Abstract
The Marching On-In-Time (MOT) unstructured Partial Element Equivalent Circuit (PEEC) method for time domain electromagnetic problems is presented. The method allows the transient analysis of electrically large electromagnetic devices consisting of conductive, dielectric, and magnetic media coupled with external lumped circuits. By re-formulating PEEC following the Coulombian interpretation of magnetization phenomena and by using electric and magnetic vector potentials, the proposed approach allows for a completely equivalent treatment of electric and magnetic media and inhomogeneous and anisotropic materials are accounted for as well. With respect to the recently proposed Marching On-In-Time PEEC approach, based on the standard (structured) discretization of PEEC, the method presented in this paper uses a different space and time MOT discretization, which allows for a reduction in the number of the unknowns. Analytical and industrial test cases consisting in electrically large devices are considered (e.g., the model of a Neutral Beam Injector adopted in thermonuclear fusion applications). Results obtained from the simulations show that the proposed method is accurate and yields good performances. Moreover, when rich harmonic content transient phenomena are considered, the unstructured MOT–PEEC method allows for a significant reduction of the memory and computation time when compared to techniques based on Inverse Discrete Fourier Transform applied to the frequency domain unstructured PEEC approach.
Highlights
Integral equation (IE) methods are suited for the study of electromagnetic (EM)devices in unbounded domains since they do not require the introduction of artificial absorbing boundary conditions for truncating the computational domain and they avoid the discretization of regions with the characteristic of vacuum [1,2,3]
Among all the different possibilities to develop Time Domain Integral Equation (TDIE) methods, the Marching On-In-Time (MOT) scheme [14] allows for naturally considering the effects of the time delay on the EM fields propagation and such scheme has been been widely adopted over the years [15]
In the context of the proposed MOT–Partial Element Equivalent Circuit (PEEC) method, in accordance with the analysis presented in [18], hat shape functions have been chosen since they provide a good trade-off between stability, accuracy, and numerical performances
Summary
Integral equation (IE) methods are suited for the study of electromagnetic (EM)devices in unbounded domains since they do not require the introduction of artificial absorbing boundary conditions for truncating the computational domain and they avoid the discretization of regions with the characteristic of vacuum [1,2,3]. IE methods such as the PEEC approach are widely used for time-harmonic EM problems and they are suited for transient analysis, usually performed by means of traditional time-stepping algorithms, e.g., forward and backward. In the context of transient analyses with electrically large devices, where time delay effects on the propagation of the EM fields need to be considered, traditional time-stepping algorithms cannot be used. Among all the different possibilities to develop Time Domain Integral Equation (TDIE) methods, the Marching On-In-Time (MOT) scheme [14] allows for naturally considering the effects of the time delay on the EM fields propagation and such scheme has been been widely adopted over the years [15]. Another PEEC based ad hoc approach for the study of a wire structure excited by a distant lightning channel has been proposed in [19]
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