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Time domain finite element solutions of Maxwell's equations require the solution of a sparse linear system involving the mass matrix at every time step. This process represents the bulk of the computational effort in time dependent simulations. As such, mass lumping techniques in which the mass matrix is reduced to a diagonal or block-diagonal matrix are very desirable. In this paper, we present a special set of high order 1-form (also known as curl-conforming) basis functions and reduced order integration rules that together, allow for a dramatic reduction in the number of non-zero entries in a vector finite element mass matrix. The method is derived from the Nedelec curl-conforming polynomial spaces and is valid for arbitrary order hexahedral basis functions for finite element solutions to the second order wave equation for the electric (or magnetic) field intensity. We present a numerical eigenvalue convergence analysis of the method and quantify its accuracy and performance via a series of computational experiments.

Capsule implosions on the National Ignition Facility (NIF) [Lindl et al., Phys. Plasmas 11, 339 (2004)] are underway with the goal of compressing deuterium-tritium (DT) fuel to a sufficiently high areal density (ρR) to sustain a self-propagating burn wave required for fusion power gain greater than unity. These implosions are driven with a carefully tailored sequence of four shock waves that must be timed to very high precision in order to keep the DT fuel on a low adiabat. Initial experiments to measure the strength and relative timing of these shocks have been conducted on NIF in a specially designed surrogate target platform known as the keyhole target. This target geometry and the associated diagnostics are described in detail. The initial data are presented and compared with numerical simulations. As the primary goal of these experiments is to assess and minimize the adiabat in related DT implosions, a methodology is described for quantifying the adiabat from the shock velocity measurements. Results are contrasted between early experiments that exhibited very poor shock timing and subsequent experiments where a modified target geometry demonstrated significant improvement.

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