Sehun Chun

We investigate the behavior and sensitivity of the frozen mode phenomenon in finite structures with anisotropic materials, including both magnetic materials and non-normal incidence. The studies are done by using a high-order accurate discontinuous Galerkin method for solving Maxwell's equations in the time domain. We confirm the existence of the phenomenon also in the time-domain and study carefully the impact of the finite crystal on the frozen mode. This sets the stage for a thorough stud

Abstract The covariant derivative is a generalization of differentiating vectors. The Euclidean derivative is a special case of the covariant derivative in Euclidean space. The covariant derivative gathers broad attention, particularly when computing vector derivatives on curved surfaces and volumes in various applications. Covariant derivatives have been computed using the metric tensor from the analytically known curved axes. However, deriving the global axis for the domain has been mathematic

We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode behavior. This is characterized by Van Hove singularities in the dispersion relation, e.g., stationary reflection points and degenerate band edge points. Hence, the optimization process modifies the dispersion relation by adjusting the geometries and material parameters. The resulting algorithm is found to be capable of recovering all known crystal con

Abstract Additional grid points are often introduced for the higher-order polynomial of a numerical solution with curvilinear elements. However, those points are likely to be located slightly outside the domain, even when the vertices of the curvilinear elements lie within the curved domain. This misallocation of grid points generates a mesh error, called geometric approximation error . This error is smaller than the discretization error but large enough to significantly degrade a long-time inte

In the numerical discretization of partial differential equations (PDEs) with moving frames on curved surfaces, the discretization error does not converge for a high p≥5. Moreover, the conservation error remains significant even in a refined mesh and does not converge as the polynomial order p increases. We postulate that the inaccurate location of the internal grid points of curved elements causes this problem; this is called the internal point error. This bottleneck of convergence persists eve

The proposed scheme, called the IOC-LP (input reduction and one block compression for low power test), compresses the test data of scan based SoCs to improve the compression ratio in the ATPG process. It does so by using the modified input reduction and novel techniques, a new scan flip-flop reordering for low power test, the newly proposed one block compression, and a novel reordering algorithm. Unlike previous approaches using the cyclic scan register architecture, the proposed scheme is able

It is widely believed that the pulmonary veins (PVs) of the atrium play the central role in the generation of atrial reentry leading to atrial fibrillation, but its mechanism has not been analytically explained. In order to improve the current clinical procedures for atrial reentry by understanding its mechanism, geometrical analysis is proposed on the conditions of conduction failure at the PVs and is validated by various computational modeling. To achieve this, a new analytic approach is propo

As another critical implementation of moving frames for partial differential equations, this paper proposes a novel numerical scheme by aligning one of three orthogonal unit vectors at each grid point along the direction of a wave propagation to construct an organized set of frames, called a connection. This connection characterizes the geometry of wave propagation depending on (1) the initial point, (2) type of wave, and (3) shape of the domain with conduction properties. The constructed connec