Institute of Geonics AS CR, v. v. i.

KBS - Large-Scale Geoenvironmental Model

Model of the prototype repository at Aspo following the KBS3 concept of storage of the spent nuclear fuel and considering thermo-mechanical behavior of 3D domain in the time period of 50 or 100 years.

Situation

The studied domain includes 65 m long deposition tunnel located 450 meters bellow surface, backfilled. There are two sections with 4 and 2 deposition holes (1.75 m diameter and 8 m deep), where cannisters with the spent nuclear fuel are stored. The used buffer material is bentonite.

Discretization

The domain is discretized in space by a regular mesh with 391 x 63 x 105 nodes. The bricks are further decomposed to six tetrahedra. In time, the finite differences are applied together with implicit Euler scheme and adaptive time stepping.

The thermal part is influenced mainly by radioactive waste as the heat source and by heat conduction in rock, buffer and backfill. It results in a sequence of linear systems, each with 2 586 465 DOF.

Moreover in predermined time points, the solution of a linear system with 7 759 395 DOF is computed. It corresponds to the mechanical part, which is influenced by initial stress loading, tunnel excavation and heat load from the nuclear waste.

Times of parallel computing

Computations performed on Natan and Thea. For the mechanical part only, in time of 2 years after the heat loading by the nuclear waste:

DD: Solution of the FEM system by two-level overlapping Schwarz method with minimal overlap, replacing of subdomain problems by incomplete factorization, creating of coarse grid problem by aggregation (two choices of aggregation 6 x 6 x 6 and 12 x 6 x 9), approximate solution of the coarse grid problem by inner PCG iterations with relative accuracy eps=0.1. The FEM system is solved from the zero initial guess up to relative residual accuracy eps=0.0001.
DiD: Displacement decomposition preconditioning, subproblems replaced by incomplete factorization (IF) or solved by inner PCG iterations (II) with inner accuracy eps=0.1. The FEM system is again solved from the zero initial guess up to relative residual accuracy eps=0.0001.

Computations performed on Simba and Ra. For the thermal part only, in time interval of 100 years after the heat loading by the nuclear waste. The adaptive choice of the time step is done and the total number of time steps is 47. The FEM system is solved up to relative residual accuracy eps=0.000001 and with the initial guess taken from the previous time step.

	Simba (OpenMP)			Simba (MPICH)			Ra (SCALI)
# P	# It	Time [s]	Speed-up	# It	Time [s]	Speed-up	# It	Time [s]	Speed-up
1	1341	6292		1344	5931.4		1344	1144.0
2	1421	4101	1.63	1424	3169.1	1.87	1421	643.2	1.78
4	1425	2082	3.44	1428	1577.0	3.76	1426	314.3	3.64
8	1514	1120	6.34	1514	833.2	7.12	1514	909.4
12	1578	872	8.48	1581	596.2	9.95	1579	1192.6
16	1614	751	10.09	1618	482.9	12.28	1616	1355.9
20				1691	471.1
24				1710	554.3