Abstract.We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we have designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve .
The process of tuning an inertial confinement fusion pulse shape to a specific target design is highly iterative process. When done manually, each iteration has large latency and is consequently time consuming. We have developed several techniques that can be used to automate much of the pulse tuning process and significantly accelerate the tuning process by removing the human induced latency. The automated data analysis techniques require specialized diagnostics to run within the simulation. To facilitate these techniques, we have embedded a loosely coupled Python interpreter within a pre-existing radiation-hydrodynamics code, Hydra. To automate the tuning process we use numerical optimization techniques and construct objective functions to identify tuned parameters.
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