lhs) :: integrand_add_integrand

+ operator.

private pure function integrand_add_integrand(lhs, rhs) result(opr)

+ operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(opr) :: integrand_add_integrand_fast

+ fast operator.

private pure subroutine integrand_add_integrand_fast(opr, lhs, rhs)

+ fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: integrand_add_real

+ real operator.

private pure function integrand_add_real(lhs, rhs) result(opr)

+ real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(self) :: integrand_dimension

Return integrand dimension.

private pure function integrand_dimension(self)

return integrand dimension.

Arguments

Type Intent Optional Attributes Name

class(integrand_oscillation), intent(in) :: self
integrand.

Return Value integer(kind=I_P)

integrand dimension.

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	self	integrand.

procedure, public, pass(lhs) :: integrand_multiply_integrand

* operator.

private pure function integrand_multiply_integrand(lhs, rhs) result(opr)

* operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(opr) :: integrand_multiply_integrand_fast

* fast operator.

private pure subroutine integrand_multiply_integrand_fast(opr, lhs, rhs)

* fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: integrand_multiply_real

* real operator.

private pure function integrand_multiply_real(lhs, rhs) result(opr)

* real_scalar operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(lhs) :: integrand_multiply_real_scalar

* real_scalar operator.

private pure function integrand_multiply_real_scalar(lhs, rhs) result(opr)

* real_scalar operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(opr) :: integrand_multiply_real_scalar_fast

* real_scalar fast operator.

private pure subroutine integrand_multiply_real_scalar_fast(opr, lhs, rhs)

* real_scalar fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
real(kind=R_P),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: integrand_sub_integrand

- operator.

private pure function integrand_sub_integrand(lhs, rhs) result(opr)

- operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(lhs) :: integrand_sub_real

- real operator.

private pure function integrand_sub_real(lhs, rhs) result(opr)

- real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(opr) :: integrand_subtract_integrand_fast

- fast operator.

private pure subroutine integrand_subtract_integrand_fast(opr, lhs, rhs)

- fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(lhs) :: local_error

||integrand_oscillation - integrand_oscillation|| operator.

private pure function local_error(lhs, rhs) result(error)

Estimate local truncation error between 2 oscillation approximations.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P)

Error estimation.

generic, public :: multiply_fast => integrand_multiply_integrand_fast, integrand_multiply_real_scalar_fast

Overloading multiply_fast method.

private pure subroutine integrand_multiply_integrand_fast(opr, lhs, rhs)

* fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

private pure subroutine integrand_multiply_real_scalar_fast(opr, lhs, rhs)

* real_scalar fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
real(kind=R_P),	intent(in)	::	rhs	Right hand side.

generic, public :: **operator(*)** => integrand_multiply_integrand, integrand_multiply_real, real_multiply_integrand, integrand_multiply_real_scalar, real_scalar_multiply_integrand

Overloading * operator.

private pure function integrand_multiply_integrand(lhs, rhs) result(opr)

* operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function integrand_multiply_real(lhs, rhs) result(opr)

* real_scalar operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function real_multiply_integrand(lhs, rhs) result(opr)

real_scalar * operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function integrand_multiply_real_scalar(lhs, rhs) result(opr)

* real_scalar operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function real_scalar_multiply_integrand(lhs, rhs) result(opr)

real_scalar * operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

generic, public :: operator(+) => integrand_add_integrand, integrand_add_real, real_add_integrand

Overloading + operator.

private pure function integrand_add_integrand(lhs, rhs) result(opr)

+ operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function integrand_add_real(lhs, rhs) result(opr)

+ real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function real_add_integrand(lhs, rhs) result(opr)

real + operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Left hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

generic, public :: operator(-) => integrand_sub_integrand, integrand_sub_real, real_sub_integrand

Overloading - operator.

private pure function integrand_sub_integrand(lhs, rhs) result(opr)

- operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function integrand_sub_real(lhs, rhs) result(opr)

- real operator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
real(kind=R_P),	intent(in)			::	rhs(1:)	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

private pure function real_sub_integrand(lhs, rhs) result(opr)

real - operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Left hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

generic, public :: operator(.lterror.) => local_error

Estimate local truncation error.

private pure function local_error(lhs, rhs) result(error)

Estimate local truncation error between 2 oscillation approximations.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	lhs	Left hand side.
class(integrand_object),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P)

Error estimation.

procedure, public, pass(self) :: output

Extract integrand state field.

private pure function output(self) result(state)

Extract integrand state field.

Arguments

Type Intent Optional Attributes Name

class(integrand_oscillation), intent(in) :: self
Integrand.

