Multigrid methods for complex engineering geometries and unstructured meshes

The convergence of standard multigrid methods decays significantly if locally poor quality cells are present, and it is found that the poor convergence is due to the local failure of the smoothing property. The high frequency error localised in regions of low quality cells is not eliminated by standard multigrid smoothers and persists through multigrid cycles. We propose a global–local combined smoother for the geometric multigrid to deal with engineering meshes with a small number of poor quality cells, which includes two steps: a global smoother on the whole domain, followed by a local correction on the subdomains with low quality cells. The high frequency error remaining in the low quality regions can be damped out completely by the local correction. The idea is extended to the algebraic multigrid (AMG), including both classical AMG and smoothed aggregation AMG. It is suggested that the high frequency error produced by the smoother propagates outward the low quality region on the fine grid to the neighbouring areas on the coarse grid. An algorithm to track low quality regions on the abstract coarse grid of AMG has been developed based on the information transfer between grid levels via the transfer operators. With the local correction applied on low quality regions tracked on the abstract coarse grid, the high frequency error due to low grid quality can be removed. In the smoothed aggregation AMG, the construction of the smoothed prolongation operator depends on the spectral radius of the system. However, regions of low quality cells in a mesh increase the largest eigenvalue of the linear system. We propose a shifted largest eigenvalue strategy to approximate a reasonable spectral radius to construct the smoothed prolongation. Two and three dimensional numerical experiments, from illustrate to complicated, are demonstrated to validate the proposed smoother. Elliptic type PDEs, including Poisson and elasticity problems, are solved. For each example, the performance of multigrid on a high quality mesh is also presented as a reference case, and it is shown that the poor convergence of multigrid for low quality meshes can be recovered to the reference case by the proposed smoother. A realistic thermomechanical simulation of turbomachinery problem has also been successfully solved

Is Russia becoming China’s other? An analysis of China’s foreign policy discourses towards Russia

Having China’s international identity as the research background, the special position Russia has in its relations with China created a myth for researchers to tackle. China frequently uses Othering in its domestic politics in portraying itself as a victim and a tendency of selfvictimization due to historical sufferings. The reasons for China to see Russia as an Other are not untraceable with China losing Outer Eastern China to Russian Empire due to unequal agreement; however, China simply gave up the disputed area in exchange for a solidified land border and China-Russia relations are ‘at its best’ since the rapprochement. The partnership did not fall apart as previous scholar works predicted. The Crimean Crisis as a key event for analysis adds up to the myth that China as a sovereignty hawk was not weary of Russia’s expansionist foreign policy which led to the annexation of Crimea; instead, China-Russia relations are brought up to the next level through efforts from both sides. The current geopolitical approach left this myth unaccounted. This thesis sets out to shed lights on how China’s identity construction of Russia have changed from March, 2013 after President Xi Jingping’s incumbent until March, 2017 with the Crimean Crisis as the key event for comparison. Based on Hansen’s theoretical framework that foreign policy discourses as the link between identity and foreign policies, this thesis conducts poststructuralist discourse analysis on Chinese official discourses and academic debate on Russia using the intertextuality research model 1 and 3B developed by Hansen (2006). The result has shown before Crimean, both official and academic discourses did not construct Russia as a radical Other but strongly linked with and supplement to the construction of China; after Crimean official discourses’ which represent China’s foreign policy attempts to create new linking to emphasize similarities of the identity construction of China and Russia upon the emergence of competing discourses in academic debate. This research focuses primarily on how the identity construction have changed in the timeframe due to the key event. To unfold the myth, researches on why the identity construction and Chinese foreign policy have changed this way are encouraged. To present a more comprehensive overview of discourses, wider text selection including intertextuality research model 2 and 3A is another angle to tackle.http://www.ester.ee/record=b4684428*es

Spatiotemporal patterns of earthquakes and their implications for earthquake hazards

