An open source thermodynamic modeling package completed on behalf of NASA. The Toolbox for the Modeling and Analysis of Thermodynamic Systems (T-MATS) package offers a MATLAB/Simulink toolbox that gives a developer the ability to create simulations of such thermodynamic systems as turbomachinery and gas turbines. Keywords: TMATS, Control System, Numerical Methods, Newton-Raphson, Jacobian Calculation, Propulsion, Aircraft Engine, Jet, Turbofan, Turbojet, Compressor, Turbine, Nozzle, Inlet, open source

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OpenMDAO is a high-performance computing platform for systems analysis and optimization that enables you to decompose your models, making them easier to build and maintain, while still solving them in a tightly-coupled manner with efficient parallel numerical methods.

Topology optimization with finite element analysis in FEniCS. Final project for CSCI-GA.2420: Numerical Methods II at New York University.

Numerical Methods in Haskell with Applications to Data Analysis, Finance and Physics

This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting rules, basis update methods, and sensitivity analysis.

Methods in numerical analysis. Includes: Lagrange interpolation, Chebyshev polynomials for optimal node spacing, iterative techniques to solve linear systems (Gauss-Seidel, Jacobi, SOR), SVD, PCA, and more.

As the field of Computational Fluid Dynamics (CFD) progresses, the fluid flows are more and more analysed by using simulations with the help of high speed computers. In order to solve and analyse these fluid flows we require intensive simulation involving mathematical equations which governs the fluid flow, these are Navier Stokes (NS) equation. Solving these equations has become a necessity as almost every problem which is related to fluid flow analysis call for solving of Navier Stokes equation. These NS equations are partial differential equations so different numerical methods are used to solve these equations. Solving these partial differential equations so different numerical methods requires large amount of computing power and huge amount of memory is in play. Only practical feasible way to solve these equation is write a parallel program to solve them, which can then be run on powerful hardware capable of parallel processing to get the desired results High speed supercomputer will provide us very good performance in terms of reduction in execution time. In paper focus will be on finite volume as a numerical method. We will also see what GPGPU (General-Purpose computing on Graphics Processing Units) is and how we are taking its advantages to solve CFD problems.

A set of notebooks related to convex optimization, variational inference and numerical methods for signal processing, machine learning, deep learning, graph analysis, bayesian programming, statistics or astronomy.

Numerics is a free and open-source library for .NET developed by USACE-RMC, providing a comprehensive set of methods and algorithms for numerical computations and statistical analysis.

SuanShu is a math library of numerical methods for numerical analysis. - http://numericalmethod.com/up/suanshu/

Numerical analysis methods implemented in Python.

A detailed educational guide explaining two essential NLP techniques, TF-IDF and Word2Vec. Learn how text is transformed into numerical vectors, compare their mathematical foundations, explore real-world use cases, and implement both methods in Python for text analysis and machine learning.

This project aims to study the impact of climate change on groundwater level in Mornag plain in Tunisia. Indeed, in the last few decades, aquifers all over the world have experienced notable water level variability due to the spatiotemporal variability of rainfall and temperature. Therefore, for a reliable groundwater management under climate change context, it is mandatory to analyze and estimate its level variability. In this study, we focus on the plain of Mornag, located in the southeast of Tunisia, since it represents 33% of the national agricultural production. From this plain, we have collected historical piezometric and pluviometric data covering the period 2005-2017. Knowing the pluviometric data, our goal is to predict the piezometric one. This issue has been already studied using classical numerical groundwater modeling such as Modflow and Feflow. Despite unsatisfactory results, these techniques are data and time consuming. To overcome all these drawbacks, we propose to use two Artificial Intelligence (AI) approaches: the Extreme Gradient Boosting (XGBoost) approach, that has shown great performances in literature, and the well used one in our context which involves the use of Long-Short Term Memory (LSTM) Neural Network. For better results, we have added supplementary features to our dataset such as the cluster zone (zones with same characteristics) and the Standardized Precipitation Index (SPI) which can identify drought at different time scales. Both approaches have been executed entirely on GPU for time acceleration. Compared with traditional existing methods, they both have shown a high level of accuracy which confirms their adequacy for groundwater level forecasting. The proposed prediction models will be used for evaluating the repercussions of climate change on groundwater levels under the different scenarios RCP 4.5 and RCP 8.5 for the period of 2017-2090. It will be evaluated for three future periods: 2017-2040 (short term), 2041-2065 (medium term) and 2066-2090 (long term). The analysis of the future results using AI will be considered as a new Decision Support System used to optimize the management of our limited resources in order to satisfy the needs of the population in terms of drinking water and agriculture production.

