ode_solver_mod Module Reference

TOP LEVEL MODULE FOR ODEs, derived type ode_solver More...

Data Types
interface	clear
interface	initialcond
	set initial conditions More...
interface	ode_solution
interface	ode_solver
	Type ode_solver. More...
interface	print
interface	solve
	Generic 'solve' for ODEs. More...
interface	valid

Functions/Subroutines
subroutine	ode_solver_clear (slv)
	destructor for ode_solver More...
type(ode_solver) function	ode_solver_create (pb, type, os_meth, SL_meth, NL_meth, L_meth, DC_meth, check_overflow, verb)
	Constructor for the type ode_solver More...
logical function	ode_solver_valid (slv)
	check ode_solver More...
subroutine	ode_solver_print (slv)
	print ode_solver More...
character(len=20) function, public	name_ode_solver_type (type)
	name the type of ode_solver More...
logical function, public	check_ode_method (method, pb_type, slv_type)
	check whether the ode method 'method' is available for the problem type 'pb_type' and for the solver type 'slv_type' More...
type(ode_solution) function	ode_solution_create (slv, pb)
	Constructor for the type ode_solution More...
subroutine	homogeneous_initialcond (sol, pb, slv, t0, y0)
	homogeneous initial condition More...
subroutine	ode_solver_solve (sol, slv, pb, t0, T, dt, KInv, output)
	Solve an ODE with constant time step More...
subroutine, public	set_ode_solver_output (slv, output)
	Load a user defined output for ODE resolution More...

Detailed Description

TOP LEVEL MODULE FOR ODEs, derived type ode_solver

This is the top level module for all modules ode_xxx.f90.
It contains the solve command for:

• classical ODE systems,
• semilinear PDEs coupled with ODE systems
  (time evolution PDEs discretised in space are ODEs).

Choral constants for ODE solver types: ODE_SLV_xxx, see the list.

ODE RESOLUTION PROCEDURE:

1. Define the ode_problem

   pb = ode_problem(problem_type, atgs) 

   see ode_problem_mod detailed description
2. Define the ode_solver

   slv = ode_solver(solver_type, pb, atgs) 

   for details see ode_solver_create.
3. Construct the ode_solution

   sol = ode_solution(sol, slv, pb) 

4. Set the initial condition

   call initialCond(sol, pb, slv, ...)

   see initialCond for details.
5. Solve with

   call solve(sol, slv, pb, ...)

   see ode_solver_solve for drtails

OPTIONAL: Output and linear system inversions.

• 1. Output
  • An 'output' routine is called at each time step and just after the last time step.
  • This toutine allows output along and after simulations, such as plotting, solution saving, ...
  • It can be defined in two ways:
    1. Pre defined output:
       • define a variable 'ode_out' of type ode_output, see ode_output_mod detailed description.
       • add it to the solve command arguments

         call solve(sol, slv, pb, ..., output=ode_out)

    2. User defined output:
       • define your own output routine 'user_def_output' as a subroutine with interface ode_output_proc,
       • associate this routine to your ode_solver 'ode_slv' with

         call set_ode_solver_output(ode_slv, user_def_output)

         see set_ode_solver_output.
       • solve with

         call solve(sol, slv, pb, ...)

  • These two ways are illustrated in ode_Lin_0d.f90, see also the examples below.

• 2. Linear system inversions:
  • ode resolutions require to solve linear systems of the form:
    \(~~~~~ (M + cS) u = {\rm rhs}, \)
  • The scalar \( c \) is given by S_prefactor.
  • These inversions can be done in two ways:
    1. Default inversion:
       • the inversion is held by a CG solver,
         (this is feasible because the matrix vector product \( u \rightarrow (M + cS)u \) is known)
       • the settings for this solver are in slv%kry
    2. User-defined inversion:
       • the user can provide its own inversion routine
         \(~~~ \) KInv: \(~~u \rightarrow (M + cS)^{-1}u \)
       • 'KInv' is of type RnToRn,
       • add 'KInv' to the solve command arguments

         call solve(sol, slv, pb, ..., KInv=KInv)

       • this allows to optimise the inversions using for instance a preconditionner.

Tutorial examples:

• ode_Lin_0d.f90: a simple linear 0D ODE.
• ode_cardio_0d.f90: a non linear ODE system in cardiac electrophysiology.
• ode_monodomain_2d.f90: a parabolic reaction-diffusion equation coupled with an ODE system,
  discretised in space with finite elements on a 2D mesh.

