57,527 research outputs found
Multidomain Spectral Method for the Helically Reduced Wave Equation
We consider the 2+1 and 3+1 scalar wave equations reduced via a helical
Killing field, respectively referred to as the 2-dimensional and 3-dimensional
helically reduced wave equation (HRWE). The HRWE serves as the fundamental
model for the mixed-type PDE arising in the periodic standing wave (PSW)
approximation to binary inspiral. We present a method for solving the equation
based on domain decomposition and spectral approximation. Beyond describing
such a numerical method for solving strictly linear HRWE, we also present
results for a nonlinear scalar model of binary inspiral. The PSW approximation
has already been theoretically and numerically studied in the context of the
post-Minkowskian gravitational field, with numerical simulations carried out
via the "eigenspectral method." Despite its name, the eigenspectral technique
does feature a finite-difference component, and is lower-order accurate. We
intend to apply the numerical method described here to the theoretically
well-developed post-Minkowski PSW formalism with the twin goals of spectral
accuracy and the coordinate flexibility afforded by global spectral
interpolation.Comment: 57 pages, 11 figures, uses elsart.cls. Final version includes
revisions based on referee reports and has two extra figure
An introduction to the adjoint approach to design
Optimal design methods involving the solution of an adjoint system of equations are an active area of research in computational fluid dynamics, particularly for aeronautical applications. This paper presents an introduction to the subject, emphasising the simplicity of the ideas when viewed in the context of linear algebra. Detailed discussions also include the extension to p.d.e.'s, the construction of the adjoint p.d.e. and its boundary conditions, and the physical significance of the adjoint solution. The paper concludes with examples of the use of adjoint methods for optimising the design of business jets.\ud
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This research was supported by funding from Rolls-Royce plc, BAe Systems plc and EPSRC grants GR/K91149 and GR/L95700
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