Browsing by Author "Dastour, Hatef"

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    Optimal Finite Difference Schemes for the Helmholtz Equation with PML
    (2019-12-17) Dastour, Hatef; Liao, Wenyuan; Ware, Antony Frank; Lamoureux, Michael P.; Zinchenko, Yuriy
    An efficient and accurate numerical scheme for solving the seismic wave equations is a key part in seismic wave propagation modeling. The pollution effect of high wavenumbers (the accuracy of the numerical results often deteriorates as the wavenumber increases) plays a critical role in the accuracy of these numerical schemes and it is inevitable in two and three dimensional Helmholtz equations. Optimal finite difference methods can offer a remedy to this problem; however, the numerical solution to a multi-dimensional Helmholtz equation can be troublesome when the perfectly matched layer (PML) boundary condition is implemented. This study develops a number of optimal finite difference schemes for solving the Helmholtz equation in the presence of PML. In doing so, we implement two common strategies, derivative-weighting and point-weighting strategies, for constructing these schemes. Furthermore, a challenge for developing such methods is being consistent with the Helmholtz equation with PML. Thus, analytical and numerical proofs are provided to show the consistency of the schemes. Moreover, for each developed optimal finite difference method, error analysis for the numerical approximation of the exact wavenumber is provided. Based on minimizing the numerical dispersion, some optimal parameters strategies for each optimal finite difference schemes are recommended. Furthermore, several examples are provided to illustrate the accuracy and effectiveness of the new methods in reducing numerical dispersion.
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    Vegetation and Forest Fire Dynamics in Alberta: A Ground and Remote Sensing Data Analysis
    (2024-07-02) Dastour, Hatef; Hassan, Quazi K.; Achari, Gopal; Ahmed, M. Razu
    This thesis presents a comprehensive analysis of the interplay between forest fires and vegetation dynamics in Alberta, Canada, under the lens of climate change. By synthesizing data from remote sensing, climate records, and fire databases, the study reveals the intricate relationships between vegetation cover changes and climatic factors throughout 2001–2022. It highlights the significant lead and lag times between the Normalized Difference Vegetation Index (NDVI) and climate variables such as Land Surface Temperature (LST), relative humidity, and precipitation, offering insights into the temporal dynamics of vegetation response to climatic influences. The research further explores the patterns and trends of forest fires, correlating them with interpolated climate data across various subregions. Using trend analysis and anomaly detection methods, the study identifies significant warming and drying trends, alongside variable precipitation changes, which have influenced both human-caused and lightning-induced forest fires. The findings underscore the differential impact of climate variables on fire occurrence and source, with notable patterns emerging in subregions like Athabasca Plain and Central Mixedwood. Building on these insights, the thesis develops a robust forest fire spread model, validated through high-precision simulations of the 2011 Slave Lake and 2016 Fort McMurray wildfires. The model leverages regional physical features, climatic data, and MODIS datasets to offer accurate fire behavior predictions. The phased simulation approach adapts to dynamic factors such as weather conditions and firefighting strategies, enhancing the model's applicability for effective fire management. Ultimately, this thesis aims to bridge the gap between theoretical understanding and practical application, providing valuable contributions to Alberta's forest fire management and community protection strategies. The research paves the way for more informed decision-making in the face of climate change by offering a nuanced understanding of fire-vegetation-climate interactions and developing an advanced predictive model.