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:
  1. Skyline Solver
  2. Sparse Solver
  3. 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)
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)
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.
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