Super Matrix Solver the high-speed and robust matrix solver
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Boundary Element Method Solver
Super Matrix Solver SMS-BEM
Special features of SMS-BEM
- Hybrid-solver (pre-processing based on direct and iterative methods)
- From several to 40 times faster calculation speed compared with conventional direct method
- Lower memory consumption: required memory size that is 1.1 to 1.3 times the size of coefficient matrix A
- Calculation time increase in squares of the size of coefficient matrix A: calculation time increase in cubes in conventional direct method solver
- Capable of Out-of-Core calculation for efficient Disk I/O control
- Adjustable calculation precision: iterative method allows for configuration of convergence criteria
- Calculates the matrices in which the coefficient matrix A is fixed, and only the value of the right-hand-side vector b changes
SMS-BEM Algorithm
SMS-BEM Summary Specifications
Items Descriptions Notes
Target Coefficient Matrix Dense matrices that are generated with boundary element method (BEM). Calculates dense matrices; however, performs well for sparse matrices.
Types of Unknowns Real (double) and Complex Numbers.
Solution Method Pre-processing + Iterative Method
Data Giving Method 1. Give coefficient matrix A, right-hand-side vector b, etc. as arguments. The result is also returned as arguments. 2. Loading the data (e.g. coefficient matrix A and right-hand-side vector b) that was once dumped into a file. The result is also returned as a file. 1. Small to medium size problems with fewer than 14,000 unknowns. 2. Large size problems that exceeds 14,000 unknowns.
Limit of Unknowns None. Basically calculates with actual (IN-CORE) memory. In case of memory insufficiency, calculates with OUT-OF-CORE capability. Allows for setting of the amount of actual (usable) memory.
Parameters 1) Target Convergence 2) Number of Iteration 3)Amount of Memory Allocated 1 and 2 can be assigned because this solution method is based on iterative method. Target convergence specified by relative residual in L2 norm.
Other Conditions Dump the data as 1D array so that i-th column and j-th element of the coefficient matrix A, and the k-th element of the 1D array relate as follows: k=(i-1)*n+j where n is the number of unknowns. Enter the data row by row in a sequence (enter the 1st row, then the 2nd, 3rd and so forth).
Method of Provision DLL format for Windows; Static library format for Linux and UNIX. Source code will not be disclosed.
Memory Requirement Estimation For IN-CORE calculation, memory addition is required that is 0.1 to 0.3 times as large as the size of the coefficient matrix A. (i.e. for the matrix size of S, the seize of required memory is 1.1S to 1.3S) OUT-OF-CORE calculation is possible with small amount of memory (e.g. 1/10 or less the size of the coefficient matrix A). However, larger the amount of usable memory, faster the calculation speed. Fastest calculation time may be attained by giving an entire memory to the solver by freeing the memory allocated by other sub-routine. Breakthrough in requirement for fewer amount of memory compared to the conventional solution method that requires large amount of memory.
Calculation Time Proportional to the squares of the size of coefficient matrix A (in case of IN-CORE).
NOTE: This material does not guarantee the performance. Specifications may be changed without notice
SMS-BEM Performance Example
Direct Method SMS-BEM Ratio (Tdirect/Tsms-bem)
Calculation Time (Tdirect) Calculation Time (Tsms-bem) Convergence
1.00 E-07
1.00 E-10
1.00 E-13
Product Information
SMS-BEM Product Introduction (PDF/950KB)
Platforms (OS)

Windows, Linux; for detailed information: SMS-BEM System Environment (PDF/13KB)

NOTE: Materials provided on this web site does not guarantee functions and performance of the product.
Product specifications may change without notice.