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The paper is concerned with well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles with local perturbations. The classical Rayleigh Expansion radiation condition does not always lead to well-posedness of the Helmholtz equation even in unperturbed periodic structures. We propose two equivalent radiation conditions to characterize the radiating behavior of time-harmonic wave fields incited by a source term in an open waveguide under impenetrable boundary conditions. With these open waveguide radiation conditions, uniqueness and existence of time-harmonic scattering by incoming point source waves, plane waves and surface waves from locally perturbed periodic structures are established under either the Dirichlet or Neumann boundary condition. A Dirichlet-to-Neumann operator without using the Green's function is constructed for proving well-posedness of perturbed scattering problems.

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For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation conditions. For scattering problems in a layered medium, standard BIE methods based on the Green's function of the background medium must evaluate the expensive Sommefeld integrals. Alternative BIE methods based on the free-space Green's function give rise to integral equations on unbounded interfaces which are not easy to truncate, since the wave fields on these interfaces decay very slowly. We develop a BIE method based on the perfectly matched layer (PML) technique. The PMLs are widely used to suppress outgoing waves in numerical methods that directly discretize the physical space. Our PML-based BIE method uses the Green's function of the PML-transformed free space to define the boundary integral operators. The method is efficient, since the Green's function of the PML-transformed free space is easy to evaluate and the PMLs are very effective in truncating the unbounded interfaces. Numerical examples are presented to validate our method and demonstrate its accuracy.

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Large open spaces are popular nowadays in office buildings. However, occupants often complain too cold and/or too warm in large open spaces. It remains a challenge to control the operation of airconditioning systems to provide occupant comfort in a large open space due to the ununiform distribution of internal heat gains and occupancy. Previous studies using CFD tools or building energy modelling tools alone did not solve the combined problem of the distributive temperature field in the space and the cooling demand from multiple terminal units. This study proposed to divide the large space into multiple subzone areas based on the layout of the terminal cooling equipment and the distribution of internal heat gains and occupancy. Then a coupling of FLUENT simulation with EnergyPlus building energy simulation is used to compute the optimal thermostat setpoint for each subzone to ensure uniform occupant comfort in the large space. EnergyPlus computes the interior wall surface temperatures and terminal unit supply air flowrate of each subzone, which are passed to the CFD simulations as boundary conditions; while FLUENT computes the temperature and PMV field, as well as airflow rates across the virtual partition walls between two adjacent subzones, which are passed to EnergyPlus for consideration as inter-zone air flow. A case study using an open office space in Hong Kong is conducted to demonstrate the validity of the methodology. Different temperature setpoints were computed for the subzones that achieved uniform occupant thermal comfort while reducing energy use due to avoiding overcooling of the occupied surrounding. The results indicated that the coupling method can effectively provide a thermally comfortable environment with less energy use in large open office served by multiple terminal units.

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