Regge Finite Elements with Applications in Solid Mechanics and Relativity

University of Minnesota Ph.D. dissertation. May 2018. Major: Mathematics. Advisor: Douglas Arnold. 1 computer file (PDF); ix, 183 pages.This thesis proposes a new family of finite elements, called generalized Regge finite elements, for discretizing symmetric matrix-valued functions and symmetric 2-tensor fields. We demonstrate its effectiveness for applications in computational geometry, mathematical physics, and solid mechanics. Generalized Regge finite elements are inspired by Tullio Regge’s pioneering work on discretizing Einstein’s theory of general relativity. We analyze why current discretization schemes based on Regge’s original ideas fail and point out new directions which combine Regge’s geometric insight with the successful framework of finite element analysis. In particular, we derive well-posed linear model problems from general relativity and propose discretizations based on generalized Regge finite elements. While the first part of the thesis generalizes Regge’s initial proposal and enlarges its scope to many other applications outside relativity, the second part of this thesis represents the initial steps towards a stable structure-preserving discretization of the Einstein’s field equation

FEniCS in Linux Containers

FEniCS'15 Workshop at Imperial College London, 29th June - 1st July 2015

SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models

Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble of forecasts. This is done by running many physics-based simulations under different conditions, which is a computationally costly process. We propose to amortize the computational cost by emulating these forecasts with deep generative diffusion models learned from historical data. The learned models are highly scalable with respect to high-performance computing accelerators and can sample hundreds to tens of thousands of realistic weather forecasts at low cost. When designed to emulate operational ensemble forecasts, the generated ones are similar to physics-based ensembles in important statistical properties and predictive skill. When designed to correct biases present in the operational forecasting system, the generated ensembles show improved probabilistic forecast metrics. They are more reliable and forecast probabilities of extreme weather events more accurately. While this work demonstrates the utility of the methodology by focusing on weather forecasting, the generative artificial intelligence methodology can be extended for uncertainty quantification in climate modeling, where we believe the generation of very large ensembles of climate projections will play an increasingly important role in climate risk assessment.Comment: fixed a mistake of the previous version; the paper has not been submitted to neurips 202

Containers for Portable, Productive, and Performant Scientific Computing

Containers are an emerging technology that holds promise for improving productivity and code portability in scientific computing. The authors examine Linux container technology for the distribution of a nontrivial scientific computing software stack and its execution on a spectrum of platforms from laptop computers through high-performance computing systems. For Python code run on large parallel computers, the runtime is reduced inside a container due to faster library imports. The software distribution approach and data that the authors present will help developers and users decide on whether container technology is appropriate for them. The article also provides guidance for vendors of HPC systems that rely on proprietary libraries for performance on what they can do to make containers work seamlessly and without performance penalty

Spatiotemporal Variation of NDVI in Anhui Province from 2001 to 2019 and Its Response to Climatic Factors

This paper intends to clarify that the spatial and temporal evolutionary patterns of regional vegetation and their relationship with climate form a premise of ecological conservation and environmental governance, and play an important role in maintaining regional ecosystem balance and promoting sustainable development. Based on measured data collected from NDVI remote sensing products and meteorological stations, NDVI variation in Anhui Province from 2001 to 2019 was determined through trend analysis and measurement methods involving coefficient of variation and Hurst index; in addition, the response to climatic factors was also explored. It was concluded that, firstly, in terms of spatiotemporal analysis, the interannual variation of NDVI in Anhui Province showed an increasing trend with a rate of 0.024/10 a, while the monthly variation showed a weak bimodal pattern, with the highest value in August and the lowest value in January. Furthermore, NDVI in Anhui Province showed significant spatial heterogeneity, with high values concentrated in mountainous regions in southern Anhui and Dabie Mountain region, and low values concentrated in the hilly areas of Jianghuai and areas along the Yangtze River. At the same time, the overall spatial variation of NDVI showed an increasing trend, and the areas with extremely significant and significant improvement in vegetation coverage accounted for 54.69% of the total area of Anhui Province. Secondly, in terms of the analysis on variation characteristics, the variation of NDVI in Anhui Province was generally stable, with an average CV coefficient of variation of 0.089, which, however, was quite different in different regions; meanwhile, the future trend of NDVI variation in the study areas was mostly in a random manner. Thirdly, the response of NDVI in Anhui Province to climatic factors showed significant spatial heterogeneity. NDVI was found to be positively correlated with precipitation and negatively correlated with temperature; in general, the impact of precipitation on NDVI was greater than that of temperature. In the 19 years studied, NDVI in Anhui Province showed an increasing trend; and climate, topography and human activities led to heterogeneous spatial distribution of vegetation. Therefore, in the future, the evolutionary trend of vegetation will be relatively random, and NDVI will be more greatly affected by temperature, than by precipitation

Modeling Biomass for Natural Subtropical Secondary Forest Using Multi-Source Data and Different Regression Models in Huangfu Mountain, China

Forest biomass estimation is an important parameter for calculating forest carbon storage, which is of great significance for formulating carbon-neutral strategies and forest resource management measures. We aimed at solving the problems of low estimation accuracy of forest biomass with complex canopy structure and high canopy density, and large differences in the estimation results of the same estimation model under complex forest conditions. The Huangfu Mountain Forest Farm in Chuzhou City was used as the research area. As predictors, we used Gaofen-1(GF-1) and Gaofen(GF-6) satellite high-resolution imaging satellite data, combined with digital elevation model (DEM) and forest resource data. Multiple stepwise regression, BP neural network and random forest estimation models were used to construct a natural subtropical secondary forest biomass estimation model with complex canopy structure and high canopy closure. We extracted image information as modeling factors, established multiple stepwise regression models of different tree types with a single data source and a comprehensive data source and determined the optimal modeling factors. On this basis, the BP neural network and random forest biomass estimation model were established for Pinus massoniana, Pinus elliottii, Quercus acutissima and mixed forests, with the coefficient of determination n (R2) and root mean square error (RMSE) as the judgment indices. The results show that the random forest model had the best biomass estimation effect among different forest types. The R2 of Quercus acutissima was the highest, reaching 0.926, but the RMSE was 11.658 t/hm2. The R2 values of Pinus massoniana and mixed forest were 0.912 and 0.904, respectively. The RMSE reached 10.521 t/hm2 and 6.765 t/hm2, respectively; the worst result was the estimation result of Pinus elliottii, with an R2 of 0.879 and an RMSE of 14.721 t/hm2. The estimation result of the BP neural network was second only to that of the random forest model in the four forest types. From high precision to low precision, the order was Quercus acutissima, Pinus massoniana, mixed forest and Pinus elliottii, with R2s of 0.897, 0.877, 0.825 and 0.753 and RMSEs of 17.899 t/hm2, 10.168 t/hm2, 18.641 t/hm2 and 20.419 t/hm2, respectively. In this experiment, the worst biomass estimation performance was seen for multiple stepwise regression, which ranked the species in the order of Quercus acutissima, Pinus massoniana, mixed forest and Pinus elliottii, with R2s of 0.658, 0.622, 0.528 and 0.379 and RMSEs of 29.807 t/hm2, 16.291 t/hm2, 28.011 t/hm2 and 23.101 t/hm2, respectively. In conclusion, GF-1 and GF-6 combined with data and a random forest algorithm can obtain the most accurate results in estimating the forest biomass of complex tree species. The random forest estimation model had a good performance in biomass estimation of primary secondary forest. High-resolution satellite data have great application potential in the field of forest parameter inversion