The frequency-domain finite-element method (FEM) results in matrix equations that have polynomial dependence on the frequency of excitation. For a wide-band fast frequency sweep technique based on a moment-matching model order reduction (MORe) process, researchers generally take one of two approaches. The first is to linearize the polynomial dependence (which will either limit the bandwidth of accuracy or require the introduction of extra degrees of freedom) and then use a well-conditioned Krylov subspace technique. The second approach is to work directly with the polynomial matrix equation and use one of the available, but ill-conditioned, asymptotic waveform evaluation (AWE) methods. For large-scale FEM simulations, introducing extra degrees of freedom, and therefore increasing the length of the MORe vectors and the amount of memory required, is not desirable; therefore, the first approach is not alluring. On the other hand, an ill-conditioned AWE process is unattractive. This paper presents a novel MORe technique for polynomial matrix equations that circumvents these problematic issues. First, this novel process does not require any additional unknowns. Second, this process is well-conditioned. Along with the presentation of the novel algorithm, which will be called well-conditioned AWE (WCAWE), numerical examples modeled using the FEM are given to illustrate its accuracy.Index Terms-Asymptotic waveform evaluation, computeraided engineering, fast frequency sweep, finite-element methods, model order reduction.
The finite-difference time-domain (FDTD) method is used to model a birdcage resonator. All the coil components, including the wires, lumped capacitors and the source, are geometrically modelled together. As such, the coupling effects within the birdcage, including the interactions of coil, source and human head, are accurately computed. A study of the transverse magnetic (B1) field homogeneity and the specific absorption rate (SAR) is presented on an anatomically detailed human head model at 64 and 200 MHz representing 1.5 and 4.7 T MRI systems respectively. Unlike that at 64 MHz, the B1 field distribution is found to be inhomogeneous at 200 MHz. Also, high local SAR values are observed in the tissue near the source due to the coupling between the source and the head at 200 MHz.
The phase error in finite-difference (FD) methods is related to the spatial resolution and thus limits the maximum grid size for a desired accuracy. Greater accuracy is typically achieved by defining finer resolutions or implementing higher order methods. Both these techniques require more memory and longer computation times. In this paper, new modified methods are presented which are optimized to problems of electromagnetics. Simple methods are presented that reduce numerical phase error without additional processing time or memory requirements. Furthermore, these methods are applied to both the Helmholtz equation in the frequency domain and the finite-difference timedomain (FDTD) method. Both analytical and numerical results are presented to demonstrate the accuracy of these new methods.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.