pf_mod_imexQ – libpfasst

IMEX Sweeper Module Module of the the derived sweeper class for doing IMEX sweeps for an equation of the form $y' = f_1(y) + f_2(y)$ The $f_1$ piece is treated explicitly and $f_2$ implicitl Afer this sweeper is initialized (usually in main), the logical flags can be changed if desired

 explicit:  Make false if there is no explicit piece

 implicit:  Make false if there is no implicit piece

The user needs to supply the feval and fcomp routines for a given example

Uses

- pf_mod_dtype
- pf_mod_utils
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Used by

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Nodes of different colours represent the following:

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Interfaces

pf_f_eval_p pf_f_comp_p

Derived Types

pf_imexQ_t

Subroutines

imexQ_sweep imexQ_initialize imexQ_destroy imexQ_integrate imexQ_residual imexQ_spreadq0 imexQ_evaluate imexQ_evaluate_all

Interfaces

interface

public subroutine pf_f_eval_p(this, y, t, level_index, f, piece)

This is the interface for the routine to compute the RHS function values Evaluate f_piece(y), where piece is one or two Evaluate f_piece(y), where piece is one or two

Arguments

Type	Intent		Name
class(pf_imexQ_t),	intent(inout)	::	this
class(pf_encap_t),	intent(in)	::	y	Argument for evaluation
real(kind=pfdp),	intent(in)	::	t	Time at evaluation
integer,	intent(in)	::	level_index	Level index
class(pf_encap_t),	intent(inout)	::	f	RHS function value
integer,	intent(in)	::	piece	Which piece to evaluate

interface

public subroutine pf_f_comp_p(this, y, t, dtq, rhs, level_index, f, piece)

Solve the equation y - dtq*f_2(y) =rhs

Arguments

Type	Intent		Name
class(pf_imexQ_t),	intent(inout)	::	this
class(pf_encap_t),	intent(inout)	::	y	Solution of implicit solve
real(kind=pfdp),	intent(in)	::	t	Time of solve
real(kind=pfdp),	intent(in)	::	dtq	dt*quadrature weight
class(pf_encap_t),	intent(in)	::	rhs	RHS for solve
integer,	intent(in)	::	level_index	Level index
class(pf_encap_t),	intent(inout)	::	f	f_2 of solution y
integer,	intent(in)	::	piece	Which piece to evaluate

Derived Types

type, public, abstract, extends(pf_sweeper_t) :: pf_imexQ_t

IMEX SDC sweeper type, extends abstract sweeper

Components

Type	Visibility	Attributes		Name		Initial
integer,	public		::	npieces
logical,	public		::	use_LUq
real(kind=pfdp),	public,	allocatable	::	QtilE(:,:)			Approximate explicit quadrature rule
real(kind=pfdp),	public,	allocatable	::	QtilI(:,:)			Approximate implicit quadrature rule
real(kind=pfdp),	public,	allocatable	::	dtsdc(:)			SDC step sizes
real(kind=pfdp),	public,	allocatable	::	QdiffE(:,:)			qmat-QtilE
real(kind=pfdp),	public,	allocatable	::	QdiffI(:,:)			qmat-QtilI
logical,	public		::	explicit	=	.true.	True if there is an explicit piece
logical,	public		::	implicit	=	.true.	True if there an implicit piece
class(pf_encap_t),	public,	allocatable	::	rhs			holds rhs for implicit solve

Type-Bound Procedures

procedure(pf_f_eval_p), public :: f_eval	RHS function evaluations
procedure(pf_f_comp_p), public :: f_comp	Implicit solver
procedure, public :: sweep => imexQ_sweep	Set the generic functions
procedure, public :: initialize => imexQ_initialize
procedure, public :: evaluate => imexQ_evaluate
procedure, public :: integrate => imexQ_integrate
procedure, public :: residual => imexQ_residual
procedure, public :: spreadq0 => imexQ_spreadq0
procedure, public :: evaluate_all => imexQ_evaluate_all
procedure, public :: destroy => imexQ_destroy
procedure, public :: imexQ_destroy

Subroutines

public subroutine imexQ_sweep(this, pf, level_index, t0, dt, nsweeps, flags)

Perform nsweep SDC sweeps on level level_index and set qend appropriately. Assign level pointer

