AP-AMG

July 10, 2006

About Us

AP-AMG is a high performance matrix solver using the AMG (Algebraic Multigrid) method we developed.

A matrix solver is a tool for solving linear equations for fluid dynamics, structural analysis or any other linear systems. The AMG method is a highly refined method which efficiently solves a system of linear equations by using coarse-grid based on the characteristics of coefficient matrix of a given fine-grid.

AP-AMG is a real-life industrial problem solver and is among the world's best.

AP-AMG

Performances of the single version of AP-AMG is described here. The following iterative solvers compared here:

Jacobi preconditioned CG solver (Jac-CG)
SSOR preconditioned CG solver (SSOR-CG)
Smoothed Aggregation-based AMG solver (SA-AMG)
AP-AMG

The problems to be solved here are the following CFD and structural problems. "Solid" and "Shell" in the column "Model" mean solid and shell elements, respectively; "Tet4" and Tet10" mean the tetrahedral linear and quadratic elements, respectively.

	Model	No. of Nodes	DOFs /Nodes	DOFs
Fluid dynamics	Solid_Tet4-F01	40,743	1	40,743
Fluid dynamics	Solid_Tet4_F02	199,450	1	199,450
Structural Mechanics	Solid_Tet4_S01	67,580	3	202740
	Solid_Tet10_S01	41,882	3	125,646
	Solid_Tet10_S02	144,544	3	433,632
	Solid_Tet10_S03	163,660	3	490,980
	Solid_Tet10_S04	450,092	3	1,350,276
	Solid_Tet10_S05	731,632	3	2,194,896
	Shell_S01	2,011	6	12,066
	Shell_S02	40,401	5	202,005

The results are shown below. The computer used is Xeon 2.8GHz with 4GB RAM. The maximum tolerance is set to be 10^-6 for both CFD and structural problems. The mark "-" in this table shows that the memory requirement exceeded available physical memory, and could not be solved.

Model CPU Time [sec]

Jac-CG SSOR-CG SA-AMG AP-AMG

Fluid
dynamics Solid_Tet4-F01 10.0 11.5 4.2 0.7

Solid_Tet4_F02 84 80 42 2.7

Structural
Mechanics Solid_Tet4_S01 118 72 39 13

Solid_Tet10_S01 3,681 2,771 314 141

Solid_Tet10_S02 16,178 9,608 1,446 350

Solid_Tet10_S03 13,329 7,951 1,110 353
Solid_Tet10_S04 4,098 2,718 - 232

Solid_Tet10_S05 17,700 12,605 - 664

Shell_S01 21 13 5 3.7

Shell_S02 402 244 67 31

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if you have any questions.

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