19,340 research outputs found
Domain decomposition preconditioners for the spectral collocation method
Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism
A combined first and second order variational approach for image reconstruction
In this paper we study a variational problem in the space of functions of
bounded Hessian. Our model constitutes a straightforward higher-order extension
of the well known ROF functional (total variation minimisation) to which we add
a non-smooth second order regulariser. It combines convex functions of the
total variation and the total variation of the first derivatives. In what
follows, we prove existence and uniqueness of minimisers of the combined model
and present the numerical solution of the corresponding discretised problem by
employing the split Bregman method. The paper is furnished with applications of
our model to image denoising, deblurring as well as image inpainting. The
obtained numerical results are compared with results obtained from total
generalised variation (TGV), infimal convolution and Euler's elastica, three
other state of the art higher-order models. The numerical discussion confirms
that the proposed higher-order model competes with models of its kind in
avoiding the creation of undesirable artifacts and blocky-like structures in
the reconstructed images -- a known disadvantage of the ROF model -- while
being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure
An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method
In this paper we propose a collocation method for solving some well-known
classes of Lane-Emden type equations which are nonlinear ordinary differential
equations on the semi-infinite domain. They are categorized as singular initial
value problems. The proposed approach is based on a Hermite function
collocation (HFC) method. To illustrate the reliability of the method, some
special cases of the equations are solved as test examples. The new method
reduces the solution of a problem to the solution of a system of algebraic
equations. Hermite functions have prefect properties that make them useful to
achieve this goal. We compare the present work with some well-known results and
show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications
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