Return Value real(kind=R_P) (1:2)

State.

procedure, public, pass(self) :: parse_cli

Initialize from command line interface.

private subroutine parse_cli(self, cli)

Initialize from command line interface.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	self	Advection field.
type(command_line_interface),	intent(inout)			::	cli	Command line interface handler.

procedure, public, pass(rhs) :: real_add_integrand

real + operator.

private pure function real_add_integrand(lhs, rhs) result(opr)

real + operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Left hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(rhs) :: real_multiply_integrand

real * operator.

private pure function real_multiply_integrand(lhs, rhs) result(opr)

real_scalar * operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(rhs) :: real_scalar_multiply_integrand

real_scalar * operator.

private pure function real_scalar_multiply_integrand(lhs, rhs) result(opr)

real_scalar * operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Right hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, pass(rhs) :: real_sub_integrand

real - operator.

private pure function real_sub_integrand(lhs, rhs) result(opr)

real - operator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=R_P),	intent(in)			::	lhs(1:)	Left hand side.
class(integrand_oscillation),	intent(in)			::	rhs	Left hand side.

Return Value real(kind=R_P), allocatable, (:)

Operator result.

procedure, public, nopass :: set_cli

Set command line interface.

private subroutine set_cli(cli)

Set command line interface.

Arguments

Type Intent Optional Attributes Name

type(command_line_interface), intent(inout) :: cli
Command line interface handler.

Type	Intent	Optional	Attributes		Name
type(command_line_interface),	intent(inout)			::	cli	Command line interface handler.

generic, public :: subtract_fast => integrand_subtract_integrand_fast

Overloading subtract_fast method.

private pure subroutine integrand_subtract_integrand_fast(opr, lhs, rhs)

- fast operator.

Arguments

Type	Intent		Name
class(integrand_oscillation),	intent(inout)	::	opr	Operator result.
class(integrand_object),	intent(in)	::	lhs	Left hand side.
class(integrand_object),	intent(in)	::	rhs	Right hand side.

procedure, public, pass(self) :: t => dU_dt

Time derivative, residuals.

private pure function dU_dt(self, t) result(dState_dt)

Time derivative of integrand_oscillation field.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(in)			::	self	Integrand.
real(kind=R_P),	intent(in),	optional		::	t	Time.

Return Value real(kind=R_P), allocatable, (:)

Integrand time derivative.

procedure, public, pass(self) :: t_fast

Time derivative, residuals, fast mode.

private subroutine t_fast(self, t)

Time derivative function of integrand class, i.e. the residuals function. Fast mode acting directly on self.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrand_oscillation),	intent(inout)			::	self	Oscillation field.
real(kind=R_P),	intent(in),	optional		::	t	Time.

Source Code

type, extends(integrand_tester_object) :: integrand_oscillation
   !< The oscillation equations field.
   !<
   !< It is a FOODIE integrand class concrete extension.
   !<
   !<### Oscillation ODEs system
   !<The (inertial) Oscillation equations system is a non linear system of pure ODEs and it can be written as:
   !<
   !<$$\begin{matrix}
   !< U_t = R(U)  \\
   !< U = \begin{bmatrix}
   !< v_1 \\
   !< v_2
   !< \end{bmatrix}\;\;\;
   !< R(U) = \begin{bmatrix}
   !< -f v_2 \\
   !< f v_1
   !< \end{bmatrix}
   !<\end{matrix}$$
   !<
   !<The frequency *f* is constant and it is here selected as *f=10^-4*.
   !<
   !<In the space *v1-v2* the path of the oscillation must be a circle, but for the frequency selected some ODE solvers are not
   !<stable leading to a wrong path, see [1].
   !<
   !<#### Bibliography
   !<
   !<[1] *Numerical Methods for Fluid Dynamics With Applications to Geophysics*, Dale R. Durran, Springer, 2010.
   !<
   !<#### State variables organization
   !< State variables are organized as an array (rank 1) of reals of *n=2* elements.
   private
   real(R_P) :: f=0._R_P                 !< Oscillation frequency (Hz).
   real(R_P) :: U0(1:2)=[0._R_P, 0._R_P] !< Initial state.
   real(R_P) :: U(1:2)=[0._R_P, 0._R_P]  !< Integrand (state) variables.
   contains
      ! auxiliary methods
      procedure, pass(self), public :: amplitude_phase !< Return amplitude and phase of the oscillation.
      procedure, pass(self), public :: output          !< Extract integrand state field.
      ! integrand_tester_object deferred methods
      procedure, pass(self), public :: description    !< Return an informative description of the test.
      procedure, pass(self), public :: error          !< Return error.
      procedure, pass(self), public :: exact_solution !< Return exact solution.
      procedure, pass(self), public :: export_tecplot !< Export integrand to Tecplot file.
      procedure, pass(self), public :: initialize     !< Initialize field.
      procedure, pass(self), public :: parse_cli      !< Initialize from command line interface.
      procedure, nopass,     public :: set_cli        !< Set command line interface.
      ! integrand_object deferred methods
      procedure, pass(self), public :: integrand_dimension !< Return integrand dimension.
      procedure, pass(self), public :: t => dU_dt          !< Time derivative, residuals.
      ! operators
      procedure, pass(lhs), public :: local_error !<`||integrand_oscillation - integrand_oscillation||` operator.
      ! +
      procedure, pass(lhs), public :: integrand_add_integrand !< `+` operator.
      procedure, pass(lhs), public :: integrand_add_real      !< `+ real` operator.
      procedure, pass(rhs), public :: real_add_integrand      !< `real +` operator.
      ! *
      procedure, pass(lhs), public :: integrand_multiply_integrand   !< `*` operator.
      procedure, pass(lhs), public :: integrand_multiply_real        !< `* real` operator.
      procedure, pass(rhs), public :: real_multiply_integrand        !< `real *` operator.
      procedure, pass(lhs), public :: integrand_multiply_real_scalar !< `* real_scalar` operator.
      procedure, pass(rhs), public :: real_scalar_multiply_integrand !< `real_scalar *` operator.
      ! -
      procedure, pass(lhs), public :: integrand_sub_integrand !< `-` operator.
      procedure, pass(lhs), public :: integrand_sub_real      !< `- real` operator.
      procedure, pass(rhs), public :: real_sub_integrand      !< `real -` operator.
      ! =
      procedure, pass(lhs), public :: assign_integrand !< `=` operator.
      procedure, pass(lhs), public :: assign_real      !< `= real` operator.
      ! override fast operators
      procedure, pass(self), public :: t_fast                              !< Time derivative, residuals, fast mode.
      procedure, pass(opr),  public :: integrand_add_integrand_fast        !< `+` fast operator.
      procedure, pass(opr),  public :: integrand_multiply_integrand_fast   !< `*` fast operator.
      procedure, pass(opr),  public :: integrand_multiply_real_scalar_fast !< `* real_scalar` fast operator.
      procedure, pass(opr),  public :: integrand_subtract_integrand_fast   !< `-` fast operator.
endtype integrand_oscillation

