Accelerated algorithm for modal frequency response calculation

1. A computer-implemented method of simulating a real-world object, the computer-implemented method comprising:

calculating modal frequency responses of a real-world object for excitation frequencies in a plurality of excitation frequency subsets, each of the plurality of excitation frequency subsets providing a plurality of frequencies; and

employing the calculated modal frequency responses in simulations of the real-world object by performing a simulation of the real-world object based at least in part on the calculated modal frequency responses, the simulation utilizing the calculated modal frequency responses as an accelerated means of calculation of modal frequency response in the plurality of frequencies.

2. The computer-implemented method of claim 1 further comprising:

obtaining a set of excitation frequencies; and

dividing the obtained set of excitation frequencies into the plurality of excitation frequency subsets.

3. The computer-implemented method of claim 1 further comprising:

calculating a solution to an eigenvalue problem; and

transforming a modal frequency response equation based on the eigenvalue problem solution.

4. The computer-implemented method of claim 3 further comprising:

calculating a plurality of invariant square dense matrices using the transformed equation; and

for each of the plurality of excitation frequency subsets, calculating a nonsingular square matrix.

5. The computer-implemented method of claim 4 further comprising:

for each of the plurality of excitation frequency subsets, factorizing the nonsingular square matrix.

6. The computer-implemented method of claim 5 wherein calculating the modal frequency responses further comprises, for each excitation frequency in a respective excitation frequency subset:

calculating a frequency response solution matrix based on the corresponding nonsingular square matrix; and

calculating the modal frequency response based on the frequency response solution matrix.

7. The computer-implemented method of claim 6 wherein calculating the modal frequency responses further comprises, for each excitation frequency in a respective excitation frequency subset:

performing forward and backward path analysis with the factorized nonsingular square matrix; and

calculating a plurality of matrix vector products.

8. The computer-implemented method of claim 1 wherein calculating the modal frequency responses further comprises, for each excitation frequency in a respective excitation frequency subset:

calculating a frequency response solution matrix; and

calculating the modal frequency response based on the frequency response solution matrix.

9. A computer device for simulating a real-world object, said computer device comprising:

a memory area; and

a processor coupled to said memory area, the processor configured to:

calculate modal frequency responses of a real-world object for excitation frequencies in a plurality of excitation frequency subsets, each of the plurality of excitation frequency subsets providing a plurality of frequencies; and

employ the calculated modal frequency responses in simulations of the real-world object by performing a simulation of the real-world object based at least in part on the calculated modal frequency responses, the simulation utilizing the calculated modal frequency responses as an accelerated means of calculation of modal frequency response in the plurality of frequencies.

10. The computer device of claim 9 wherein said processor is further configured to:

obtain a set of excitation frequencies; and

divide the obtained set of excitation frequencies into the plurality of excitation frequency subsets.

11. The computer device of claim 9 wherein the processor is further configured to:

calculate a solution to an eigenvalue problem; and

transform a modal frequency response equation based on the eigenvalue problem solution.

12. The computer device of claim 11 wherein the processor is further configured to:

calculate a plurality of invariant square dense matrices using the transformed equation; and

for each of the plurality of excitation frequency subsets, calculate a nonsingular square matrix.

13. The computer device of claim 12 wherein the processor is further configured to:

for each of the plurality of excitation frequency subsets, factorize the nonsingular square matrix.

14. The computer device of claim 13 wherein the processor is further configured, for each excitation frequency in a respective excitation frequency subset, to:

calculate a frequency response solution matrix based on the corresponding nonsingular square matrix; and

calculate the modal frequency response based on the frequency response solution matrix.

15. The computer device of claim 14 wherein the processor is further configured, for each excitation frequency in a respective excitation frequency subset, to:

perform forward and backward path analysis with the factorized nonsingular square matrix; and

calculate a plurality of matrix vector products.

16. The computer device of claim 9 wherein the processor is further configured, for each excitation frequency in a respective excitation frequency subset, to:

calculate a frequency response solution matrix; and

calculate the modal frequency based on the frequency response solution matrix.

17. A computer program product executed by a server in communication across a network with one or more clients and comprising:

a non-transitory computer readable medium, the computer readable medium comprising program instructions for simulating a real-world object, the program instructions, when executed by a processor, causes the processor to:

calculate modal frequency responses of the real-world object for excitation frequencies in a plurality of excitation frequency subsets, each of the plurality of excitation frequency subsets providing a plurality of frequencies; and

employ the calculated modal frequency responses in simulations of the real-world object by performing a simulation of the real-world object based at least in part on the calculated modal frequency responses, the simulation utilizing the calculated modal frequency responses as an accelerated means of calculation of modal frequency response in the plurality of frequencies.

18. The computer program product of claim 17 wherein, the program instructions, when executed by the processor, further cause the processor to:

obtain a set of excitation frequencies; and

divide the obtained set of excitation frequencies into the plurality of excitation frequency subsets.

19. The computer program product of claim 17 wherein, the program instructions, when executed by the processor, further cause the processor to:

calculate a solution to an eigenvalue problem; and

transform a modal frequency response equation based on the eigenvalue problem solution.

20. The computer program product of claim 19 wherein, the program instructions, when executed by the processor, further cause the processor to:

calculate a plurality of invariant square dense matrices using the transformed equation; and

for each of the plurality of excitation frequency subsets, calculate a nonsingular square matrix.