As a first application of the new adaptive mesh functionality pseudospectral numerical relativity code bamps, we evolve twist-free, axisymmetric gravitational waves close to threshold collapse. We consider six different one-parameter families Brill wave initial data; two centered and four off-centered families. Of these latter have not been treated before. Within each family, tune parameter tow...

In adirect collocation pseudospectralmethod, a continuous-time optimal control problem is transcribed to afinitedimensional nonlinear programming problem. Solving this nonlinear programming problem as efficiently as possible requires that sparsity at both the firstand second-derivative levels be exploited. In this paper, a computationally efficient method is developed for computing the first an...

This paper addresses the problem of determining a minimum-fuel maneuver sequence to reconfigure a tetrahedral formation. The objective of this work is to develop a single orbit, minimum-fuel reconfiguration strategy such that, after reconfiguration, the four spacecraft are able to return to an acceptable tetrahe-dral configuration in a region of interest near apogee for a period of three weeks ...

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the appli...

A comparison is made between three pseudospectral methods used to numerically solve optimal control problems. In particular, the accuracy of the state, control, and costate obtained using the Legendre, Radau, and Gauss pseudospectral methods is compared. Three examples with different degrees of complexity are used to identify key differences between the three methods. The results of this study ...

Polynomial approximations of computationally intensive models are central to uncertainty quantification. This paper describes an adaptive method for nonintrusive pseudospectral approximation, based on Smolyak’s algorithm with generalized sparse grids. We rigorously analyze and extend the nonadaptive method proposed in [P. G. Constantine, M. S. Eldred, and E. T. Phipps, Comput. Methods Appl. Mec...