integrand_oscillation Derived Type

Source Code

type, public, extends(integrand_tester_object) :: integrand_oscillation

Inherited By

Source Code

Components

Type-Bound Procedures

generic, public :: add_fast => integrand_add_integrand_fast

private pure subroutine integrand_add_integrand_fast(opr, lhs, rhs)

Arguments

procedure, public, pass(self) :: amplitude_phase

private function amplitude_phase(self) result(ap)

Arguments

Return Value real(kind=R_P) (1:2)

procedure, public, pass(lhs) :: assign_integrand

private pure subroutine assign_integrand(lhs, rhs)

Arguments

procedure, public, pass(lhs) :: assign_real

private pure subroutine assign_real(lhs, rhs)

Arguments

generic, public :: assignment(=) => assign_integrand, assign_real

private pure subroutine assign_integrand(lhs, rhs)

Arguments

private pure subroutine assign_real(lhs, rhs)

Arguments

procedure, public, pass(self) :: description

private pure function description(self, prefix) result(desc)

Arguments

Return Value character(len=:), allocatable

procedure, public, pass(self) :: error

private pure function error(self, t, t0, U0)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(self) :: exact_solution

private pure function exact_solution(self, t, t0, U0) result(exact)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(self) :: export_tecplot

private subroutine export_tecplot(self, file_name, t, scheme, close_file, with_exact_solution, U0)

Arguments

procedure, public, pass(self) :: initialize

private pure subroutine initialize(self, Dt)

Arguments

procedure, public, pass(lhs) :: integrand_add_integrand

private pure function integrand_add_integrand(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(opr) :: integrand_add_integrand_fast

private pure subroutine integrand_add_integrand_fast(opr, lhs, rhs)

Arguments

procedure, public, pass(lhs) :: integrand_add_real

private pure function integrand_add_real(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(self) :: integrand_dimension

private pure function integrand_dimension(self)

Arguments

Return Value integer(kind=I_P)

procedure, public, pass(lhs) :: integrand_multiply_integrand

private pure function integrand_multiply_integrand(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(opr) :: integrand_multiply_integrand_fast

private pure subroutine integrand_multiply_integrand_fast(opr, lhs, rhs)

Arguments

procedure, public, pass(lhs) :: integrand_multiply_real

private pure function integrand_multiply_real(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(lhs) :: integrand_multiply_real_scalar

private pure function integrand_multiply_real_scalar(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

procedure, public, pass(opr) :: integrand_multiply_real_scalar_fast

private pure subroutine integrand_multiply_real_scalar_fast(opr, lhs, rhs)

Arguments

procedure, public, pass(lhs) :: integrand_sub_integrand

private pure function integrand_sub_integrand(lhs, rhs) result(opr)

Arguments

Return Value real(kind=R_P), allocatable, (:)

generic, public :: **operator(*)** => integrand_multiply_integrand, integrand_multiply_real, real_multiply_integrand, integrand_multiply_real_scalar, real_scalar_multiply_integrand