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This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work [D. Green et al., Comput. Phys. Commun., 9 (2022), 108333]. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods. [ABSTRACT FROM AUTHOR]

Large-scale full-wave simulations are performed to investigate radar wave propagation inside buildings. In principle, a radar system combined with sophisticated numerical methods for inverse problems can be used to determine the internal structure of a building. The composition of the walls (cinder block, rebar) may effect the propagation of the radar waves in a complicated manner. In order to provide a benchmark solution of radar propagation in buildings, including the effects of cinder block and rebar, we performed large-scale full-wave simulations using a finite-element time domain (FETD) method. This particular FETD implementation is tuned for the special case of an orthogonal Cartesian mesh and hence resembles finite-difference time domain (FDTD) in accuracy and efficiency. The method was implemented on a general-purpose massively parallel computer. In this paper we briefly describe the radar propagation problem, the FETD implementation, and we present results of simulations that used over 10-billion elements. Index Terms--Electromagnetic propagation in nonhomogenous media, electromagnetic scattering, finite element methods, parallel processing, time domain analysis, ultrawideband radar.

We are concerned with the solution of time-dependent electromagnetic eddy-current problems using a finite-element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. To meet this requirement, we propose a volume-to-surface boundary condition based on the Biot-Savart law. We found the Biot-Savart approach to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot--Savart law. Index Terms--Biot-Savart law, computational electromagnetics, eddy currents, electromagnetic diffusion, low-rank approximation, Maxwell's equations, parallel processing.