Arguments

Type	Intent	Optional	Attributes		Name
class(pf_imexQ_t),	intent(inout)			::	this	Inputs
type(pf_pfasst_t),	intent(inout),		target	::	pf	PFASST structure
integer,	intent(in)			::	level_index	which level to sweep on
real(kind=pfdp),	intent(in)			::	t0	Time at beginning of time step
real(kind=pfdp),	intent(in)			::	dt	time step size
integer,	intent(in)			::	nsweeps	number of sweeps to do
integer,	intent(in),	optional		::	flags

public subroutine imexQ_initialize(this, lev)

Subroutine to initialize matrices and space for sweeper Array of substep sizes

Arguments

Type	Intent	Optional	Attributes		Name
class(pf_imexQ_t),	intent(inout)			::	this
class(pf_level_t),	intent(inout)			::	lev	Current level

public subroutine imexQ_destroy(this, lev)

Subroutine to deallocate sweeper

Arguments

Type	Intent	Optional	Attributes		Name
class(pf_imexQ_t),	intent(inout)			::	this
class(pf_level_t),	intent(inout)			::	lev	Current level

public subroutine imexQ_integrate(this, lev, qSDC, fSDC, dt, fintSDC, flags)

Subroutine to compute Picard integral of function values

Arguments

Type	Intent	Optional		Name
class(pf_imexQ_t),	intent(inout)		::	this
class(pf_level_t),	intent(in)		::	lev	Current level
class(pf_encap_t),	intent(in)		::	qSDC(:)	Solution values
class(pf_encap_t),	intent(in)		::	fSDC(:,:)	RHS Function values
real(kind=pfdp),	intent(in)		::	dt	Time step
class(pf_encap_t),	intent(inout)		::	fintSDC(:)	Integral from t_n to t_m
integer,	intent(in),	optional	::	flags

public subroutine imexQ_residual(this, lev, dt, flags)

Subroutine to compute Residual

Arguments

Type	Intent	Optional		Name
class(pf_imexQ_t),	intent(inout)		::	this
class(pf_level_t),	intent(inout)		::	lev	Current level
real(kind=pfdp),	intent(in)		::	dt	Time step
integer,	intent(in),	optional	::	flags

public subroutine imexQ_spreadq0(this, lev, t0, flags, step)

Arguments

Type	Intent	Optional		Name
class(pf_imexQ_t),	intent(inout)		::	this
class(pf_level_t),	intent(inout)		::	lev
real(kind=pfdp),	intent(in)		::	t0
integer,	intent(in),	optional	::	flags
integer,	intent(in),	optional	::	step

public subroutine imexQ_evaluate(this, lev, t, m, flags, step)

Subroutine to evaluate function value at node m

Arguments

Type	Intent	Optional		Name
class(pf_imexQ_t),	intent(inout)		::	this
class(pf_level_t),	intent(inout)		::	lev	Current level
real(kind=pfdp),	intent(in)		::	t	Time at which to evaluate
integer,	intent(in)		::	m	Node at which to evaluate
integer,	intent(in),	optional	::	flags
integer,	intent(in),	optional	::	step

public subroutine imexQ_evaluate_all(this, lev, t, flags, step)

Subroutine to evaluate the function values at all nodes

Arguments

Type	Intent	Optional		Name
class(pf_imexQ_t),	intent(inout)		::	this
class(pf_level_t),	intent(inout)		::	lev	Current level
real(kind=pfdp),	intent(in)		::	t(:)	Array of times at each node
integer,	intent(in),	optional	::	flags
integer,	intent(in),	optional	::	step

pf_mod_imexQ Module

Contents

Interfaces

Derived Types

Subroutines

Uses

Used by

Contents

Interfaces

Derived Types

Subroutines

Interfaces

interface

public subroutine pf_f_eval_p(this, y, t, level_index, f, piece)

Arguments

interface

public subroutine pf_f_comp_p(this, y, t, dtq, rhs, level_index, f, piece)

Arguments

Derived Types

type, public, abstract, extends(pf_sweeper_t) :: pf_imexQ_t

Components

Type-Bound Procedures

Subroutines

public subroutine imexQ_sweep(this, pf, level_index, t0, dt, nsweeps, flags)

Arguments

public subroutine imexQ_initialize(this, lev)

Arguments

public subroutine imexQ_destroy(this, lev)

Arguments

public subroutine imexQ_integrate(this, lev, qSDC, fSDC, dt, fintSDC, flags)

Arguments

public subroutine imexQ_residual(this, lev, dt, flags)

Arguments

public subroutine imexQ_spreadq0(this, lev, t0, flags, step)

Arguments

public subroutine imexQ_evaluate(this, lev, t, m, flags, step)

Arguments

public subroutine imexQ_evaluate_all(this, lev, t, flags, step)

Arguments