This is a draft presentation with the first application of the BEq model ... now it is published on http://onlinelibrary.wiley.com/doi/10.1002/wrcr.20072/abstract
Mathematical models play a fundamental role in many scientific and en- gineering fields in today’s world. They are used for example in geotechnics to evalute the hillslope stability, in weather science to predict weather trends and produce weather reports, in structural design to study the resistance to stress, and in fluid dynamics to compute fluid flows and air flows.
Consequently mathematical models are evolving all the time: more and more new numerical methods are being invented to solve the Partial Dif- ferential Equations (PDE)s that describe physical problems with increasing precision, and more and more complex and efficient processor units are being created to reduce the computational time.
Therefore, the code into which the mathematical models are translated has to be “dynamic” in order to be easily updated on the basis of the con- tinuous developments (Formetta et al. (2014) [16]).
On the other hand, completely different physical problems are often de- scribed using similar PDEs. For this reason, the numerical methods which provide solutions to different problems can be the same. This suggest the implementation of an IT infrastructure that hosts a standard structure for solving PDEs and that can serve various disciplines with the minimum of hassles.
This work is focused on the application of what is envisioned above, with the main purpose of the creation of an abstract code for implementing every type of mathematical model described by PDEs.
We work on hydrological topics but we hope to design a structure of general interest. Obviously the final goal of any work of this type is to find a proper numerical solver, and therefore, part of the thesis is devoted to the analysis of the problem under scrutiny, and the description of the solution found.
This document presents a fully coupled 2D surface-subsurface hydrological model. It implements a robust conservative scheme that accounts for nonlinearities like drying and wetting. The model discretizes and solves the shallow water equation for surface flow and the Boussinesq equation for groundwater flow on structured or unstructured grids. It was verified for a mountain catchment in the Alps and resulted in a mass budget precision of 10-8. Future work outlined includes implementing unsaturated zone processes, applying the model at larger scales, extending it to 3D subsurface flow modeling, and improving model output and analysis capabilities.
- Vancouver housing markets continued to surge in February 2011, driving up provincial housing statistics. The average home price in BC rose 18% compared to February 2010.
- Sales activity in Vancouver's pricier communities pushed up average home prices more than market conditions would suggest, according to BCREA's chief economist. The average home price in Vancouver rose 19% versus a more modest 4% increase in benchmark home prices.
- Residential sales dollar volume in BC increased 15% in the first two months of 2011 compared to the same period in 2010, while residential unit sales remained relatively unchanged. The average home price climbed nearly 16% year-to-date.
This document discusses conducting a survey to determine people's perceptions of the advantages and risks of social media. The survey will use a descriptive research method with a questionnaire containing Likert scale questions distributed directly to respondents. Responses will be analyzed both qualitatively and quantitatively. The analysis will show what respondents think about social media and if they understand the benefits as well as risks of using social media.
Bed bug testing icr lab - 505-0030 protocolentogenex
The document describes a study protocol to evaluate the efficacy of Bio d’ Bug Bed Bug Control Solution spray against bed bugs. Ten bed bugs will be sprayed with the test product or a control in 5 replicates each. Bed bugs will be observed for knockdown at various time points and mortality will be recorded at 24 and 48 hours. The objective is to determine the product's ability to knock down and kill bed bugs.
This document appears to be an IKEA product listing or manual. It includes the product code "AA-189267-3" mentioned several times alongside other numbers that seem to indicate quantities, sizes or other specifications for the IKEA product. The document also includes the text "BENNO" but no other context.
Mathematical models play a fundamental role in many scientific and en- gineering fields in today’s world. They are used for example in geotechnics to evalute the hillslope stability, in weather science to predict weather trends and produce weather reports, in structural design to study the resistance to stress, and in fluid dynamics to compute fluid flows and air flows.
Consequently mathematical models are evolving all the time: more and more new numerical methods are being invented to solve the Partial Dif- ferential Equations (PDE)s that describe physical problems with increasing precision, and more and more complex and efficient processor units are being created to reduce the computational time.
Therefore, the code into which the mathematical models are translated has to be “dynamic” in order to be easily updated on the basis of the con- tinuous developments (Formetta et al. (2014) [16]).
On the other hand, completely different physical problems are often de- scribed using similar PDEs. For this reason, the numerical methods which provide solutions to different problems can be the same. This suggest the implementation of an IT infrastructure that hosts a standard structure for solving PDEs and that can serve various disciplines with the minimum of hassles.
This work is focused on the application of what is envisioned above, with the main purpose of the creation of an abstract code for implementing every type of mathematical model described by PDEs.
We work on hydrological topics but we hope to design a structure of general interest. Obviously the final goal of any work of this type is to find a proper numerical solver, and therefore, part of the thesis is devoted to the analysis of the problem under scrutiny, and the description of the solution found.
This document presents a fully coupled 2D surface-subsurface hydrological model. It implements a robust conservative scheme that accounts for nonlinearities like drying and wetting. The model discretizes and solves the shallow water equation for surface flow and the Boussinesq equation for groundwater flow on structured or unstructured grids. It was verified for a mountain catchment in the Alps and resulted in a mass budget precision of 10-8. Future work outlined includes implementing unsaturated zone processes, applying the model at larger scales, extending it to 3D subsurface flow modeling, and improving model output and analysis capabilities.
- Vancouver housing markets continued to surge in February 2011, driving up provincial housing statistics. The average home price in BC rose 18% compared to February 2010.
