The Supernode eigensolver works by taking the matrix structure of the stiffness and mass matrix from the original FEA model and internally breaking it into pieces (supernodes). These supernodes are then used to reduce the original FEA matrix to a much smaller system of equations. The solver then computes all of the modes and mode shapes within the requested frequency range on this smaller system of equations. Then, the supernodes are used again to transform (or expand) the smaller mode shapes back to the larger problem size from the original FEA model.
The power of this eigensolver is best experienced when solving for a high number of modes, usually more than 200 modes. Another benefit is that this eigensolver typically performs much less I/O than the Block Lanczos eigensolver and, therefore, is especially useful on typical desktop machines that often have limited disk space and/or slow I/O transfer speeds.
Performance information for the Supernode Eigensolver is printed by default to the file Jobname.DSP. Use the command SNOPTION,,,,,,PERFORMANCE to print this same information, along with additional solver information, to the standard output file.
When studying performance of this eigensolver, each of the three key steps described above (reduction, solution, expansion) should be examined. The first step of forming the supernodes and performing the reduction increases in time as the original problem size increases; however, it typically takes about the same amount of computational time whether 10 modes or 1000 modes are requested. In general, the larger the original problem size is relative to the number of modes requested, the larger the percentage of solution time spent in this reduction process.
The next step, solving the reduced eigenvalue problem, increases in time as the number of modes in the specified frequency range increases. This step is typically a much smaller portion of the overall solver time and, thus, does not often have a big effect on the total time to solution. However, this depends on the size of the original problem relative to the number of requested modes. The larger the original problem, or the fewer the requested modes within the specified frequency range, the smaller will be the percentage of solution time spent in this step. Choosing a frequency range that covers only the range of frequencies of interest will help this step to be as efficient as possible.
The final step of expanding the mode shapes can be an I/O intensive step and, therefore, typically warrants the most attention when studying the performance of the Supernode eigensolver. The solver expands the final modes using a block of vectors at a time. This block size is a controllable parameter and can help reduce the amount of I/O done by the solver, but at the cost of more memory usage.
Example 6.6: DSP File for Supernode (SNODE) Solver shows a part of the Jobname.DSP file that reports the performance statistics described above for a 1.5 million DOF modal analysis that computes 1000 modes and mode shapes. The output shows the cost required to perform the reduction steps (A), the cost to solve the reduced eigenvalue problem (B), and the cost to expand and output the final mode shapes to the Jobname.rst and Jobname.mode files (C). The block size for the expansion step is also shown (D). At the bottom of this file, the total size of the files written by this solver is printed with the total amount of I/O transferred.
In this example, the reduction time is by far the most expensive piece. The expansion computations are running at over 3000 Mflops, and this step is not relatively time consuming. In this case, using more than one core would certainly help to significantly reduce the time to solution.
Example 6.6: DSP File for Supernode (SNODE) Solver
number of equations = 1495308
no. of nonzeroes in lower triangle of a = 41082846
no. of nonzeroes in the factor l = 873894946
ratio of nonzeroes in factor (min/max) = 1.0000
number of super nodes = 6554
maximum order of a front matrix = 6324
maximum size of a front matrix = 19999650
maximum size of a front trapezoid = 14547051
no. of floating point ops for eigen sol = 8.0502D+12
no. of floating point ops for eigen out = 1.2235D+12
no. of equations in global eigenproblem = 5983
factorization panel size = 256
supernode eigensolver block size = 40 <---D
number of cores used = 1
time (cpu & wall) for structure input = 1.520000 1.531496
time (cpu & wall) for ordering = 4.900000 4.884938
time (cpu & wall) for value input = 1.050000 1.045083
time (cpu & wall) for matrix distrib. = 3.610000 3.604622
time (cpu & wall) for eigen solution = 1888.840000 1949.006305
computational rate (mflops) for eig sol = 4261.983276 4130.414801
effective I/O rate (MB/sec) for eig sol = 911.661409
time (cpu & wall) for eigen output = 377.760000 377.254216
computational rate (mflops) for eig out = 3238.822665 3243.164948
effective I/O rate (MB/sec) for eig out = 1175.684097
cost (elapsed time) for SNODE eigenanalysis
-----------------------------
Substructure eigenvalue cost = 432.940317 <---A (Reduction)
Constraint mode & Schur complement cost = 248.458204 <---A (Reduction)
Guyan reduction cost = 376.112464 <---A (Reduction)
Mass update cost = 715.075189 <---A (Reduction)
Global eigenvalue cost = 146.099520 <---B (Reduced Problem)
Output eigenvalue cost = 377.254077 <---C (Expansion)
i/o stats: unit-Core file length amount transferred
words mbytes words mbytes
---- ---------- -------- ---------- --------
17- 0 628363831. 4794. MB 16012767174. 122168. MB
45- 0 123944224. 946. MB 1394788314. 10641. MB
46- 0 35137755. 268. MB 70275407. 536. MB
93- 0 22315008. 170. MB 467938080. 3570. MB
94- 0 52297728. 399. MB 104582604. 798. MB
98- 0 22315008. 170. MB 467938080. 3570. MB
99- 0 52297728. 399. MB 104582604. 798. MB
------- ---------- -------- ---------- --------
Totals: 936671282. 7146. MB 18622872263. 142081. MB
Total Memory allocated = 561.714 MB