Eigen augmentation methods for electromagnetic modelling and simulation

1. A method for electromagnetic (EM) modelling and simulation of an EM structure, the EM structure being an electronic equipment that is to emit EM radiation, to ensure electromagnetic compatibility and to reduce electromagnetic interference of the EM structure, the method comprising:

obtaining Eigen vectors of a first EM structure from solution of Maxwell's equations for the first EM structure, wherein Maxwell's equations for the first EM structure are solved during EM modelling and simulation of the first EM structure;

when a mesh structure of the first EM structure is different from that of a second EM structure, interpolating the Eigen vectors of the first EM structure to a second EM structure, wherein the second EM structure is a design variant of the first EM structure;

augmenting Krylov subspace of a second EM structure with Eigen vectors of the first EM structure to form an augmented space;

performing EM modelling and simulation of the second EM structure;

solving Maxwell's equations for the second EM structure using the augmented space to perform the EM modelling and simulation of the second EM structure; and

determining, based on the solving, whether the EM radiation of the second EM structure is within a threshold EM radiation limit to ascertain electromagnetic compatibility of the second EM structure.

2. The method as claimed in claim 1 , wherein interpolating the Eigen vectors of the first EM structure to the second EM structure comprises:

interpolating Krylov vectors of the first EM structure to the second EM structure; and

generating interpolated Eigen vectors based on interpolated Krylov vectors.

3. The method as claimed in claim 2 , wherein interpolating the Krylov vectors comprises:

mapping each edge centre in the mesh structure of the second EM structure to a corresponding mesh component in the mesh structure of the first EM structure; and

applying a set of linear transformations to generate the interpolated Krylov vectors.

4. The method as claimed in claim 1 , wherein the second EM structure has a larger or smaller dimension than the first EM structure.

5. The method as claimed in claim 1 , wherein the Maxwell's equations for the second EM structure are solved using a Generalized Minimal Residual (GMRES) process in the augmented space.

6. The method as claimed in claim 1 , comprising selecting Eigen vectors that are to be augmented in the Krylov subspace based on Eigen values corresponding to the Eigen vectors.

7. The method as claimed in claim 6 , wherein each of the Eigen values has one of a small, medium, and large magnitude, and wherein selecting the Eigen vectors comprises selecting Eigen vectors whose corresponding Eigen values have one of small and medium magnitudes.

8. A method for electromagnetic (EM) modelling and simulation of an EM structure, the EM structure being an electronic equipment that is to emit EM radiation, to ensure electromagnetic compatibility and to reduce electromagnetic interference, the method comprising:

obtaining Eigen vectors of a first EM structure from solution of Maxwell's equations for the first EM structure, wherein Maxwell's equations for the first EM structure are solved during EM modelling and simulation of the first EM structure;

interpolating Krylov vectors of the first EM structure to a second EM structure, wherein the second EM structure is a design variant of the first EM structure and the first EM structure is already EM modelled and simulated and wherein mesh structure of the first EM structure is different from that of the second EM structure;

augmenting Krylov subspace of the second EM structure with the interpolated Krylov vectors to form an augmented Krylov subspace;

interpolating Eigen vectors of the first EM structure to the second EM structure;

augmenting the augmented Krylov subspace of the second EM structure with interpolated Eigen vectors of the first EM structure to form an augmented space;

performing EM modelling and simulation of the second EM structure;

solving Maxwell's equations for the second EM structure using the augmented space to perform the EM modelling and simulation of the second EM structure; and

determining, based on the solving, whether the EM radiation of the second EM structure is within a threshold EM radiation limit to ascertain electromagnetic compatibility of the second EM structure.

9. The method as claimed in claim 8 , comprising generating the interpolated Eigen vectors based on the interpolated Krylov vectors.

10. A system for performing electromagnetic (EM) modelling and simulation of an EM structure, the EM structure being an electronic equipment that is to emit electromagnetic radiation, to ensure electromagnetic compatibility and to reduce electromagnetic interference, the system comprising:

a processor;

an EM modelling module coupled to the processor to:

obtain Eigen vectors of a first EM structure from solution of Maxwell's equations for the first EM structure, wherein Maxwell's equations for the first EM structure are solved during EM modelling and simulation of the first EM structure;

when a mesh structure of the first EM structure is different from that of the second EM structure, interpolate Eigen vectors of the first EM structure to a second EM structure, wherein the second EM structure is a design variant of the first EM structure;

augment Krylov subspace of the second EM structure with the Eigen vectors of the first EM structure to form an augmented subspace;

augment the augmented Krylov subspace of the second EM structure with interpolated Eigen vectors of the first EM structure to form an augmented space;

performing EM modelling and simulation of the second EM structure;

solve Maxwell's equations for the second EM structure using the augmented space to perform the EM modelling and simulation of the second EM structure; and

determine, based on the solving, whether the EM radiation of the second EM structure is within a threshold EM radiation limit to ascertain electromagnetic compatibility of the second EM structure.

11. The system as claimed in claim 10 , wherein to interpolate the Krylov vectors, the EM modelling module is to:

map each edge centre in the mesh structure of the second EM structure to a corresponding mesh component in the mesh structure of the first EM structure; and

apply a set of linear transformations to generate the interpolated Krylov vectors.

12. The system as claimed in claim 10 , wherein the EM modelling module is to generate the interpolated Eigen vectors based on the interpolated Krylov vectors.

13. The system as claimed in claim 10 , wherein the EM modelling module is to select Eigen vectors that are to be interpolated based on Eigen values corresponding to the Eigen vectors.

14. The system as claimed in claim 10 , wherein, to interpolate the Eigen vectors of the first EM structure to the second EM structure, the EM modelling module is to:

interpolate Krylov vectors of the first EM structure to the second EM structure; and

generate interpolated Eigen vectors based on the interpolated Krylov vectors.