- Sales activity in Vancouver's pricier communities pushed up average home prices more than market conditions would suggest, according to BCREA's chief economist. The average home price in Vancouver rose 19% versus a more modest 4% increase in benchmark home prices.
- Residential sales dollar volume in BC increased 15% in the first two months of 2011 compared to the same period in 2010, while residential unit sales remained relatively unchanged. The average home price climbed nearly 16% year-to-date.
This document discusses conducting a survey to determine people's perceptions of the advantages and risks of social media. The survey will use a descriptive research method with a questionnaire containing Likert scale questions distributed directly to respondents. Responses will be analyzed both qualitatively and quantitatively. The analysis will show what respondents think about social media and if they understand the benefits as well as risks of using social media.
Bed bug testing icr lab - 505-0030 protocolentogenex
The document describes a study protocol to evaluate the efficacy of Bio d’ Bug Bed Bug Control Solution spray against bed bugs. Ten bed bugs will be sprayed with the test product or a control in 5 replicates each. Bed bugs will be observed for knockdown at various time points and mortality will be recorded at 24 and 48 hours. The objective is to determine the product's ability to knock down and kill bed bugs.
This document appears to be an IKEA product listing or manual. It includes the product code "AA-189267-3" mentioned several times alongside other numbers that seem to indicate quantities, sizes or other specifications for the IKEA product. The document also includes the text "BENNO" but no other context.
The document presents the results of a study evaluating the toxicity of TMOF, an insecticide, and its formulations (WP TMOF and Rice Husk TMOF) on Elaeidobius kamerunicus, a pollinator of oil palms. Exposure to the insecticide formulations resulted in mortality rates of less than 20% for the pollinator at 24, 48, and 72 hours, classifying the toxicity as "harmless" according to international standards. This confirms that TMOF and its products have little to no adverse effects on non-target insects like E. kamerunicus.
The document discusses search engine optimization (SEO) strategies for 2014. It notes that SEO focuses on long-term organic search results, while paid search provides immediate but costly clicks. Top factors for search rankings include technical elements, backlinks, social signals and user behavior. The presentation recommends automating technical SEO and prioritizing engaging content that tells a story and is worth spreading on social media. Marketers are advised to focus on driving traffic and conversions rather than simply aiming for the #1 search ranking. An optimal workflow incorporates SEO best practices from the start of a website's development.
This document presents a collection of 11 unusual hernia cases seen at a busy Emergency Department. For each case, the document summarizes the clinical history, imaging findings, diagnosis, pathogenesis, epidemiology, clinical presentation, and outcome. The cases include rare hernias such as bilateral Spigelian hernias, transdiaphragmatic intercostal hernia, superior lumbar hernia, retroperitoneal herniation of gastric diverticulum, incarcerated vesico-inguinal hernia, internal paraduodenal hernia, internal foramen of Winslow hernia, direct inguino-labial hernia, parastomal herniation of gallbladder, obturator hernia, and an
The document discusses production and consumption in a marketplace economy. It explains how a production possibilities curve can illustrate trade-offs and opportunity costs using two goods or services. It also discusses demand, production methods like barter and money, credit, the relationship between supply and demand, and how higher demand for one product can lead other consumers to want to purchase from that company.
This document appears to be a slide presentation on effective note-taking techniques for university students. It introduces the Cornell note-taking method, which involves structuring notes with headings, cues, and summaries. It also discusses listening strategies, such as focusing on main ideas and examples. Additional methods covered include outlining, mind maps, and the 5R method of recording, reducing, reciting, reflecting and reviewing notes. The presentation emphasizes identifying key concepts and relationships between ideas, as well as regularly reviewing and summarizing notes. It directs students to campus resources for further developing effective study skills.
The document summarizes the author's pilgrimage to religious sites in South Karnataka associated with Adi Sankara Bhagavatpada, a famous 8th century Indian philosopher. They traveled from their home in Thrissur, Kerala to destinations like Udupi, Kollur Mookambika Temple, Sringeri Sarada Mutt, and Mangalore. These places were important to Sankara and blessed by his presence. The author describes their multi-day journey, visits to temples, and experiences at each location on the trail of Sankara.
This document discusses food orders and a brief conversation. It begins with one person asking what another would like for dinner, with a response requesting steak and chips but also saying salad could be had instead of chips. A second conversation is between David and Helen where they greet each other, with a comment that David couldn't remember Helen. Mary then asks how a product presentation can be done, showing some confusion between PowerPoint and a spreadsheet.
The document outlines a first day schedule for a new student at Westside High School, suggesting they be assigned to a house, visit the library or see the mascot, enjoy lunch, attend an assembly, join JROTC, work out, try out for baseball, or have practice for their favorite sport.
FOR THOSE INTERESTED IN SUBMITTING INFORMATION FOR YOUR ORGANIZATION TO THE WEEKLY NEWS UPDATE, PLEASE SUBMIT BY June 12, 2012 FOR THE NEXT WEEKLY NEWS UPDATE. SUBMISSIONS NEED TO BE SENT TO stacie.dumas@us.army.mil
Within the framework of the theory of plane steady filtration of an incompressible fluid according to Darcy’s law, two limiting schemes modeling the filtration flows under the Joukowski tongue through a soil massive spread over an impermeable foundation or strongly permeable confined water bearing horizon are considered.
Basics of Contaminant Transport in Aquifers (Lecture)Amro Elfeki
This is a basic lecture on contaminant transport in aquifers. It covers various aspects. Types of transport in aquifers. Reactive and non-reactive, governing equations of solute transport. Method of solutions and simulations.
