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We discuss analytically and numerically the propagation and energy transmission of electromagnetic waves caused by the coupling of surface plasmon polaritons (SPPs) between two spatially separated layers of 2D materials, such as graphene, at subwavelength distances. We construct an adaptive finite-element method to compute the ratio of energy transmitted within these waveguide structures reliably and efficiently. At its heart, the method is built upon a goal-oriented a posteriori error estimation with the dual-weighted residual method (DWR). Furthermore, we derive analytic solutions of the two-layer system, compare those to (known) single-layer configurations, and compare and validate our numerical findings by comparing numerical and analytical values for optimal spacing of the two-layer configuration. Additional aspects of our numerical treatment, such as local grid refinement, and the utilization of perfectly matched layers (PMLs) are examined in detail. [ABSTRACT FROM AUTHOR]

This paper provides an overview of the new features of the finite element library deal.II version 9.0. [ABSTRACT FROM AUTHOR]

This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators that are derived in the general context of the dual weighted residual (DWR) method. Based on the optimization approach a postprocessing strategy is formulated that lifts the requirement of strict a priori knowledge about applicability and quality of effective models. This allows for the systematic, \goal-oriented" tuning of effective models with respect to a quantity of interest. The framework is tested numerically on elliptic difusion problems with different types of heterogeneous, random coefficients, as well as an advection-difusion problem with a strong microscopic, random advection field. [ABSTRACT FROM AUTHOR]

This paper provides an overview of the new features of the finite element library deal.II version 8.5. [ABSTRACT FROM AUTHOR]

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon–polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed. [ABSTRACT FROM AUTHOR]

This paper introduces an framework for adaptivity for a class of heterogeneous multiscale finite element methods for elliptic problems, which is suitable for a posteriori error estimation with separated quantification of the model error as well as the macroscopic and microscopic discretization errors. The method is derived within a general framework for 'goal-oriented' adaptivity, the so-called Dual Weighted Residual (DWR) method. This allows for a systematic a posteriori balancing of multiscale modeling and discretization. The developed method is tested numerically at elliptic diffusion problems for different types of heterogeneous oscillatory coefficients. [ABSTRACT FROM AUTHOR]

The accuracy of magnetostatic finite element simulations depends largely on the quality of the magnetization curves used to model ferromagnetic materials. Established measuring approaches either suffer from a time-consuming preparation of samples or a reduced accuracy in measuring the sample’s field strength. Therefore, a simulation-based approach was developed that replaces the problematic field strength measurement with a finite element simulation while maintaining a convenient sample geometry. The proposed method’s requirements and feasibility were discussed using a simple magnetic circuit. The method’s accuracy in determining a correct magnetization curve was shown on a closed simulation model using a known magnetization curve as reference. Influences of measurement and simulation errors were determined and compared with the typical simulation accuracies. [ABSTRACT FROM AUTHOR]

We present a fully discrete approximation technique for the compressible Navier–Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time step is the standard hyperbolic CFL condition, i.e. τ ≲ O (h) ∕ V where V is some reference velocity scale and h the typical meshsize. • We present a fully discrete approximation technique for the compressible Navier–Stokes equations. • The method is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. • The restriction on the time step is the standard hyperbolic CFL condition, i.e. τ ≲ O (h) ∕ V where V is some reference velocity scale and h the typical meshsize. [ABSTRACT FROM AUTHOR]

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier–Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is second-order accurate in time and space. Robustness here means that the method is proved to be invariant domain preserving under the hyperbolic CFL time step restriction, and the method delivers results that are reproducible. The proposed technique is shown to be accurate on challenging 2D and 3D realistic benchmarks. • Second-order accurate Finite element solver for the compressible Navier-Stokes equations. • Provable invariant-domain preservation under the hyperbolic CFL time step restriction. • Detailed treatment of robust, invariant-domain preserving boundary conditions. • Demonstrated accuracy and scalability of the method on parallel computer architectures. • Source code and test vectors have been made available to allow comparison of methods. [ABSTRACT FROM AUTHOR]