Strand7 Software: In Detail: Solvers: Technology

Strand7 Solver Technology

Strand7 offers three different technologies for the solution of the global matrices assembled by the solvers:

Skyline Solver
Sparse Solver
Preconditioned Conjugate Gradient (PCG) Solver

The skyline solver gives good performance when solving small models or when solving models that produce dense (i.e. non-sparse) matrices (e.g. regular meshes consisting of high-order solid elements). This solver has the highest disk space requirements of the three solvers, but usually requires less memory than the sparse solver. Considering the amount of data it needs to manipulate, the skyline solver is very efficient due to pre-determined column heights in the matrix.

The direct sparse solver provides the best overall performance in the vast majority of models, especially large models consisting of beam and shell elements. The performance gain over the skyline solver for such models can be very significant. The disk space requirements of this solver are usually lower than for the skyline solver, whilst memory requirements are usually higher. What gives this solver a significant advantage is that if the matrix is sparse, much of the elimination work can be completely skipped.

While the skyline and the sparse solvers are direct solvers (i.e. they solve the matrix system of equations by a method closely related to Gaussian elimination), the PCG solver is an iterative solver: it uses a conjugate gradient algorithm to iteratively improve an initial estimate of the solution. Unlike the other two solvers, the total disk space required by the PCG solver is not affected by the node ordering, and this solver will require the least disk space of the three. The memory requirements of this solver are usually less than those of the other solvers, however, unlike the other solvers, when the available memory is less than the amount required, solution time can increase significantly. The PCG solver is most useful for 3D solid models, particularly when the elements are high-order elements.

The table below compares the performance of the skyline and sparse solvers for a range of models. The models were run on a 64-bit Windows 7 computer with 16 GB RAM and Intel i7 CPU running at 3.4 GHz.

Model	Elements	Solver	Result Cases	Equations	Skyline (hh:mm:ss)	Sparse (hh:mm:ss)
Model	Elements	Solver	Result Cases	Equations	Skyline (hh:mm:ss)	Sparse (hh:mm:ss)
	91 483 Nodes 1 102 Beams 90 656 Plates	Linear Static	7	541 242	00:19:47	00:00:24
	364 521 Nodes 1 102 Beams 358 786 Plates	Linear Static	7	2 165 646	NA	00:03:12
	807 357 Nodes 1 102 Beams 815 904 Plates	Linear Static	7	4 808 838	NA	00:11:06
	807 357 Nodes 1 102 Beams 815 904 Plates	Natural Frequency	24 modes	4 808 838	NA	01:14:56
	10 179 Nodes 8 625 Beams 12 781 Plates	Linear Transient	10 time steps	60 990	00:00:44	00:00:07
	14 808 Nodes 5 630 Beams 14 529 Plates	Linear Static	1	86 082	00:01:54	00:00:05
	11 794 Nodes 423 Beams 11 201 Plates 384 Bricks	Non-linear Transient	100 time steps	68 896	03:31:30	00:09:04
	29 662 Nodes 3 676 Beams 32 579 Plates	Linear Static	1	177 186	00:01:15	00:00:49
	29 662 Nodes 3 676 Beams 32 579 Plates	Linear Buckling	20 modes	177 186	00:12:40	00:02:58
	19 923 Nodes 4 169 Beams 6 806 Plates 58 808 Bricks	Linear Static	1	73 887	00:04:06	00:00:05
	35 138 Nodes 142 642 Tet4	Natural Frequency	20 modes	102 764	00:15:20	00:00:43
	42 945 Nodes 42 880 Hex8	Linear Static	2	141 027	00:14:48	00:00:45
	83 030 Nodes 18 090 Hex20	Linear Static	2	244 446	01:12:51	00:05:51
	91 737 Nodes 393 284 Tet4	Linear Static	1	257 067	00:58:22	00:01:19
	91 737 Nodes 393 284 Tet4	Natural Frequency	20 modes	275 067	NA	00:03:01
	352 082 Nodes 218 298 Tet10	Linear Static	1	1 064 373	NA	00:26:17
	60 986 Nodes 3 052 Beams 58 467 Plates	Linear Static	1	348 197	00:17:21	00:00:14
	177 565 Nodes 3 052 Beams 58 467 Plates	Linear Static	1	1 047 671	NA	00:02:24

Model	Elements	Solver	Skyline (hh:mm:ss)	Sparse (hh:mm:ss)
Model	Elements	Solver	Skyline (hh:mm:ss)	Sparse (hh:mm:ss)
	91 483 Nodes 1 102 Beams 90 656 Plates	Linear Static	00:19:47	00:00:24
	364 521 Nodes 1 102 Beams 358 786 Plates	Linear Static	NA	00:03:12
	807 357 Nodes 1 102 Beams 815 904 Plates	Linear Static	NA	00:11:06
	807 357 Nodes 1 102 Beams 815 904 Plates	Natural Frequency	NA	01:14:56
	10 179 Nodes 8 625 Beams 12 781 Plates	Linear Transient	00:00:44	00:00:07
	14 808 Nodes 5 630 Beams 14 529 Plates	Linear Static	00:01:54	00:00:05
	11 794 Nodes 423 Beams 11 201 Plates 384 Bricks	Non-linear Transient	03:31:30	00:09:04
	29 662 Nodes 3 676 Beams 32 579 Plates	Linear Static	00:01:15	00:00:49
	29 662 Nodes 3 676 Beams 32 579 Plates	Linear Buckling	00:12:40	00:02:58
	19 923 Nodes 4 169 Beams 6 806 Plates 58 808 Bricks	Linear Static	00:04:06	00:00:05
	35 138 Nodes 142 642 Tet4	Natural Frequency	00:15:20	00:00:43
	42 945 Nodes 42 880 Hex8	Linear Static	00:14:48	00:00:45
	83 030 Nodes 18 090 Hex20	Linear Static	01:12:51	00:05:51
	91 737 Nodes 393 284 Tet4	Linear Static	00:58:22	00:01:19
	91 737 Nodes 393 284 Tet4	Natural Frequency	NA	00:03:01
	352 082 Nodes 218 298 Tet10	Linear Static	NA	00:26:17
	60 986 Nodes 3 052 Beams 58 467 Plates	Linear Static	00:17:21	00:00:14
	177 565 Nodes 3 052 Beams 58 467 Plates	Linear Static	NA	00:02:24

For more information on solver technology, see Strand7 Webnotes - Theory / Solvers or refer to the Strand7 Theoretical Manual.