New Mathematical Tools for the Financial SectorSSA KPI
AACIMP 2010 Summer School lecture by Gerhard Wilhelm Weber. "Applied Mathematics" stream. "Modern Operational Research and Its Mathematical Methods with a Focus on Financial Mathematics" course. Part 5.
More info at http://summerschool.ssa.org.ua
Large variance and fat tail of damage by natural disasterHang-Hyun Jo
In order to account for large variance and fat tail of damage by natural disaster, we study a simple model by combining distributions of disaster and population/property with their spatial correlation. We assume fat-tailed or power-law distributions for disaster and population/property exposed to the disaster, and a constant vulnerability for exposed population/property. Our model suggests that the fat tail property of damage can be determined either by that of disaster or by those of population/property depending on which tail is fatter. It is also found that the spatial correlations of population/property can enhance or reduce the variance of damage depending on how fat the tails of population/property are. In case of tornadoes in the United States, we show that the damage does have fat tail property. Our results support that the standard cost-benefit analysis would not be reliable for social investment in vulnerability reduction and disaster prevention.
http://ascelibrary.org/doi/abs/10.1061/9780784413609.277
http://arxiv.org/abs/1407.6209
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document discusses resampling SMOS maps to match the resolution and incidence angles of AQUARIUS in order to enable synergistic analysis between the two missions. It describes using discrete Fourier transforms and Kaiser windows to resample SMOS maps while minimizing interpolation artifacts. The optimal Kaiser window parameters are determined through non-linear optimization to degrade SMOS pixels to equivalent AQUARIUS resolutions. An example resampling of SMOS brightness temperature maps for an overpass is provided. The procedure enables accurate resampling of SMOS maps for direct comparison with AQUARIUS observations.
A travel time model for estimating the water budget of complex catchmentsRiccardo Rigon
This is the presentation given by Marialaura Bancheri for her admission to the final exam to achieve a Ph.D. in Environmental Engineering. It contains a synthesis of her studies about spatially integrated models of the water budget, and about travel time theory. A model structure is also presented preliminarily containing five reservoirs.
Text Book: An Introduction to Mechanics by Kleppner and Kolenkow
Chapter 1: Vectors and Kinematics
-Explain the concept of vectors.
-Explain the concepts of position, velocity and acceleration for different kinds of motion.
References:
Halliday, Resnick and Walker
Berkley Physics Volume-1
The document presents the results of a study evaluating the toxicity of TMOF, an insecticide, and its formulations (WP TMOF and Rice Husk TMOF) on Elaeidobius kamerunicus, a pollinator of oil palms. Exposure to the insecticide formulations resulted in mortality rates of less than 20% for the pollinator at 24, 48, and 72 hours, classifying the toxicity as "harmless" according to international standards. This confirms that TMOF and its products have little to no adverse effects on non-target insects like E. kamerunicus.
The document discusses search engine optimization (SEO) strategies for 2014. It notes that SEO focuses on long-term organic search results, while paid search provides immediate but costly clicks. Top factors for search rankings include technical elements, backlinks, social signals and user behavior. The presentation recommends automating technical SEO and prioritizing engaging content that tells a story and is worth spreading on social media. Marketers are advised to focus on driving traffic and conversions rather than simply aiming for the #1 search ranking. An optimal workflow incorporates SEO best practices from the start of a website's development.
This document presents a collection of 11 unusual hernia cases seen at a busy Emergency Department. For each case, the document summarizes the clinical history, imaging findings, diagnosis, pathogenesis, epidemiology, clinical presentation, and outcome. The cases include rare hernias such as bilateral Spigelian hernias, transdiaphragmatic intercostal hernia, superior lumbar hernia, retroperitoneal herniation of gastric diverticulum, incarcerated vesico-inguinal hernia, internal paraduodenal hernia, internal foramen of Winslow hernia, direct inguino-labial hernia, parastomal herniation of gallbladder, obturator hernia, and an
The document discusses production and consumption in a marketplace economy. It explains how a production possibilities curve can illustrate trade-offs and opportunity costs using two goods or services. It also discusses demand, production methods like barter and money, credit, the relationship between supply and demand, and how higher demand for one product can lead other consumers to want to purchase from that company.
This document appears to be a slide presentation on effective note-taking techniques for university students. It introduces the Cornell note-taking method, which involves structuring notes with headings, cues, and summaries. It also discusses listening strategies, such as focusing on main ideas and examples. Additional methods covered include outlining, mind maps, and the 5R method of recording, reducing, reciting, reflecting and reviewing notes. The presentation emphasizes identifying key concepts and relationships between ideas, as well as regularly reviewing and summarizing notes. It directs students to campus resources for further developing effective study skills.
The document summarizes the author's pilgrimage to religious sites in South Karnataka associated with Adi Sankara Bhagavatpada, a famous 8th century Indian philosopher. They traveled from their home in Thrissur, Kerala to destinations like Udupi, Kollur Mookambika Temple, Sringeri Sarada Mutt, and Mangalore. These places were important to Sankara and blessed by his presence. The author describes their multi-day journey, visits to temples, and experiences at each location on the trail of Sankara.
This document discusses food orders and a brief conversation. It begins with one person asking what another would like for dinner, with a response requesting steak and chips but also saying salad could be had instead of chips. A second conversation is between David and Helen where they greet each other, with a comment that David couldn't remember Helen. Mary then asks how a product presentation can be done, showing some confusion between PowerPoint and a spreadsheet.
