KrylovMG Class Reference

Krylov multigroup solver. More...

Inheritance diagram for KrylovMG:

Collaboration diagram for KrylovMG:

List of all members.

Public Member Functions
function	KrylovMG (in input, in)
	Class constructor.
function	set_keff (in this, in k)
function	solve (in this)
	Solve the multigroup fixed source problem.
function	reset_convergence (in this, in max_iters, in tolerance)
	Solve the within-group problem.
function	display_me (in this)
Public Attributes
Property	d_keff
Protected Member Functions
function	print_iteration (in this, in iteration, in flux_error, in total_inners)
function	build_fission_source (in this, in g, in phi)
	Build the fission source.
function	apply (in x, in this)
	Apply the multigroup transport operator.
function	setup_base (in this, in)
	Setup the base solver.
function	initialize_scatter (in this)
	Prebuild scattering matrix for each cell.
function	build_scatter_source (in this, in g, in phi)
	Build the within-group scattering source.
function	build_all_scatter_source (in this, in g, in phi)
	Build all the scattering sources.
function	build_fixed_source (in this, in g)
	Build source for this group excluding within-group scatter.
function	build_external_source (in this, in g)
function	check_convergence (in this, in iteration, in flux_error)
function	print_iteration (in this, in it, in e0, in e1, in e2)
Protected Attributes
Property	d_input
	User input.
Property	d_state
	State vectors.
Property	d_boundary
	Boundary fluxes.
Property	d_mesh
	Problem mesh (either Cartesian mesh or MOC tracking)
Property	d_mat
	Materials definitions.
Property	d_quadrature
	Angular mesh.
Property	d_equation
	Spatial discretization.
Property	d_sweeper
	Sweeper over the space-angle domain.
Property	d_external_source
	User-defined external source.
Property	d_fission_source
	Fission source, if used.
Property	d_fixed_source
	Any source that remains "fixed" within the group solve.
Property	d_scatter_source
	The within group scattering source.
Property	d_sigma_s
	Scattering cross-section vector for faster source computation.
Property	d_max_iters
Property	d_tolerance
Property	d_g
Property	d_M
	Moments to discrete operator.

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Detailed Description

Krylov multigroup solver.

Traditionally, the Gauss-Seidel method has been used for multigroup problems. For each group, the within-group equation is solved, and the the fluxes are updated for use in the next group. However, for problems with significant upscatter, Gauss-Seidel can be quite expensive, even when GMRES (or some better-than-source-iteration) is used for the within group solve. As an alternativel, we can apply GMRES (or other Krylov solvers) to the multigroup problem directly. The linear system is then

Of course, this can be written succinctly the same way we did the within- group equation:

where is the sweeping operator with moment contributions added implicitly, and where the Krylov vectors are energy-dependent.

Reference: Evans, T., Davidson, G. and Mosher, S. "Parallel Algorithms for Fixed-Source and Eigenvalue Problems", NSTD Seminar (ORNL), May 27, 2010.

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Constructor & Destructor Documentation

function KrylovMG	(	in	input,
		in
	)

Class constructor.

Parameters:

input	User input.
state	State vectors.
boundary	Boundary flux container.
mesh	Geometry.
mat	Material database.
quadrature	Angular mesh.
external_source	Fixed source.
fission_source	Fission source.

Returns:

Instance of the KrylovMG class.

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Member Function Documentation

function apply	(	in	x,
		in	this
	)		[protected]

Apply the multigroup transport operator.

Returns:

Matrix-vector

function build_all_scatter_source	(	in	this,
		in	g,
		in	phi
	)		[protected, inherited]

Build all the scattering sources.

Parameters:

g	Group for this problem. (I.e. row in MG).
phi	Current MG flux.

function build_external_source	(	in	this,
		in	g
	)		[protected, inherited]

function build_fission_source	(	in	this,
		in	g,
		in	phi
	)		[protected]

Build the fission source.

This is intended for fixed source problems with multiplication.

Parameters:

g	Group for this problem. (I.e. row in MG).
phi	Current MG flux.

function build_fixed_source	(	in	this,
		in	g
	)		[protected, inherited]

Build source for this group excluding within-group scatter.

Parameters:

g	Group for this problem.

function build_scatter_source	(	in	this,
		in	g,
		in	phi
	)		[protected, inherited]

Build the within-group scattering source.

Parameters:

g	Group for this problem.
phi	Current group flux.

function check_convergence	(	in	this,
		in	iteration,
		in	flux_error
	)		[protected, inherited]

function display_me

(

in

this

)

[inherited]

function initialize_scatter

(

in

this

)

[protected, inherited]

Prebuild scattering matrix for each cell.

While not the most *memory* efficient, this saves *time* by eliminate lots of loops.

function print_iteration	(	in	this,
		in	it,
		in	e0,
		in	e1,
		in	e2
	)		[protected, inherited]

function print_iteration	(	in	this,
		in	iteration,
		in	flux_error,
		in	total_inners
	)		[protected]

function reset_convergence	(	in	this,
		in	max_iters,
		in	tolerance
	)		[inherited]

Solve the within-group problem.

Parameters:

g	Group of the problem to be solved.

Returns:

Flux residual (L-inf norm) and iteration count. Reset convergence criteria. It can be useful to use a dynamically changing convergence criteria, especially for eigenproblems. For regular power iteration, it is wasteful to use tight tolerances on the inners when the source is not as tightly known.

Parameters:

max_iters	Maximum number of iterations.
tolerance	Maximum point-wise error in flux

function set_keff	(	in	this,
		in	k
	)

function setup_base	(	in	this,
		in
	)		[protected, inherited]

Setup the base solver.

By keeping everything out of the constructor, we can avoid having to copy the signature for all derived classes, both in their definitions and whereever thisects are instantiated. However, derived classes have other setup issues that need to be done, and so this serves as a general setup function that must be called before other setup stuff.

Parameters:

input	Input database.
state	State vectors, etc.
boundary	Boundary fluxes.
mesh	Problem mesh.
mat	Material definitions.
quadrature	Angular mesh..
external_source	User-defined external source.
fission_source	Fission source.

function solve

(

in

this

)

Solve the multigroup fixed source problem.

Currently, I'm not adding much flexibility. In the future, it would be great to add a multigroup preconditioner, other solvers, etc. Of course, reflective conditions are still on the to-do list; but response functions don't need them!

Returns:

Output, including error and iteration count.

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Member Data Documentation

Property d_boundary [protected, inherited]

Boundary fluxes.

Property d_equation [protected, inherited]

Spatial discretization.

Property d_external_source [protected, inherited]

User-defined external source.

Property d_fission_source [protected, inherited]

Fission source, if used.

Property d_fixed_source [protected, inherited]

Any source that remains "fixed" within the group solve.

Property d_g [protected, inherited]

Property d_input [protected, inherited]

User input.

Property d_keff

Property d_M [protected, inherited]

Moments to discrete operator.

Property d_mat [protected, inherited]

Materials definitions.

Property d_max_iters [protected, inherited]

Property d_mesh [protected, inherited]

Problem mesh (either Cartesian mesh or MOC tracking)

Property d_quadrature [protected, inherited]

Angular mesh.

Property d_scatter_source [protected, inherited]

The within group scattering source.

Property d_sigma_s [protected, inherited]

Scattering cross-section vector for faster source computation.

Property d_state [protected, inherited]

State vectors.

Property d_sweeper [protected, inherited]

Sweeper over the space-angle domain.

Property d_tolerance [protected, inherited]

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The documentation for this class was generated from the following file:

• /home/robertsj/Research/matlab_transport_pack/source/KrylovMG.m