Novel Numerical Basis Sets for Electromagnetic Field Expansion in Arbitrary Inhomogeneous Objects.

Area of Science:

• Computational electromagnetics
• Numerical analysis

Background:

• Accurate modeling of electromagnetic fields within complex objects is crucial for applications like MRI.
• Existing methods can be computationally intensive for arbitrary geometries.

Purpose of the Study:

• To develop a computationally efficient method for constructing low-order subspace basis sets for electromagnetic field representation.
• To enable accurate modeling of electromagnetic fields generated by external sources interacting with inhomogeneous objects.

Main Methods:

• Singular value decomposition (SVD) of Green's functions integro-differential operators.
• Development of a novel numerical framework for computing characteristic modes.
• Validation against analytical solutions for a uniform spherical object.

Main Results:

• A stable, reduced-order model for electromagnetic field representation was derived.
• The method's accuracy and convergence properties were validated.
• Discretization of the Huygens's surface showed minimal impact on accuracy.

Conclusions:

• The proposed SVD-based method provides an accurate and efficient approach for electromagnetic field modeling.
• The framework is suitable for analyzing performance limits in magnetic resonance imaging.
• Accuracy is primarily dependent on electromagnetic solver resolution and approximation order.