Author

Charles Pierre

Function/Subroutine Documentation

check_ode_method()

logical function, public ode_solver_mod::check_ode_method	(	integer, intent(in)	method,
		integer, intent(in)	pb_type,
		integer, intent(in)	slv_type
	)

check whether the ode method 'method' is available for the problem type 'pb_type' and for the solver type 'slv_type'

Definition at line 495 of file ode_solver_mod.f90.

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homogeneous_initialcond()

subroutine ode_solver_mod::homogeneous_initialcond ( type(ode_solution), intent(inout)  sol, type(ode_problem ), intent(in)  pb, type(ode_solver), intent(in)  slv, real(rp), intent(in)  t0, real(rp), dimension(:), intent(in)  y0  )

private

homogeneous initial condition

Definition at line 626 of file ode_solver_mod.f90.

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name_ode_solver_type()

character(len=20) function, public ode_solver_mod::name_ode_solver_type

(

integer, intent(in)

type

)

name the type of ode_solver

Definition at line 467 of file ode_solver_mod.f90.

ode_solution_create()

type(ode_solution) function ode_solver_mod::ode_solution_create ( type(ode_solver), intent(in)  slv, type(ode_problem), intent(in)  pb  )

private

Constructor for the type ode_solution

• OUTPUT:
  • sol = ode_solution

• INPUT:
  • slv = ode_solver
  • pb = ode_problem

Definition at line 553 of file ode_solver_mod.f90.

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ode_solver_clear()

subroutine ode_solver_mod::ode_solver_clear ( type(ode_solver), intent(inout)  slv )

private

destructor for ode_solver

Definition at line 246 of file ode_solver_mod.f90.

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ode_solver_create()

type(ode_solver) function ode_solver_mod::ode_solver_create ( type(ode_problem), intent(in)  pb, integer, intent(in)  type, integer, intent(in), optional  os_meth, integer, intent(in), optional  SL_meth, integer, intent(in), optional  NL_meth, integer, intent(in), optional  L_meth, integer, intent(in), optional  DC_meth, logical, intent(in), optional  check_overflow, integer, intent(in), optional  verb  )

private

Constructor for the type ode_solver

• OUTPUT:
  • slv = ode_solver

• INPUT:
  • type = solver type
  • pb = ode_problem . optional arguments
  • os_meth = operator splitting method
  • L_meth = linear ode method
  • SL_meth = semilinear ode method
  • DC_meth = deferred correction method
  • NL_meth = non linear ODE method
  • verb = verbosity level
  • check_overflow = checks overflow when solving

Definition at line 285 of file ode_solver_mod.f90.

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ode_solver_print()

subroutine ode_solver_mod::ode_solver_print ( type(ode_solver), intent(in)  slv )

private

print ode_solver

Definition at line 412 of file ode_solver_mod.f90.

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ode_solver_solve()

subroutine ode_solver_mod::ode_solver_solve ( type(ode_solution), intent(inout)  sol, type(ode_solver), intent(inout)  slv, type(ode_problem), intent(in)  pb, real(rp), intent(in)  t0, real(rp), intent(in)  T, real(rp), intent(in)  dt, procedure(linsystem_solver), optional  KInv, type(ode_output), optional  output  )

private

Solve an ODE with constant time step

• OUTPUT:
  • sol = ode_solution

• INPUT:
  • slv = ode_solver
  • pb = ode_problem
  • t0, t = starting and final time
  • dt = time step
  Optional:
  • KInv = inversion of the linear system \( (M + cS)u = {\rm rhs} \)
  • output = ode_output type definition
  Detail on 'KInv' and on 'output' are in ode_solver_mod detailed description.

Definition at line 715 of file ode_solver_mod.f90.

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ode_solver_valid()

logical function ode_solver_mod::ode_solver_valid ( type(ode_solver), intent(in)  slv )

private

check ode_solver

Definition at line 344 of file ode_solver_mod.f90.

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set_ode_solver_output()

subroutine, public ode_solver_mod::set_ode_solver_output	(	type(ode_solver), intent(inout)	slv,
		procedure(ode_output_proc)	output
	)

Load a user defined output for ODE resolution

Set slv%output

• OUTPUT:
  • sol = ode_solver

• INPUT:
  • output_proc = procedural arg with interface ode_output_proc

Definition at line 872 of file ode_solver_mod.f90.