In this paper, we propose a composite Laguerre-Legendre pseudospectral method for exterior problems with a square obstacle. Some results on the composite Laguerre-Legendre interpolation, which is a set of piecewise mixed interpolations coupled with domain decomposition, are established. As examples of applications, the composite pseudospectral schemes are provided for two model problems. The co...

Numerical solutions are presented for steady two-dimensional motion within a circular cylinder generated by uid injecting radially over one small arc and ejecting radially over another arc. These solutions are based on a mixed nite-diierence pseudospectral method. Previous calculations were able to obtain convergent results only for a range of Reynolds numbers from R = 0 to R = 20. The main obj...

Systems of m PDEs of Adv-Diff-React type have the following form, where the dependent variables (unknowns) are u = (u j (x, t)) m j=1 : Systems of m PDEs of Adv-Diff-React type have the following form, where the dependent variables (unknowns) are u = (u j (x, t)) m j=1 : ∂ ∂t u j + ∇ · (a j u j) = ∇ · (D j ∇u j) + f j , These PDEs model a lot of important phenomena, see These PDEs model a lot o...

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...

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...

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...