Adaptive Wavelet Solution to the Stokes Problem

This paper deals with the design and analysis of adaptive wavelet method for the Stokes problem. First, the limitation of Richardson iteration is explained and the multiplied matrix M0 in the paper of Bramble and Pasciak is proved to be the simplest possible in an appropiate sense. Similar to the divergence operator, an exact application of its dual is shown; Second, based on these above observations, an adaptive wavelet algorithm for the Stokes problem is designed. Error analysis and computational complexity are given; Finally, since our algorithm is mainly to deal with an elliptic and positive definite operator equation, the last section is devoted to the Galerkin solution of an elliptic and positive definite equation. It turns out that the upper bound for error estimation may be improved.

Sub-30 fs Yb-fiber laser source based on a hybrid cascaded nonlinear compression approach

Ultrafast lasers with high repetition rate,high energy,and ultrashort pulse duration have enabled numerous applications in science and technology.One efficient route to generate such pulses is postcompression of high-power Yb-doped lasers.Here,we report on the generation of 24.5 fs pulses with an output energy of 1.6μJ and a repetition rate of 500 kHz.The pulses are obtained by using a hybrid cascaded nonlinear compression of the pulses delivered by a Yb-based fiber chirped pulse amplification(CPA)system.In the first stage,the initial 390 fs laser pulses are compressed to 100.7 fs based on spectral broadening in three fused silica plates.In the second stage,the pulses have been shortened to sub-30 fs by means of nonlinear compression in a hollow-core fiber.Overall,we could achieve∼16 times temporal shortening with the proposed approach.The results show that our system can effectively generate few-cycle pulses at a relatively high repetition rate and high energy,which can benefit future possible applications.