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Numerical illustration of a novel analysis framework for consensus-based optimization (CBO) and numerical experiments demonstrating the practicability of the method

Computational Methods for Numerical Analysis

Compute the motion of droplets and particles in Stokes flows in axisymmetric domains using the Boundary Element Method (BEM) or the Spectral Boundary Integral Method (SBIM). The code is written in MATLAB with some possibility to use pre-compiled c-fuctions. The code includes: direct numerical simulations (DNS) with time stepping, Newton method, Continuation Method, Linear Stability Analysis and Edge Tracking Method.

This is a comprehensive MATLAB-based software platform developed for real-time measurement and feedback control of a custom mask-projection photopolymerization based additive manufacturing system (referred as "ECPL", i.e., Exposure Controlled Projection Lithography) using a lab-built interferometry (referred as "ICM&M", i.e., Interferometric Curing Monitoring and Measurement). A graphical user interface using the graphical user interface development environment (GUIDE) of MATLAB was created to implement the ICM&M method for the ECPL process. The software interfaces with the hardware of the ECPL system’s ultraviolet lamp and DMD, and the ICM&M system’s camera. It was designed to streamline the operation of the ECPL process with the aid of parallel computing that implements online both the ICM&M acquisition and measurement analysis as well as the feedback control method. The application logs the acquired interferogram video data, performs numerical computations for the ICM&M measurement algorithms and control law, saves the real-time data and measurement results for all voxels in the region of interest. Meanwhile, it displays interferogram frames and visualize the photocuring process without a substantial sacrifice in temporal performance of other key functions such as data acquisition and measurement & control analysis. The software could be extended to real-time process measurement and control for other additive manufacturing systems, for example, metal based additive manufacturing aided by in-situ thermal images analysis.

Ecosystem of numerical methods for microbial kinetics data analysis, from preprocessing to result interpretation.

The reliability analysis is studied for stiffened Kirchhoff's plate bending using the Finite Element Method in MATLAB. We used the Hsieh-Clough-Tocher (HCT) element with 4 nodes and 10 degree of freedom for each triangular element. The applied force and Young’s Modulus were random, and we used the First-Order Reliability Method (FORM). The numerical results and probability of failure were justified and compared with the Finite Element ReliabilityUsing Matlab (FERUM 4.1)

OpenCossan represents the core of COSSAN software. All the algorithms and methods have been coded in a matlab toolbox allowing numerical analysis, reliability analysis, simulation, sensitivity, optimization, robust design and much more. Released under the LGPL license, the engine can be used, modified and redistributed free of charge. It is supported by an extensive documentation and tutorials.

The library provides a set of tools and functions for various subject areas, including Analysis and Data Structures (AISD), Probability Theory and Mathematical Statistics (TViMS), Machine Learning (ML), and Numerical Methods (NM).

Automated codes from Numerical analysis / numerical methods / Numerical calculus algorithms for TI-Nspire cx cas II calculators.

This repository contains the numerical method for calculating the secret key rates of QKD with the finite key analysis.

If you find any errors in the work of algorithms, you can fix them by creating a pull request

Numerical Methods Using Java: For Data Science, Analysis, and Engineering https://www.amazon.com/Numerical-Methods-Using-Java-Engineering/dp/1484267966

同济大学汽车学院课程：计算方法

This is a Numerical Analysis course project, implementing numerical analysis methods.

The finite element method (FEM) is a numerical analysis method for finding the solution to boundary value problems for partial differential equations (PDE). The finite element method has a variety of applications. The most popular application for this method is used for numerical modeling of physical systems in engineering and physics. Using FEM, computers can model thermodynamics, electromagnetism and fluid dynamics.