Parallel Implementation of FEM Solver for Shared Memory Using OpenMP

Algorithm 2

Parallel Conjugate Gradient algorithm.

Input: (A, ,x, N, r^tt1, r^tr2, p^tAp)
Output:x
(1)	fork (A, ,x, N, r^tt1, r^tr2, p^tAp) {shared variables}
(2)	Th_id, Tt_id (Thread id and Total Thread by OS)
(3)	St_RowId ← Ed_RowId ← 0 {Start and end ids}
(4)	IfTh_id ＜ N % Tt_ththen
(5)	St_RowID ← Th_id∗N/Tt+Th_id
(6)	Ed_RowID ← St_RowID+N/Tt_th+1
(7)	else
(8)	St_RowID ← Th_id ∗ N/Tt_th+Tt_th
(9)	Ed_RowID ← St_RowID+N/Tt_th
(10)	end_if
(11)	r^tr1 ← r^tr2 ← t_r^tr ← 0
(12)	foreachi ← St_RowID.Ed_RowIDdo
(13)	p[i] ← r[i] ← b[i]-
(14)	t_r^tr ← t_r^tr + r[i] ∗ r[i]
(15)	end for
(16)	lock r^tr2 ← r^tr2 + t_r^tr unlock
(17)	barrier
(18)	while>Threshold do
(19)	r^tr1 ← r^tr2
(20)	r^tr2 ← t_p^tAp ← 0
(21)	foreachi ← St_RowID, Ed_RowIDdo
(22)	t_p'Ap ← t_p^tAp+p[i].
(23)	end for
(24)	lock p^tAp ← p^tAp+t_p^tAp unlock
(25)	barrier
(26)	t_r^tr ← 0
(27)	foreachi ← St_RowID, Ed_RowIDdo
(28)	x[i] ← x[i]+(r^tr1/p^tAp).p[i]
(29)	r[i] ← r[i]+(r^tr1/p^tAp).
(30)	t_r^tr ← t_r^tr+r[i] ∗ r [i]
(31)	end for
(32)	p^tAp ← 0
(33)	lock r^tr2 ← r^tr2+t_r^tr unlock
(34)	barrier
(35)	foreachi ← St_RowID, Ed_RowIDdo
(36)	p[i] ← r[i]+(r^tr2/r^tr1).p[i]
(37)	end for
(38)	end while
(39)	join