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: 

The skyline solver gives good performance when solving small models or when solving models
that produce dense (i.e. nonsparse) matrices (e.g. regular meshes consisting of highorder 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 predetermined 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 highorder elements. The table below compares the performance of the skyline and sparse solvers for a range of models. The models were run on a 64bit 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 
Nonlinear 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 
Nonlinear 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. 