bicgstab Module Reference

Provides a CPU implementation of the BiCGStab method.

Data Types
type	bicgstab_t
	CPU implementation of the right-preconditioned BiCGStab method. More...

Functions/Subroutines
subroutine	bicgstab_init (this, n, max_iter, m, rel_tol, abs_tol, monitor)
	Initialise a CPU BiCGStab solver.
subroutine	bicgstab_free (this)
	Free a CPU BiCGStab solver.
type(ksp_monitor_t) function	bicgstab_solve (this, ax, x, f, n, coef, bc_projector, gs_h, niter)
	Solve a linear system with the CPU BiCGStab method.
subroutine	bicgstab_check_inner_product (inner_product, norm_a, norm_b, quantity)
	Check an inner product for a BiCGStab breakdown.
subroutine	bicgstab_product_and_norm (product, norm_squared, a, b, mult, n)
	Compute a weighted inner product and squared norm in one reduction.
real(kind=rp) function	bicgstab_sqrt (value, quantity)
	Return the square root of a valid squared norm.
type(ksp_monitor_t) function, dimension(3)	bicgstab_solve_coupled (this, ax, x, y, z, fx, fy, fz, n, coef, bc_projector, gs_h, niter)
	Solve three independent systems with the CPU BiCGStab method.

Function/Subroutine Documentation

bicgstab_check_inner_product()

subroutine bicgstab::bicgstab_check_inner_product ( real(kind=rp), intent(in)  inner_product, real(kind=rp), intent(in)  norm_a, real(kind=rp), intent(in)  norm_b, character(len=*), intent(in)  quantity  )

private

The comparison is normalised by both vector norms. Dividing by the larger norm first avoids overflow in their product and preserves scale invariance.

Parameters

inner_product	Weighted inner product of the two vectors.
norm_a	Norm of the first vector.
norm_b	Norm of the second vector.
quantity	Name of the algorithmic quantity for error reporting.

Definition at line 372 of file bicgstab.f90.

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bicgstab_free()

subroutine bicgstab::bicgstab_free ( class(bicgstab_t), intent(inout)  this )

private

Definition at line 138 of file bicgstab.f90.

bicgstab_init()

subroutine bicgstab::bicgstab_init	(	class(bicgstab_t), intent(inout), target	this,
		integer, intent(in)	n,
		integer, intent(in)	max_iter,
		class(pc_t), intent(in), optional, target	m,
		real(kind=rp), intent(in), optional	rel_tol,
		real(kind=rp), intent(in), optional	abs_tol,
		logical, intent(in), optional	monitor
	)

Parameters

n	Number of degrees of freedom.
max_iter	Maximum number of iterations.
M	Optional preconditioner. An identity preconditioner is used if absent.
rel_tol	Optional relative convergence tolerance.
abs_tol	Optional absolute convergence tolerance.
monitor	Optional switch for logging the residual at each iteration.

Definition at line 94 of file bicgstab.f90.

bicgstab_product_and_norm()

subroutine bicgstab::bicgstab_product_and_norm ( real(kind=rp), intent(out)  product, real(kind=rp), intent(out)  norm_squared, real(kind=rp), dimension(n), intent(in)  a, real(kind=rp), dimension(n), intent(in)  b, real(kind=rp), dimension(n), intent(in)  mult, integer, intent(in)  n  )

private

Combining the two values avoids adding a global synchronisation solely for the scale used by the breakdown checks.

Parameters

product	Weighted inner product of a and b.
norm_squared	Weighted squared norm of b.
a	First vector in the inner product.
b	Second vector in the inner product and vector whose norm is taken.
mult	Spectral element multiplicity weights.
n	Number of vector entries.

Definition at line 403 of file bicgstab.f90.

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bicgstab_solve()

type(ksp_monitor_t) function bicgstab::bicgstab_solve ( class(bicgstab_t), intent(inout)  this, class(ax_t), intent(in)  ax, type(field_t), intent(inout)  x, real(kind=rp), dimension(n), intent(in)  f, integer, intent(in)  n, type(coef_t), intent(inout)  coef, class(scalar_bc_projector_t), intent(inout)  bc_projector, type(gs_t), intent(inout)  gs_h, integer, intent(in), optional  niter  )

private

The initial guess in x is discarded and the iteration starts from zero.

Parameters

Ax	Linear operator.
x	Solution field.
f	Right-hand side.
n	Number of degrees of freedom.
coef	Spectral element coefficients and multiplicity weights.
bc_projector	Projector for dirichlet boundary nodes.
gs_h	Gather-scatter handle used to assemble the operator result.
niter	Optional maximum number of iterations, overriding the configured value.

Returns

Convergence information for the solve.

Definition at line 189 of file bicgstab.f90.

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bicgstab_solve_coupled()

type(ksp_monitor_t) function, dimension(3) bicgstab::bicgstab_solve_coupled ( class(bicgstab_t), intent(inout)  this, class(ax_t), intent(in)  ax, type(field_t), intent(inout)  x, type(field_t), intent(inout)  y, type(field_t), intent(inout)  z, real(kind=rp), dimension(n), intent(in)  fx, real(kind=rp), dimension(n), intent(in)  fy, real(kind=rp), dimension(n), intent(in)  fz, integer, intent(in)  n, type(coef_t), intent(inout)  coef, class(vector_bc_projector_t), intent(inout)  bc_projector, type(gs_t), intent(inout)  gs_h, integer, intent(in), optional  niter  )

private

This routine sequentially invokes the scalar solver for each component.

Parameters

Ax	Linear operator.
x	Solution field for the first component.
y	Solution field for the second component.
z	Solution field for the third component.
fx	Right-hand side for the first component.
fy	Right-hand side for the second component.
fz	Right-hand side for the third component.
n	Number of degrees of freedom per component.
coef	Spectral element coefficients and multiplicity weights.
blstx	Boundary conditions for the first component.
blsty	Boundary conditions for the second component.
blstz	Boundary conditions for the third component.
gs_h	Gather-scatter handle used to assemble operator results.
niter	Optional maximum number of iterations, overriding the configured value.

Returns

Convergence information for each component.

Definition at line 468 of file bicgstab.f90.

bicgstab_sqrt()

real(kind=rp) function bicgstab::bicgstab_sqrt ( real(kind=rp), intent(in)  value, character(len=*), intent(in)  quantity  )

private

Parameters

value	Weighted squared norm.
quantity	Name of the vector for error reporting.

Returns

The non-negative square root.

Definition at line 436 of file bicgstab.f90.

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