The document outlines a first day schedule for a new student at Westside High School, suggesting they be assigned to a house, visit the library or see the mascot, enjoy lunch, attend an assembly, join JROTC, work out, try out for baseball, or have practice for their favorite sport.
FOR THOSE INTERESTED IN SUBMITTING INFORMATION FOR YOUR ORGANIZATION TO THE WEEKLY NEWS UPDATE, PLEASE SUBMIT BY June 12, 2012 FOR THE NEXT WEEKLY NEWS UPDATE. SUBMISSIONS NEED TO BE SENT TO stacie.dumas@us.army.mil
Within the framework of the theory of plane steady filtration of an incompressible fluid according to Darcy’s law, two limiting schemes modeling the filtration flows under the Joukowski tongue through a soil massive spread over an impermeable foundation or strongly permeable confined water bearing horizon are considered.
Basics of Contaminant Transport in Aquifers (Lecture)Amro Elfeki
This is a basic lecture on contaminant transport in aquifers. It covers various aspects. Types of transport in aquifers. Reactive and non-reactive, governing equations of solute transport. Method of solutions and simulations.
New Mathematical Tools for the Financial SectorSSA KPI
AACIMP 2010 Summer School lecture by Gerhard Wilhelm Weber. "Applied Mathematics" stream. "Modern Operational Research and Its Mathematical Methods with a Focus on Financial Mathematics" course. Part 5.
More info at http://summerschool.ssa.org.ua
Large variance and fat tail of damage by natural disasterHang-Hyun Jo
In order to account for large variance and fat tail of damage by natural disaster, we study a simple model by combining distributions of disaster and population/property with their spatial correlation. We assume fat-tailed or power-law distributions for disaster and population/property exposed to the disaster, and a constant vulnerability for exposed population/property. Our model suggests that the fat tail property of damage can be determined either by that of disaster or by those of population/property depending on which tail is fatter. It is also found that the spatial correlations of population/property can enhance or reduce the variance of damage depending on how fat the tails of population/property are. In case of tornadoes in the United States, we show that the damage does have fat tail property. Our results support that the standard cost-benefit analysis would not be reliable for social investment in vulnerability reduction and disaster prevention.
http://ascelibrary.org/doi/abs/10.1061/9780784413609.277
http://arxiv.org/abs/1407.6209
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document discusses resampling SMOS maps to match the resolution and incidence angles of AQUARIUS in order to enable synergistic analysis between the two missions. It describes using discrete Fourier transforms and Kaiser windows to resample SMOS maps while minimizing interpolation artifacts. The optimal Kaiser window parameters are determined through non-linear optimization to degrade SMOS pixels to equivalent AQUARIUS resolutions. An example resampling of SMOS brightness temperature maps for an overpass is provided. The procedure enables accurate resampling of SMOS maps for direct comparison with AQUARIUS observations.
A travel time model for estimating the water budget of complex catchmentsRiccardo Rigon
This is the presentation given by Marialaura Bancheri for her admission to the final exam to achieve a Ph.D. in Environmental Engineering. It contains a synthesis of her studies about spatially integrated models of the water budget, and about travel time theory. A model structure is also presented preliminarily containing five reservoirs.
Text Book: An Introduction to Mechanics by Kleppner and Kolenkow
Chapter 1: Vectors and Kinematics
-Explain the concept of vectors.
-Explain the concepts of position, velocity and acceleration for different kinds of motion.
References:
Halliday, Resnick and Walker
Berkley Physics Volume-1
The document discusses Floquet theory applied to analyze the stability of internal gravity waves in a density-stratified fluid. It summarizes previous approaches to studying gravity wave instability, and outlines the author's thesis goal of using Floquet-Fourier computation to identify all physically unstable modes. This involves analyzing the Floquet exponents as a Riemann surface with complex wavenumber, to distinguish the two primary sheets corresponding to the physically relevant unstable solutions.
This document presents the basic flow equations, including the Navier-Stokes equation and Euler's equations for frictionless flow. It also introduces several dimensionless numbers that are used to characterize different types of fluid flow and heat and mass transfer, such as the Reynolds number, Prandtl number, Schmidt number, and more. These equations and numbers provide a theoretical framework for analyzing fluid flow, while practical applications require further assumptions and simplifications.
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.
JEE Mathematics/ Lakshmikanta Satapathy/ 3D Geometry theory part 7/ Equation of a Plane through a given point and normal to given vector in vector and Cartesian forms
More than fifty years ago, Paul Erd˝os and Alfred R´enyi discovered that the random graph G(n, p) underwent a phase transition (in modern language) near p = 1/n. For p a bit smaller (e.g., 0.99/n) all of the components were very small and had simple structures. But for p a bit bigger (e.g., 1.01/n) a “giant component” had emerged with a complex behavior. We now understand how to slow down this process so as to see the incipient giant component (the dominant component) at an early stage and to define a Critical Window through which the process moves from subcriticality to supercriticality.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document summarizes a research paper that investigates the scattering of oblique water waves by bottom undulations in the presence of a submerged thin vertical barrier. The paper uses perturbation analysis to obtain analytical expressions for the first-order reflection and transmission coefficients in terms of integrals involving the bottom shape function and the solution for wave scattering by the barrier alone. For sinusoidal bottom undulations symmetric about the barrier, the first-order transmission coefficient is found to vanish. Numerical results are presented for the first-order reflection coefficient for different parameters.
