The ultraconvergence property of a derivative recovery technique recently proposed by Zienkiewicz and Zhu is analyzed for two-point boundary value problems. Under certain regularity assumptions on the exact solution, it is shown that the convergence rate of the recovered derivative at an internal nodal point is two orders higher than the optimal global convergence rate when even-order finite el...

We present a computationally efficient and accurate adjoint method for calculating coupled sensitivities of complex frequency-domain excitation and emission fluence to any underlying optical parameters in highly scattering media. The method is shown to be general and accurate. Novel vectorized implementations for finite element global matrix assembly and adjoint sensitivity calculations are sho...

We derive new a-priori and a-posteriori error estimates for mixed nite element discretizations of second-order elliptic problems with general Robin boundary conditions, parameterized by a non-negative and piecewise constant function ε ≥ 0. The estimates are robust over several orders of magnitude of ε, ranging from pure Dirichlet conditions to pure Neumann conditions. A series of numerical expe...

A highly parallelizable domain decomposition solution technique for adaptive hp finite element methods is developed. The technique uses good partitioning strategies and a subspace decomposition based preconditioned iterative solver, Two level orthogonalization is used to obtain a reduced system which is preconditioned by a coarse grid operator. Numerical results show fast cOIl\'ergence for the ...

D. Schurig North Carolina State University, Department of ECE, Campus Box 7911, Raleigh, NC, 27695 Abstract: Starting from the Luneberg lens index profile, we apply the transformation design method to the problem of far-field imaging of (infinitely) distant objects. This analysis yields a single element lens with a planar image surface, zero aberrations of all orders, zero F-number and (in some...

Superconvergence phenomenon of the Legendre spectral collocation method and the p-version finite element method is discussed under the one dimensional setting. For a class of functions that satisfy a regularity condition (M): ‖u‖L∞ ≤ cMk on a bounded domain, it is demonstrated, both theoretically and numerically, that the optimal convergent rate is supergeometric. Furthermore, at proper Gaussia...

The leading coefficient of the Alexander polynomial of a knot is the most informative element in this invariant, and the growth of orders of the first homology of cyclic branched covering spaces is also a familiar subject. Accordingly, there are a lot of investigations into each subject. However, there is no study which deal with the both subjects in a same context. In this paper, we show that ...