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Poster to be presented at Stochastic Numerics and Statistical Learning: Theory and Applications Workshop 2024, Kaust, Saudi Arabia, https://cemse.kaust.edu.sa/stochnum/events/event/snsl-workshop-2024. In this work we have considered a setting that mimics the Henry problem \cite{Simpson2003,Simpson04_Henry}, modeling seawater intrusion into a 2D coastal aquifer. The pure water recharge from the ``land side'' resists the salinisation of the aquifer due to the influx of saline water through the ``sea side'', thereby achieving some equilibrium in the salt concentration. In our setting, following \cite{GRILLO2010}, we consider a fracture on the sea side that significantly increases the permeability of the porous medium. The flow and transport essentially depend on the geological parameters of the porous medium, including the fracture. We investigated the effects of various uncertainties on saltwater intrusion. We assumed uncertainties in the fracture width, the porosity of the bulk medium, its permeability and the pure water recharge from the land side. The porosity and permeability were modeled by random fields, the recharge by a random but periodic intensity and the thickness by a random variable. We calculated the mean and variance of the salt mass fraction, which is also uncertain. The main question we investigated in this work was how well the MLMC method can be used to compute statistics of different QoIs. We found that the answer depends on the choice of the QoI. First, not every QoI requires a hierarchy of meshes and MLMC. Second, MLMC requires stable convergence rates for $\EXP{g_{\ell} - g_{\ell-1}}$ and $\Var{g_{\ell} - g_{\ell-1}}$. These rates should be independent of $\ell$. If these convergence rates vary for different $\ell$, then it will be hard to estimate $L$ and $m_{\ell}$, and MLMC will either not work or be suboptimal. We were not able to get stable convergence rates for all levels $\ell=1,\ldots,5$ when the QoI was an integral as in \eqref{eq:integral_box}. We found that for $\ell=1,\ldots 4$ and $\ell=5$ the rate $\alpha$ was different. Further investigation is needed to find the reason for this. Another difficulty is the dependence on time, i.e. the number of levels $L$ and the number of sums $m_{\ell}$ depend on $t$. At the beginning the variability is small, then it increases, and after the process of mixing salt and fresh water has stopped, the variance decreases again. The number of random samples required at each level was estimated by calculating the decay of the variances and the computational cost for each level. These estimates depend on the minimisation function in the MLMC algorithm. To achieve the efficiency of the MLMC approach presented in this work, it is essential that the complexity of the numerical solution of each random realisation is proportional to the number of grid vertices on the grid levels.
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In this slide, we'll dive into the "First Expired, First Out" (FEFO) removal strategy in Odoo 17, specifically designed for managing perishable products. We'll explore its benefits, setup process, and how it helps minimize waste and maximize efficiency.
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Capitol Tech Univ Doctoral Presentation -May 2024
ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...
ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...
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Features of Video Calls in the Discuss Module in Odoo 17
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Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45
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Improved Approval Flow in Odoo 17 Studio App
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Poster_density_driven_with_fracture_MLMC.pdf
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Mattingly "AI and Prompt Design: LLMs with Text Classification and Open Source"
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Implanted Devices - VP Shunts: EMGuidewire's Radiology Reading Room
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjj
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjj
Championnat de France de Tennis de table/
Championnat de France de Tennis de table/
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Graduate Outcomes Presentation Slides - English (v3).pptx
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The Ball Poem- John Berryman_20240518_001617_0000.pptx
The Liver & Gallbladder (Anatomy & Physiology).pptx
The Liver & Gallbladder (Anatomy & Physiology).pptx
SURVEY I created for uni project research
SURVEY I created for uni project research
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Removal Strategy _ FEFO _ Working with Perishable Products in Odoo 17
Blended Learning
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Blended Learning Alex
Enkerli Department of Sociology and Anthropology [email_address]
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