This is a lecture on the hydraulics of gradually varied flow in open channels. It shows the profiles common in the open channels and some numerical examples using numerical integration.
This document presents a method for stochastic hydroelastic analysis of pontoon-type very large floating structures (VLFS) considering directional wave spectra. The analysis is performed in the frequency domain using modal expansion to represent the floating structure's motion and the water's velocity potential. Response spectra are computed using random vibration analysis assuming the directional wave spectrum can be described as a Gaussian process. The distribution of extremes is estimated to obtain mean extreme response values relevant for design. The method is demonstrated on an example VLFS to investigate the effect of mean wave angle on the stochastic response.
IL CLIMA, IL CICLO DELLACQUA, UN MODELLO IDROLOGICO: L’INIZIO DI UNA APPLICAZ...Emanuele Cordano
Presentazione divulgativa sul clima e sul ciclo dell'acqua avvenuta presso l'Ecofiera di Montagna 2018, il 6 ottobre 2018 a Tione di Trento (TN). Una applicazione sulla distribuzione del manto nevoso in Val Rendena e Giudicarie è stata mostrata.
RMAWGEN is a software for generating daily multi-site weather data using an R-based vector autoregressive model (VAR). It was created to downscale climate predictions from global models to generate realistic daily time series for temperature and precipitation at multiple sites in Trentino, Italy. The VAR model uses past weather data as predictors and can include exogenous variables. RMAWGEN calibrates the VAR coefficients using least squares and performs diagnostics on the residuals to check for serial correlation and non-normality. It then uses a quantile-matching method to gaussianize the weather variables' marginal distributions.
RMAWGEN: A software project for a daily Multi-Site Weather Generator with R E...Emanuele Cordano
The RMAWGEN R package aims to generate future daily weather conditions using vector autoregressive (VAR) models to maintain temporal and spatial correlations in historical daily weather data. The package calibrates VAR model parameters using time series data on minimum and maximum temperature and precipitation from a Trentino, Italy dataset. Generated daily weather outputs can then be used for applications like climate change impact assessments.
RMAWGEN: a software project for Daily Multi-Site Weather GeneratorEmanuele Cordano
RMAWGEN is a software package for R that generates daily weather conditions using vector autoregressive (VAR) models. The VAR model maintains temporal and spatial correlations between variables like minimum and maximum temperature using historical daily weather data from multiple sites. The package aims to produce realistic future weather simulations for applications like assessing climate change impacts on agriculture.
The RMAWGEN R package aims to generate future daily weather conditions using a vector autoregressive (VAR) model to maintain temporal and spatial correlations among variables like minimum and maximum temperature and precipitation. Historical time series data for these variables from the Trentino dataset are used to calibrate the parameters of a VAR model, which is then stored as an object that inherits the varest class to allow for weather simulation. The package provides a tool for multi-site daily weather generation using R.
The RMAWGEN R package aims to generate future daily weather conditions using a vector autoregressive (VAR) model to maintain temporal and spatial correlations among variables like minimum and maximum temperature and precipitation. Historical time series data for these variables from the Trentino dataset are used to calibrate the parameters of a VAR model, which is then stored as an object that inherits the varest class to allow for weather simulation. The package provides a tool for multi-site daily weather generation using R.
Use of a Weather Generator for analysis of projections of future daily temper...Emanuele Cordano
This document describes the use of a weather generator technique called RMAWGEN to downscale climate change scenarios for daily temperature projections. Temperature data from 41 weather stations in Italy from 1958-2010 were preprocessed and homogenized. Climate indices were calculated from the observed and generated time series to validate the model over 1981-2010. The RMAWGEN model showed good results for several indices with autoregression orders of 1 and 10. Climate projections were statistically downscaled for two future 30-year periods using RMAWGEN.
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
TrustArc Webinar - 2024 Global Privacy SurveyTrustArc
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
Threats to mobile devices are more prevalent and increasing in scope and complexity. Users of mobile devices desire to take full advantage of the features
available on those devices, but many of the features provide convenience and capability but sacrifice security. This best practices guide outlines steps the users can take to better protect personal devices and information.
Maruthi Prithivirajan, Head of ASEAN & IN Solution Architecture, Neo4j
Get an inside look at the latest Neo4j innovations that enable relationship-driven intelligence at scale. Learn more about the newest cloud integrations and product enhancements that make Neo4j an essential choice for developers building apps with interconnected data and generative AI.
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!SOFTTECHHUB
As the digital landscape continually evolves, operating systems play a critical role in shaping user experiences and productivity. The launch of Nitrux Linux 3.5.0 marks a significant milestone, offering a robust alternative to traditional systems such as Windows 11. This article delves into the essence of Nitrux Linux 3.5.0, exploring its unique features, advantages, and how it stands as a compelling choice for both casual users and tech enthusiasts.
Climate Impact of Software Testing at Nordic Testing DaysKari Kakkonen
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
UiPath Test Automation using UiPath Test Suite series, part 5DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 5. In this session, we will cover CI/CD with devops.
Topics covered:
CI/CD with in UiPath
End-to-end overview of CI/CD pipeline with Azure devops
Speaker:
Lyndsey Byblow, Test Suite Sales Engineer @ UiPath, Inc.
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
UiPath Test Automation using UiPath Test Suite series, part 6DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
How to Get CNIC Information System with Paksim Ga.pptxdanishmna97
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
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Development Practices: Best practices for creating, maintaining, and scaling open-source libraries, including code hygiene, CI/CD, and fast iteration.