[EMBARGOED UNTIL 5/31/2023] This work focuses on characterizing spatiotemporal patterns of earthquakes, their possible causes, and their implications for seismic hazard assessment. I studied both local and global earthquakes in the view of complex fault systems. Specifically, I studied the background seismicity and long-lived aftershock activities in intraplate North China and the Central and Eastern United State (CEUS), and characterized the correlation between strain rate and seismicity and evaluated the prediction power of strain rate in different tectonic settings. I found that periodic or quasiperiodic earthquake recurrence on individual faults, as predicted by the elastic rebound model, is not common in nature. Instead, most earthquake sequences are complex and variable, and often show clusters of events separated by long but irregular intervals of quiescence. The common earthquake clustering may be caused by earthquake-induced viscoelastic relaxation and fault interaction. Most earthquake sequences are burstier than the Poisson model, implying a higher probability of repeating events soon after a large earthquake. Possible long-lived aftershocks are found in intraplate North China and the CEUS. Background seismicity in intraplate regions may vary with time, highlighting the complexity of intraplate seismicity. Mistakenly identifying long-lived aftershocks as background earthquakes may overestimate seismic hazard in intraplate regions. The correlation between strain rate and seismicity varies between different tectonic settings and is time-dependent. Good strain rate-seismicity correlations are found in plate boundary regions and during seismically active periods, while no correlations are found in stable continents and during inactive periods. All these variations need to be considered in hazard assessment.Includes bibliographical references

Transition metal dichalcogenide MoSe₂ nanostructures

Transition metal dichalcogenides (TMDs) are a family of van der Waals (vdW) layered materials exhibiting unique electronic, optical, magnetic, and transport properties. Their technological potentials hinge critically on the ability to achieve controlled fabrication of desirable nanostructures. Here I present three kinds of nanostructures of semiconducting TMD MoSe₂, created by molecular beam epitaxy (MBE) and characterized by scanning tunneling microscopy and spectroscopy (STM/STS). The three kinds of nanostructures are two-dimensional (2D) nanoislands, quasi one-dimensional (1D) nanoribbons, and heterostructures. The successful growth of 2D nanoislands lays the foundation for the preparation of the other two structures. By properly controlling the substrate temperature and Se over-pressure, the MoSe₂ atomic layers undergo a dramatic three-stage shape transformation: from fractal to compact 2D nanoislands, and eventually to nanoribbons, in stark contrast to the traditional two-stage growth behaviour involving only the transformation from the fractal to compact regime. Experimentally, it is found that the Se:Mo flux ratio during MBE growth plays a central role in controlling the nanoribbon formation. Theoretically, first-principles calculations show that the abundance/deficiency of extra Se atoms at different island edges significantly modifies the relative step energies between zigzag and armchair edges, which in turn impacts the island shape evolution during nonequilibrium growth. The successful preparation of MoSe2/hBN/Ru(0001) heterostructure is a demonstration that MBE technique is suitable for fabricating vdW heterostructures. Surprisingly, we found that the quasi-particle gap of the MoSe₂ on hBN/Ru is about 0.25 eV smaller than those on graphene or graphite substrates. We attribute this result to the strong interaction between hBN/Ru which causes residual metallic screening from the substrate. The surface of MoSe₂ exhibits Moiré pattern that replicates the Moiré pattern of hBN/Ru. In addition, the electronic structure and the work function of MoSe₂ are modulated electrostatically with an amplitude of ~ 0.13 eV. Most interestingly, this electrostatic modulation is spatially in phase with the Moiré pattern of hBN on Ru(0001) whose surface also exhibits a work function modulation of the same amplitudePhysic

Molecular beam epitaxy of topological insulator Bi₂Se₃

textIn this thesis, I show my effort in growing atomically flat Bi₂Se₃ thin films using molecular beam epitaxy (MBE) method. Bi₂Se₃ is a kind of topological insulator, whose exotic surface states have been found in the samples that I grew.Physic

Multigrid on unstructured meshes with regions of low quality cells

The convergence of multigrid methods degrades significantly if a small number of low quality cells are present in a finite element mesh, and this can be a barrier to the efficient and robust application of multigrid on complicated geometric domains. The degraded performance is observed also if intermediate levels in a non-nested geometric multigrid problem have low quality cells, even when the fine grid is high quality. It is demonstrated for geometric multigrid methods that the poor convergence is due to the local failure of smoothers to eliminate parts of error around cells of low quality. To overcome this, a global--local combined smoother is developed to maintain effective relaxation in the presence of a small number of poor quality cells. The smoother involves the application of a standard smoother on the whole domain, followed by local corrections for small subdomains with low quality cells. Two- and three-dimensional numerical experiments demonstrate that the degraded convergence of multigrid for low quality meshes can be restored to the high quality mesh reference case using the proposed smoother. The effect is particularly pronounced for higher-order finite elements. The results provide a basis for developing efficient, non-nested geometric multigrid methods for complicated engineering geometries