Complex component modal synthesis (CMS) method and modal solutions
Examples described herein relate to apparatuses and methods for a computer simulation platform to solve a computer model, including splitting complex vectors generated for the computer model into real components and imaginary components by generating a first matrix corresponding to real components and a second matric corresponding to imaginary components, generating an appended matrix by appending the first matrix to the second matrix, generating a set of real, orthogonal vectors by running the appended matrix through a residual vector logic, and performing a real arithmetic-based computer simulation solution using the set of real, orthogonal vectors.
1. A method for a computer simulation platform to solve a computer model, the method comprising:
importing the computer model;
splitting, by a transformation circuit, complex vectors generated for the computer model into real components and imaginary components by generating a first matrix corresponding to real components and a second matrix corresponding to imaginary components, wherein the complex vectors are complex eigenvectors determined using a complex eigenvalue solution;
generating, by the transformation circuit, an appended matrix by appending the first matrix to the second matrix;
generating, by the transformation circuit, a set of real, orthogonal vectors by running the appended matrix through a residual vector logic;
performing, by a simulation circuit, a real arithmetic-based computer simulation solution using the set of real, orthogonal vectors as inputs to the real arithmetic-based computer simulation solution;
displaying, by an interface, results of the real arithmetic-based computer simulation.
2. The method of claim 1 , wherein the complex vectors comprise the real components and the imaginary components.
3. The method of claim 1 , wherein the first matrix and the second matrix are real matrices.
4. The method of claim 1 , wherein linear combination of the set of real, orthogonal vectors results in the complex vectors.
5. The method of claim 1 , further comprising verifying that the set of real, orthogonal vectors are capable of calculating the complex vectors.
6. The method of claim 5 , wherein verifying that the set of real, orthogonal vectors are capable of calculating the complex vectors comprises:
converting the computer model to modal coordinates using the set of real, orthogonal vectors; and
performing the complex eigenvalue solution.
7. The method of claim 1 , wherein the real arithmetic-based computer simulation solution comprises at least one of component modal synthesis (CMS) analysis, transient response analysis, structural analysis, or modal solutions.
8. A non-transitory computer-readable medium having computer-readable instructions, such that when executed, causes a processor of a computer simulation platform to solve a computer model by:
importing the computer model;
splitting complex vectors generated for the computer model into real components and imaginary components by generating a first matrix corresponding to real components and a second matrix corresponding to imaginary components, wherein the complex vectors are complex eigenvectors determined using a complex eigenvalue solution;
generating an appended matrix by appending the first matrix to the second matrix;
generating a set of real, orthogonal vectors by running the appended matrix through a residual vector logic;
performing a real arithmetic-based computer simulation solution using the set of real, orthogonal vectors as inputs to the real arithmetic-based computer simulation solution;
displaying results of the real arithmetic-based computer simulation.
9. The non-transitory computer-readable medium of claim 8 , wherein the complex vectors comprise the real components and the imaginary components.
10. The non-transitory computer-readable medium of claim 8 , wherein the first matrix and the second matrix are real matrices.
11. The non-transitory computer-readable medium of claim 8 , wherein linear combination of the set of real, orthogonal vectors results in the complex vectors.
12. The non-transitory computer-readable medium of claim 8 , wherein the processor is further configured to verify that the set of real, orthogonal vectors are capable of calculating the complex vectors.
13. The non-transitory computer-readable medium of claim 12 , wherein verifying that the set of real, orthogonal vectors are capable of calculating the complex vectors comprises:
converting the computer model to modal coordinates using the set of real, orthogonal vectors; and
performing the complex eigenvalue solution.
14. The non-transitory computer-readable medium of claim 8 , wherein the real arithmetic-based computer simulation solution comprises at least one of component modal synthesis (CMS) analysis, transient response analysis, structural analysis, or modal solutions.
15. A computer simulation platform configured to solve a computer model, the computer simulation platform comprises:
an interface;
a memory; and
a processor configured to:
importing the computer model;
split complex vectors generated for the computer model into real components and imaginary components by generating a first matrix corresponding to real components and a second matrix corresponding to imaginary components, wherein the complex vectors are complex eigenvectors determined using a complex eigenvalue solution;
generate an appended matrix by appending the first matrix to the second matrix;
generate a set of real, orthogonal vectors by running the appended matrix through a residual vector logic;
perform real arithmetic-based computer simulation solution using the set of real, orthogonal vectors as inputs to the real arithmetic-based computer simulation solution;
display results of the real arithmetic-based computer simulation.