Community Building: Strategies for making adoption easy, iterating quickly, and fostering a vibrant, engaged community.
Marketing: Both online and offline marketing tactics, focusing on real, impactful interactions and collaborations.
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Key insights include the importance of automation, making the adoption process seamless, and leveraging offline interactions for marketing. The presentation also emphasizes the need for continuous small improvements and building a friendly, inclusive community that contributes to the project's growth.
Vladimir Iglovikov brings his extensive experience as a Kaggle Grandmaster, ex-Staff ML Engineer at Lyft, sharing valuable lessons and practical advice for anyone looking to enhance the adoption of their open-source projects.
Explore more about Albumentations and join the community at:
GitHub: https://github.com/albumentations-team/albumentations
Website: https://albumentations.ai/
LinkedIn: https://www.linkedin.com/company/100504475
Twitter: https://x.com/albumentations
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
2. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
2
Boussinesq Equation for subsurface flow (theory)
s
∂η
∂t
= ∇ · [KS H(η, x, y) ∇η] + Q
2D Boussinesq Equation: water mass balance in a point + Darcy’s law
Symbol Dimension Definition
s, s(x,y) porosity
t [T] time
x,y [L] space (planimetric) coordinate
H,H(x, y, η) [L] water-table thickness
KS [L T -1
] saturated hydraulic conductivity
Q [L T -1
] source term (water-table discharge)
η, η(x, y, t) [L] water surface elevation in a generic point (x, y, t)
Friday, June 7, 2013
3. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
3
Boussinesq Equation for subsurface flow (theory)
s
∂η
∂t
= ∇ · [KS H(η, x, y) ∇η] + Q
accumulation term: time derivative of water content
Symbol Dimension Definition
s, s(x,y) porosity
t [T] time
x,y [L] space (planimetric) coordinate
H,H(x, y, η) [L] water-table thickness
KS [L T -1
] saturated hydraulic conductivity
Q [L T -1
] source term (water-table discharge)
η, η(x, y, t) [L] water surface elevation in a generic point (x, y, t)
Friday, June 7, 2013
4. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
4
Boussinesq Equation for subsurface flow (theory)
sfrac {partial eta} {partial t} = nabla cdot left[ K_S , H (eta,x,y) , nabla eta right]+Q
s
∂η
∂t
= ∇ · [KS H(η, x, y) ∇η] + Q
(-) divergence of water flux (vector) described by Darcy’law
Symbol Dimension Definition
s, s(x,y) porosity
t [T] time
x,y [L] space (planimetric) coordinate
H,H(x, y, η) [L] water-table thickness
KS [L T -1
] saturated hydraulic conductivity
Q [L T -1
] source term (water-table discharge)
η, η(x, y, t) [L] water surface elevation in a generic point (x, y, t)
Friday, June 7, 2013
5. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
5
Boussinesq Equation for subsurface flow (theory)
sfrac {partial eta} {partial t} = nabla cdot left[ K_S , H (eta,x,y) , nabla eta right]+Q
s
∂η
∂t
= ∇ · [KS H(η, x, y) ∇η] + Q
source term (water-table dicharge due to rainfall or sinks, etc.
Symbol Dimension Definition
s, s(x,y) porosity
t [T] time
x,y [L] space (planimetric) coordinate
H,H(x, y, η) [L] water-table thickness
KS [L T -1
] saturated hydraulic conductivity
Q [L T -1
] source term (water-table discharge)
η, η(x, y, t) [L] water surface elevation in a generic point (x, y, t)
Friday, June 7, 2013
6. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
6
Boussinesq Equation for subsurface flow (theory)
sfrac {partial eta} {partial t} = nabla cdot left[ K_S , H (eta,x,y) , nabla eta right]+Q
s
∂η
∂t
= ∇ · [KS H(η, x, y) ∇η] + Q
2D Boussinesq Equation: water mass balance in a point + Darcy’s law
Symbol Dimension Definition
s, s(x,y) porosity
t [T] time
x,y [L] space (planimetric) coordinate
H,H(x, y, η) [L] water-table thickness
KS [L T -1
] saturated hydraulic conductivity
Q [L T -1
] source term (water-table discharge)
η, η(x, y, t) [L] water surface elevation in a generic point (x, y, t)
Friday, June 7, 2013
7. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
7
Vi(ηn+1
i ) − ∆tn
j∈Si
KS Aj(ηn
i,m(i,j))
ηn+1
m(i,j) − ηn+1
i
δi,m(i,j)
= Vi(ηn
i ) + ∆ tn
Qn+1
i pi
Discretized Boussinesq Equation (implicit)
water volume at the next time step (unknown)
Symbol Dimension Definition
l(j) index of the cell on the left-hand side of the j-th line segment
m(i,j) index of the cell that shares the j-th line segment with the i-th cell
pi [L2
] topographic area of the i-th cell
r(j) index of the cell on the right-hand side of the j-th line segment
Ai(ηr(j),l(j)) [L2
] Vertical area over the j-th line
Qn
i [L T -1
] source term (water-table discharge) at the i-th cell in the n-th time instant
Si * set of the edges of the i-th cell
Vi(ηi) [L3
] water volume stored in the i-th cell defined as a function of water surface elevation ηi
V(η) [L3
] vectors of water volume stored each cell defined as a function of vector of water surface elevation η
δiq [L] euclidean distance between the centroids of the i-th and q-th cells
