CONVERGENCE ANALYSIS FOR THE ITERATED DEFECT CORRECTION SCHEME OF FINITE ELEMENT METHODS ON RECTANGLE GRIDS

This paper develops a new method to analyze convergence of the iterated defect correction scheme of finite element methods on rectangular grids in both two and three dimensions. The main idea is to formulate energy inner products and energy （semi）norms into matrix forms. Then, two constants of two key inequalities involved are min and max eigenvalues of two associated generalized eigenvalue problems, respectively. Local versions on the element level of these two generalized eigenvalue problems are exactly solved to obtain sharp （lower） upper bounds of these two constants. This and some essential observations for iterated solutions establish convergence in 2D and the monotone decreasing property in 3D. For two dimensions the results herein improve those in literature; for three dimensions the results herein are new. Numerical results are presented to examine theoretical results.

Simulation of the 3D viscoelastic free surface flow by a parallel corrected particle scheme

In this work, the behavior of the three-dimensional （3D） jet coiling based on the viscoelastic Oldroyd-B model is investigated by a corrected particle scheme, which is named the smoothed particle hydrodynamics with corrected symmetric kernel gradient and shifting particle technique （SPH_CS_SP） method. The accuracy and stability of SPH_CS_SP method is first tested by solving Poiseuille flow and Taylor-Green flow. Then the capacity for the SPH_CS_SP method to solve the viscoelastic fluid is verified by the polymer flow through a periodic array of cylinders. Moreover, the convergence of the SPH CS_SP method is also investigated. Finally, the proposed method is further applied to the 3D viscoelastic jet coiling problem, and the influences of macroscopic parameters on the jet coiling are discussed. The numerical results show that the SPH_CS_SP method has higher accuracy and better stability than the traditional SPH method and other corrected SPH method, and can improve the tensile instability.

Dynamic-Analogue Correction of the Decadal Change of East Asian Summer Precipitation in the Late 1990s

This paper systematically evaluates the deviations that appear in the hindcasts of the East Asian summer precipitation（EASP） decadal change in the late 1990 s in two global coupled models（BCC-CGCM and BCC-CSM）.The possible causes for the deviations between the model hindcasts and observations are analyzed.The results show that the hindcasts of EASP by BCC-CGCM and BCC-CSM deviate from observations,with the anomaly correlation coefficient（ACC） being-0.01 and-0.09 for the two models,respectively.The SST anomalies in North and West Pacific and the SST index values predicted by the two models also deviate from the observations,indicating that inconsistent SST fields may be the key factor leading to the deviation in the prediction of the EASP decadal shift.Thus,a dynamic-analogue scheme is proposed to correct the precipitation hindcasts by using SSTs,where SST and EASP are highly correlated,to select historical analogue cases.Cross validations show that the average ACC of the temporal-latitude distribution of the EASP between the corrected hindcasts and observations is 0.18 for BCC-CGCM and0.02 for BCC-CSM;both are much higher than the uncorrected hindcasts.Applying the dynamic-analogue correction scheme in both models successfully improves prediction of the EASP decadal change in the late1990 s.

THE INITIAL WIND SCHEME OF THE HEMISPHERIC SPECTRAL MODEL AND ITS EFFECT ON THE DATA ASSIMILATION

A series of data assimilation and forecast test have been carried out with a hemispheric spectral model(T42L9H).It is found that the numerical scheme for determining hemispheric initial wind is important to data assimilation and forecast.An inappropriate scheme may cause computational sources of divergence near the equator,which are responsible for the spurious strong precipitation and corresponding latent heat release.Obviously,this problem differs from either the hemispheric/global domain effect or the tropical data effect pointed by Dalley et al.(1981).Based on the previous studies,the new scheme of divergence and vorticity correction is presented,and the difference with other schemes and its effects on the data assimilation are discussed against the control test. Preliminary tests have shown that the new divergence correction scheme proposed in this paper may be a preferable choice to overcome the initial computational errors in the hemispheric data assimilation.

A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.