bicgstab_device Module Reference

Provides a device implementation of the BiCGStab method.

Data Types
type	bicgstab_device_t
	Device implementation of the right-preconditioned BiCGStab method. More...
interface	hip_bicgstab_part1
interface	hip_bicgstab_part2
interface	hip_bicgstab_product_and_norm
interface	hip_bicgstab_update_p

Functions/Subroutines
subroutine	device_bicgstab_update_p (p_d, r_d, v_d, beta, omega, n)
	Search direction update \(p = r + \beta (p - \omega v)\).
subroutine	device_bicgstab_product_and_norm (product, norm_squared, a_d, b_d, mult_d, n)
	Weighted inner product and squared norm in one reduction.
real(kind=rp) function	device_bicgstab_part1 (s_d, r_d, v_d, mult_d, alpha, n)
	BiCGStab part 1, \(s = r - \alpha v\).
subroutine	device_bicgstab_part2 (rtr, rho, x_d, r_d, p_hat_d, s_hat_d, s_d, t_d, f_d, mult_d, alpha, omega, n)
	BiCGStab part 2, \(x = x + \alpha \hat{p} + \omega \hat{s}\) and \(r = s - \omega t\).
subroutine	bicgstab_device_init (this, n, max_iter, m, rel_tol, abs_tol, monitor)
	Initialise a device BiCGStab solver.
subroutine	bicgstab_device_free (this)
	Free a device BiCGStab solver.
type(ksp_monitor_t) function	bicgstab_device_solve (this, ax, x, f, n, coef, bc_projector, gs_h, niter)
	Solve a linear system with the device BiCGStab method.
subroutine	bicgstab_device_check_inner_product (inner_product, norm_a, norm_b, quantity)
	Check an inner product for a BiCGStab breakdown.
real(kind=rp) function	bicgstab_device_sqrt (value, quantity)
	Return the square root of a valid squared norm.
type(ksp_monitor_t) function, dimension(3)	bicgstab_device_solve_coupled (this, ax, x, y, z, fx, fy, fz, n, coef, bc_projector, gs_h, niter)
	Solve three independent systems with the device BiCGStab method.

Function/Subroutine Documentation

bicgstab_device_check_inner_product()

subroutine bicgstab_device::bicgstab_device_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 796 of file bicgstab_device.F90.

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bicgstab_device_free()

subroutine bicgstab_device::bicgstab_device_free ( class(bicgstab_device_t), intent(inout)  this )

private

Definition at line 557 of file bicgstab_device.F90.

bicgstab_device_init()

subroutine bicgstab_device::bicgstab_device_init ( class(bicgstab_device_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  )

private

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 502 of file bicgstab_device.F90.

bicgstab_device_solve()

type(ksp_monitor_t) function bicgstab_device::bicgstab_device_solve ( class(bicgstab_device_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 632 of file bicgstab_device.F90.

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bicgstab_device_solve_coupled()

type(ksp_monitor_t) function, dimension(3) bicgstab_device::bicgstab_device_solve_coupled ( class(bicgstab_device_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.
bc_projector	Boundary conditions for the three components.
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 851 of file bicgstab_device.F90.

bicgstab_device_sqrt()

real(kind=rp) function bicgstab_device::bicgstab_device_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 821 of file bicgstab_device.F90.

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device_bicgstab_part1()

real(kind=rp) function bicgstab_device::device_bicgstab_part1 ( type(c_ptr)  s_d, type(c_ptr)  r_d, type(c_ptr)  v_d, type(c_ptr)  mult_d, real(kind=rp)  alpha, integer  n  )

private

Parameters

s_d	Intermediate residual, written.
r_d	Residual.
v_d	Operator action \(A\hat{p}\).
mult_d	Spectral element multiplicity weights.
alpha	BiCGStab \(\alpha\).
n	Number of vector entries.

Returns

The weighted squared norm \(s^T M s\).

Definition at line 398 of file bicgstab_device.F90.

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device_bicgstab_part2()

subroutine bicgstab_device::device_bicgstab_part2 ( real(kind=rp), intent(out)  rtr, real(kind=rp), intent(out)  rho, type(c_ptr)  x_d, type(c_ptr)  r_d, type(c_ptr)  p_hat_d, type(c_ptr)  s_hat_d, type(c_ptr)  s_d, type(c_ptr)  t_d, type(c_ptr)  f_d, type(c_ptr)  mult_d, real(kind=rp)  alpha, real(kind=rp)  omega, integer  n  )

private

The rho inner product of the next iteration is reduced together with the residual norm, since both are taken against the residual this routine writes.

Parameters

rtr	Weighted squared norm \(r^T M r\) of the new residual.
rho	Weighted inner product \(f^T M r\) of the new residual.
x_d	Solution, updated in place.
r_d	Residual, written.
p_hat_d	Preconditioned search direction.
s_hat_d	Preconditioned intermediate residual.
s_d	Intermediate residual.
t_d	Operator action \(A\hat{s}\).
f_d	Right-hand side, which is also the shadow residual.
mult_d	Spectral element multiplicity weights.
alpha	BiCGStab \(\alpha\).
omega	BiCGStab \(\omega\).
n	Number of vector entries.

Definition at line 452 of file bicgstab_device.F90.

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device_bicgstab_product_and_norm()

subroutine bicgstab_device::device_bicgstab_product_and_norm ( real(kind=rp), intent(out)  product, real(kind=rp), intent(out)  norm_squared, type(c_ptr)  a_d, type(c_ptr)  b_d, type(c_ptr)  mult_d, integer  n  )

private

Combining the two values avoids 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_d	First vector in the inner product.
b_d	Second vector in the inner product and vector whose norm is taken.
mult_d	Spectral element multiplicity weights.
n	Number of vector entries.

Definition at line 351 of file bicgstab_device.F90.

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device_bicgstab_update_p()

subroutine bicgstab_device::device_bicgstab_update_p ( type(c_ptr)  p_d, type(c_ptr)  r_d, type(c_ptr)  v_d, real(kind=rp)  beta, real(kind=rp)  omega, integer  n  )

private

Parameters

p_d	Search direction, updated in place.
r_d	Residual.
v_d	Operator action \(A\hat{p}\) of the previous iteration.
beta	BiCGStab \(\beta\).
omega	BiCGStab \(\omega\) of the previous iteration.
n	Number of vector entries.

Definition at line 319 of file bicgstab_device.F90.

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