ηi [L] water surface elevation at the i-th cell
ηi,d [L] averaged water surface elevation between the i-th and d-th cells
ηn
i [L] water surface elevation at the i-th cell in the n-th time instant
∆tn
[T] time step between the n-th and the (n+1)-th time instants
Friday, June 7, 2013
8. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
8
Vi(ηn+1
i ) − ∆tn
j∈Si
KS Aj(ηn
i,m(i,j))
ηn+1
m(i,j) − ηn+1
i
δi,m(i,j)
= Vi(ηn
i ) + ∆ tn
Qn+1
i pi
Discretized Boussinesq Equation (implicit)
net out-going fluxes (unknown) derived by discretized Darcy’s Law
Symbol Dimension Definition
l(j) index of the cell on the left-hand side of the j-th line segment
m(i,j) index of the cell that shares the j-th line segment with the i-th cell
pi [L2
] topographic area of the i-th cell
r(j) index of the cell on the right-hand side of the j-th line segment
Ai(ηr(j),l(j)) [L2
] Vertical area over the j-th line
Qn
i [L T -1
] source term (water-table discharge) at the i-th cell in the n-th time instant
Si * set of the edges of the i-th cell
Vi(ηi) [L3
] water volume stored in the i-th cell defined as a function of water surface elevation ηi
V(η) [L3
] vectors of water volume stored each cell defined as a function of vector of water surface elevation η
δiq [L] euclidean distance between the centroids of the i-th and q-th cells
ηi [L] water surface elevation at the i-th cell
ηi,d [L] averaged water surface elevation between the i-th and d-th cells
ηn
i [L] water surface elevation at the i-th cell in the n-th time instant
∆tn
[T] time step between the n-th and the (n+1)-th time instants
Friday, June 7, 2013
9. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
9
Vi(ηn+1
i ) − ∆tn
j∈Si
KS Aj(ηn
i,m(i,j))
ηn+1
m(i,j) − ηn+1
i
δi,m(i,j)
= Vi(ηn
i ) + ∆ tn
Qn+1
i pi
Discretized Boussinesq Equation (implicit)
water volume at the previous time step (known)
Symbol Dimension Definition
l(j) index of the cell on the left-hand side of the j-th line segment
m(i,j) index of the cell that shares the j-th line segment with the i-th cell
pi [L2
] topographic area of the i-th cell
r(j) index of the cell on the right-hand side of the j-th line segment
Ai(ηr(j),l(j)) [L2
] Vertical area over the j-th line
Qn
i [L T -1
] source term (water-table discharge) at the i-th cell in the n-th time instant
Si * set of the edges of the i-th cell
Vi(ηi) [L3
] water volume stored in the i-th cell defined as a function of water surface elevation ηi
V(η) [L3
] vectors of water volume stored each cell defined as a function of vector of water surface elevation η
δiq [L] euclidean distance between the centroids of the i-th and q-th cells
ηi [L] water surface elevation at the i-th cell
ηi,d [L] averaged water surface elevation between the i-th and d-th cells
ηn
i [L] water surface elevation at the i-th cell in the n-th time instant
∆tn
[T] time step between the n-th and the (n+1)-th time instants
Friday, June 7, 2013
10. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
10
Vi(ηn+1
i ) − ∆tn
j∈Si
KS Aj(ηn
i,m(i,j))
ηn+1
m(i,j) − ηn+1
i
δi,m(i,j)
= Vi(ηn
i ) + ∆ tn
Qn+1
i pi
Discretized Boussinesq Equation (implicit)
source term (in-coming water volume during the time-step) (known)
Symbol Dimension Definition
l(j) index of the cell on the left-hand side of the j-th line segment
m(i,j) index of the cell that shares the j-th line segment with the i-th cell
pi [L2
] topographic area of the i-th cell
r(j) index of the cell on the right-hand side of the j-th line segment
Ai(ηr(j),l(j)) [L2
] Vertical area over the j-th line
Qn
i [L T -1
] source term (water-table discharge) at the i-th cell in the n-th time instant
Si * set of the edges of the i-th cell
Vi(ηi) [L3
] water volume stored in the i-th cell defined as a function of water surface elevation ηi
V(η) [L3
] vectors of water volume stored each cell defined as a function of vector of water surface elevation η
δiq [L] euclidean distance between the centroids of the i-th and q-th cells
ηi [L] water surface elevation at the i-th cell
ηi,d [L] averaged water surface elevation between the i-th and d-th cells
ηn
i [L] water surface elevation at the i-th cell in the n-th time instant
∆tn
[T] time step between the n-th and the (n+1)-th time instants
Friday, June 7, 2013
11. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
11
Vi(ηn+1
i ) − ∆tn
j∈Si
KS Aj(ηn
i,m(i,j))
ηn+1
m(i,j) − ηn+1
i
δi,m(i,j)
= Vi(ηn
i ) + ∆ tn
Qn+1
i pi
Discretized Boussinesq Equation (implicit)
Water volume budget for each cell of the domain (algebaraic equation system)
Symbol Dimension Definition
l(j) index of the cell on the left-hand side of the j-th line segment
m(i,j) index of the cell that shares the j-th line segment with the i-th cell
pi [L2
] topographic area of the i-th cell
r(j) index of the cell on the right-hand side of the j-th line segment
Ai(ηr(j),l(j)) [L2
] Vertical area over the j-th line
Qn
i [L T -1
] source term (water-table discharge) at the i-th cell in the n-th time instant
Si * set of the edges of the i-th cell
Vi(ηi) [L3
] water volume stored in the i-th cell defined as a function of water surface elevation ηi
