2,884 research outputs found
Accuracy, Scalability, and Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows
The unstructured, mixed-element, cell-centered, finite-volume flow solver USM3D is enhanced with new capabilities including parallelization, line generation for general unstructured grids, improved discretization scheme, and optimized iterative solver. The paper reports on the new developments to the flow solver and assesses the accuracy, scalability, and efficiency. The USM3D assessments are conducted using a baseline method and the recent hierarchical adaptive nonlinear iteration method framework. Two benchmark turbulent flows, namely, a subsonic separated flow around a three-dimensional hemisphere-cylinder configuration and a transonic flow around the ONERA M6 wing are considered
Boundary control of time-harmonic eddy current equations
Motivated by various applications, this article develops the notion of
boundary control for Maxwell's equations in the frequency domain. Surface curl
is shown to be the appropriate regularization in order for the optimal control
problem to be well-posed. Since, all underlying variables are assumed to be
complex valued, the standard results on differentiability do not directly
apply. Instead, we extend the notion of Wirtinger derivatives to complexified
Hilbert spaces. Optimality conditions are rigorously derived and higher order
boundary regularity of the adjoint variable is established. The state and
adjoint variables are discretized using higher order N\'ed\'elec finite
elements. The finite element space for controls is identified, as a space,
which preserves the structure of the control regularization. Convergence of the
fully discrete scheme is established. The theory is validated by numerical
experiments, in some cases, motivated by realistic applications.Comment: 25 pages, 6 figure
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