Computational electrodynamics (CED), the numerical solution of Maxwell's equations, plays an incredibly important role in several problems in science and engineering. High accuracy solutions are desired, and the discontinuous Galekin (DG) method is one of the better ways of delivering high accuracy in numerical CED. Maxwell's equations have a pair of involution constraints for which mimetic schemes that globally satisfy the constraints at a discrete level are highly desirable. Balsara and Käppeli (2018) presented a von Neumann stability analysis of globally constraint-preserving DG schemes for CED up to fourth order. That paper was focused on developing the theory and documenting the superior dissipation and dispersion of DGTD schemes in media with constant permittivity and permeability. In this paper we present working DGTD schemes for CED that go up to fifth order of accuracy and analyze their performance when permittivity and permeability vary strongly in space.Our DGTD schemes achieve constraint preservation by collocating the electric displacement and magnetic induction as well as their higher order modes in the faces of the mesh. Our first finding is that at fourth and higher orders of accuracy, one has to evolve some zone-centered modes in addition to the face-centered modes. It is well-known that the limiting step in DG schemes causes a reduction of the optimal accuracy of the scheme; though the schemes still retain their formal order of accuracy with WENO-type limiters. In this paper we document simulations where permittivity and permeability vary by almost an order of magnitude without requiring any limiting of the DG scheme. This very favorable second finding ensures that DGTD schemes retain optimal accuracy even in the presence of large spatial variations in permittivity and permeability. We also study the conservation of electromagnetic energy in these problems. Our third finding shows that the electromagnetic energy is conserved very well even when permittivity and permeability vary strongly in space; as long as the conductivity is zero.
Deep Neural Network (DNN)-based methods are suitable for the rapid inversion of borehole resistivity measurements. They approximate the forward and the inverse problem offline during the training phase and they only require a fraction of a second for the online evaluation (aka prediction). Herein, we propose a DNN-based iterative algorithm to design a borehole instrument such that the inverse solution is unique for a given earth parametrization. We select a large set of electromagnetic measurement systems routinely employed in logging operations, and our proposed DNN algorithm selects a subset of measurements that are suitable for inversion purposes. Numerical results with synthetic data confirm that this approach can provide valuable insight when designing borehole logging instruments.
Magnetic Resonance Imaging (MRI) is a widely applied non-invasive imaging modality based on non-ionizing radiation which gives excellent images and soft tissue contrast of living tissues. We consider the modified Bloch problem as a model of MRI for flowing spins in an incompressible flow field. After establishing the well-posedness of the corresponding evolution problem, we analyze its spatial semi-discretization using discontinuous Galerkin methods. The high frequency time evolution requires a proper explicit and adaptive temporal discretization. The applicability of the approach is shown for basic examples.
Mean and standard deviation velocities and Re based on the mean velocity for diferent operating voltages of the Ćow pump at temperature 16 • C (kinematic viscosity ν = 1.1092 × 10 −2 cm 2 /s [137]). . . . . . . . . and magnetic gradient Ąelds. Altering this pattern, which is commonly known as a MRI pulse sequence, it is possible to exploit a wide range of contrast mechanisms including access to physiological functions such as difusion, Ćow, blood oxygenation, cellular metabolism and tissue temperature. Therefore, MRI is not restricted to a qualitative description of anatomy, but also serves as a powerful tool for interventional, functional, metabolic and quantitative studies, which have a huge signiĄcance in diagnostic imaging.
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