V(η) [L3
] vectors of water volume stored each cell defined as a function of vector of water surface elevation η
δiq [L] euclidean distance between the centroids of the i-th and q-th cells
ηi [L] water surface elevation at the i-th cell
ηi,d [L] averaged water surface elevation between the i-th and d-th cells
ηn
i [L] water surface elevation at the i-th cell in the n-th time instant
∆tn
[T] time step between the n-th and the (n+1)-th time instants
Friday, June 7, 2013
12. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
12
V(ηn+1
) + T · ηn+1
= b3
b3i = Vi(ηn
i ) + ∆ tn
Qn+1
i pi
T · ηn+1
i
= −∆tn
j∈Si
KS Aj(ηn
i,m(i,j))
ηn+1
m(i,j) − ηn+1
i
δi,m(i,j)
Symbol Dimension Definition
b3 [L3
] vector of known terms
T [L2
] symmetric matrix introduced in the equation systems derived by Darcy’s law
V(η) [L3
] vectors of water volume stored each cell defined as a function of vector of water surface e
Nonlinear Algebraic Equation System
Friday, June 7, 2013
13. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
13
m+1
ηn+1
=m
ηn+1
−
Ws(m
ηn+1
) + T
−1
V(m
ηn+1
) + T ·m
ηn+1
− b3
Wsi(ψi) =
dVi(ηi)
dηi
Nonlinear Algebraic Equation System (2)
•Resolution with a Newton-like iterative scheme (Casulli,2008):
Symmetric and Positive-Defined Matrix which is solved with
the Conjugate Gradient Method
where
Friday, June 7, 2013
14. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
14
Algorithm of the Conjugate Gradient Method from “ A
Introduction to the Conjugate Gradient Method Without the
Agonizing Pain” by Jonathan Richard Shewchuk, 1994
(http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)
Friday, June 7, 2013
15. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
15
Boussinesq Equation for subsurface flow:
Results of two simulations of water drainege in a
mountain catchment
Friday, June 7, 2013
16. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
16
A “drying” study case: Matsch Valley,
(bottom elevation [m] at 20 m resolution
Friday, June 7, 2013
17. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
17
Initial Conditions and Parameters
(*) water table 1 m over the averaged elevation of the cell of the coarse
grid (in this case averaged on the 60 m resolution)
No rainfall, impermeable boundary condition
Index kS [m/s] Porosity Basin Code Cell Res. [m] ∆t [s] Initial Conditions
1 10−1
0.4 Matsch v2.1.4 60 104
1 m of w.th.(*)
2 10−1
0.4 Matsch v3.1 60 104
1 m of w.th.(*)
Code according to Brugnano Casulli, 2008 (v2.1.4) , general case (v3.1)
Friday, June 7, 2013
18. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
18
Water Table Thickness (case 1)
[cm]
time 10^4 s time 10^5 s time 10^6 s time 5 10^6 s
Friday, June 7, 2013
19. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
19
Water Table Thickness (case 2)
[cm]
time 10^4 s time 10^5 s time 10^6 s time 5 10^6 s
Friday, June 7, 2013
20. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
20
Resume
Index Stored Water Volume [m3
] Global Relative Error
1 3.94 · 107
10−7
2 3.94 · 107
10−7
Friday, June 7, 2013
21. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
21
Analysis of the number of iterations: CG and NP vs time
0e+00 1e+06 2e+06 3e+06 4e+06
050010001500200025003000
Max CG Iterations in a time step
time
0e+00 1e+06 2e+06 3e+06 4e+06
0246810
Newton/Picard Iteration in a time step
time
Newton-PicardIterationinatimestep
v2.1.4 (blue) , v3.1 (red)
Friday, June 7, 2013
22. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
22
0 500 1000 1500 2000 2500 3000
05001000150020002500
Max Iteration of Conjugate Gradient Method (v3.1 vs v2.1.4)
Max CG Iterations in v2.4.1
MaxCGIterationsinv3.1
Analysis of the number of CG iterations: v2.1.4 vs v3.1
Friday, June 7, 2013
23. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
23
Work in Progress: simulation with v3.1
Index kS [m/s] Porosity Basin FG Res.[m] CG Res. [m] Initial Conditions
3 10−1
0.4 Matsch 20 60 1 m of w.th. over CG (averaged)
Water thickness [cm] at 10^6 s
Too many CG iterations: more
than 2000 per each time step
Friday, June 7, 2013
24. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
24
Preconditioner from “ An Introduction to the Conjugate Gradient
Method Without the Agonizing Pain” by Jonathan Richard
Shewchuk, 1994
(http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)
conditioning number
number of CG iteration
tollerance
Friday, June 7, 2013
25. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
25
Preconditioner (algorithm): http://www.cs.cmu.edu/~quake-
papers/painless-conjugate-gradient.pdf
Friday, June 7, 2013
26. Double-grid 2D solver for Boussinesq Equation
Emanuele Cordano
26
Major details about the numerical theory with newer applications are now
discussed by Cordano and Rigon, 2013
Other Numerical references:
Casulli, V. (2009), A high-resolution wetting and drying algorithm for freesurface
hydrodynamics, Int. J. Numer. Methods Fluids, 60(4), 391–408,
doi:10.1002/fld.1896.
Brugnano, L., and V. Casulli (2008), Iterative solution of piecewise linear
systems, J. Sci. Comput., 30(1), 463–472.
Friday, June 7, 2013