Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations

The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability restriction when using an explicit time discretization. In this paper, we propose several efficient semi-implicit schemes to remove this stiffness from the Immersed Boundary method for the two-dimensional Stokes flow. First, we obtain a novel unconditionally stable semi-implicit discretization for the immersed boundary problem. Using this unconditionally stable discretization as a building block, we derive several efficient semi-implicit schemes for the immersed boundary problem by applying the Small Scale Decomposition to this unconditionally stable discretization. Our stability analysis and extensive numerical experiments show that our semi-implicit schemes offer much better stability property than the explicit scheme. Unlike other implicit or semi-implicit schemes proposed in the literature, our semi-implicit schemes can be solved explicitly in the spectral space. Thus the computational cost of our semi-implicit schemes is comparable to that of an explicit scheme, but with a much better stability property.Comment: 40 pages with 8 figure

Sparse Time-Frequency decomposition for multiple signals with same frequencies

In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven time-frequency analysis by updating the instantaneous frequencies simultaneously. Moreover, based on the simultaneously sparsity approximation and fast Fourier transform, some efficient algorithms is developed. Since the information of multiple signals is used, this method is very robust to the perturbation of noise. And it is applicable to the general nonperiodic signals even with missing samples or outliers. Several synthetic and real signals are used to test this method. The performances of this method are very promising

On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data

In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time frequency decomposition is unique up to an error that is determined by the scale separation property of the signal. We further show that the unique decomposition can be obtained approximately by the sparse time frequency decomposition using nonlinear matching pursuit

Superconducting properties of Gd-Ba-Cu-O single grains processed from a new, Ba-rich precursor compound

Gd-Ba-Cu-O (GdBCO) single grains have been previously melt-processed successfully in air using a generic Mg-Nd-Ba-Cu-O (Mg-NdBCO) seed crystal. Previous research has revealed that the addition of a small amount of BaO2 to the precursor powders prior to melt processing can suppress the formation of Gd/Ba solid solution, and lead to a significant improvement in superconducting properties of the single grains. Research into the effects of a higher Ba content on single grain growth, however, has been limited by the relatively small grain size in the earlier studies. This has been addressed by developing Ba-rich precursor compounds Gd-163 and Gd-143, fabricated specifically to enable the presence of greater concentrations of Ba during the melt process. In this study, we propose a new processing route for the fabrication of high performance GdBCO single grain bulk superconductors in air by enriching the precursor powder with these new Ba rich compounds. The influence of the addition of the new compounds on the microstructures and superconducting properties of GdBCO single grains is reported