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Advanced Methods for Computational Electromagnetics

Research Project
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01.10.2010
 - 30.09.2012

1. Our project aims at the development of new computational methods for the simulation of electromagnetic phenomena. Both theoretical and computational aspects are investigated. We pursue the development of flexible and efficient numerical methods for acoustic or electromagnetic wave propagation, which combine modern developments in numerical analysis, such as discontinuous Galerkin finite element methods, local time stepping, and high-order local nonreflecting boundary conditions. 2. The accurate and reliable simulation of electromagnetic fields is of fundamental importance in a wide range of engineering applications such as fiber optics, wireless communication, radar technology, inverse scattering, non-invasive testing, and optical microscopy. Furthermore, the methods developed here can directly be applied to (the much simpler) acoustic wave phenomena, pervasive in medical applications, such as ultra-sound imaging and microscopy. 3. Computational electromagnetics (CEM) presents a number of challenges. First, electromagnetic fields tend to be highly oscillatory and wave-dominated; moreover, they can develop singularities at material interfaces and boundaries. Second, the phenomena of interest typically involve complicated geometries, multi-physics, inhomogeneous media, and even nonlinear materials. Third, the underlying partial differential equations often need to be solved in an unbounded domain, which needs to be truncated by an artificial boundary to confine the region of interest to a finite computational domain. To fully address this wide range of difficulties, great flexibility is needed from any computational approach. In continuation of our previous work, we shall pursue the development of novel discontinuous Galerkin (DG) techniques to achieve the required flexibility. These discretization techniques greatly facilitate the handling of material interfaces and non-matching grids; they also permit the coupling of different elements of arbitrary shapes and local spaces of different types. In particular, starting from our new symmetric, interior penalty DG finite element discretization we wish to develop the first explicit, energy conserving, local time-stepping DG-method for time dependent electromagnetic wave propagation. To handle problems in unbounded domains, we shall use either standard Perfectly Matched Layers or our new local high-order Nonreflecting Boundary Condition (NBC). In particular, we shall derive the first completely local NBC for time dependent multiple scattering problems.

Publications

Grote, Marcus J. and Sim, Imbo (2011) ‘Local nonreflecting boundary condition for time-dependent multiple scattering’, Journal of Computational Physics, 230(8), pp. 3135–3154. Available at: https://doi.org/10.1016/j.jcp.2011.01.017.

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Members (3)

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Marcus J. Grote

Principal Investigator
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Michaela Mehlin

Project Member
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Teodora Mitkova

Project Member