Numerical differential equations

In numerical analysis, adaptive mesh refinement (AMR) is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated. When solutions are calculated numerically, they are often limited to pre-determined quantified grids as in the Cartesian plane which constitute the computational grid, or 'mesh'. Many problems in numerical analysis, however, do not require a uniform precision in the numerical grids used for graph plotting or computational simulation, and would be better suited if specific areas of graphs which needed precision could be refined in quantification only in the regions requiring the added precision. Adaptive mesh refinement provides such a dynamic programming environment for adapting the precision of the numerical computation based on the requirements of a computation problem in specific areas of multi-dimensional graphs which need precision while leaving the other regions of the multi-dimensional graphs at lower levels of precision and resolution. This dynamic technique of adapting computation precision to specific requirements has been accredited to Marsha Berger, Joseph Oliger, and Phillip Colella who developed an algorithm for dynamic gridding called local adaptive mesh refinement. The use of AMR has since then proved of broad use and has been used in studying turbulence problems in hydrodynamics as well as in the study of large scale structures in astrophysics as in the Bolshoi Cosmological Simulation. (Wikipedia).

Computational Methods for Numerical Relativity, Part 3 Frans Pretorius

Computational Methods for Numerical Relativity, Part 3 Frans Pretorius Princeton University July 22, 2009

From playlist PiTP 2009

How To Build User-Adaptive Interfaces

Users have indicated many preferences on their devices these days. They want the operating system and apps to look and feel like their own. User-adaptive interfaces are those which are ready to use these preferences to enhance the user experience, to make it feel more at home. If done corr

From playlist Web Design: CSS / SVG

An introduction to Beamforming

This video talks about how we actually have more control over the shape of the beam than just adding additional elements or adjusting the position and orientation of the elements. We can also adjust the gain of the signal to each element and apply phase unevenly to each element, and that

From playlist Understanding Phased Array Systems and Beamforming

Adaptive Quadrature | Lecture 41 | Vector Calculus for Engineers

What is adaptive quadrature? Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1

From playlist Numerical Methods for Engineers

Adaptive Fluid Simulations | Two Minute Papers #10

There are computer programs that can simulate the behavior of fluids, such as water, milk, honey and many others. However, creating detailed simulations takes a really long time, up to days even for a few seconds of video footage. Adaptive algorithms are a class of techniques that try to

From playlist Fluid, Cloth and Hair Simulations (Two Minute Papers)

Astronomy - Ch. 6: Telescopes (13 of 21) Adaptive Optics to Our Atmosphere

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how adaptive optics are use to counter our atmosphere.

From playlist ASTRONOMY 6 TELESCOPES

This video introduces the concept of phased arrays. An array refers to multiple sensors, arranged in some configuration, that act together to produce a desired sensor pattern. With a phased array, we can electronically steer that pattern without having to physically move the array simply b

From playlist Understanding Phased Array Systems and Beamforming

Raúl Tempone: Adaptive strategies for Multilevel Monte Carlo

Abstract: We will first recall, for a general audience, the use of Monte Carlo and Multi-level Monte Carlo methods in the context of Uncertainty Quantification. Then we will discuss the recently developed Adaptive Multilevel Monte Carlo (MLMC) Methods for (i) It Stochastic Differential Equ

From playlist Probability and Statistics

DDPS | Towards reliable, efficient, and automated model reduction of parametrized nonlinear PDEs

Description: Many engineering tasks, such as parametric study and uncertainty quantification, require rapid and reliable solution of partial differential equations (PDEs) for many different configurations. In this talk, we consider goal-oriented model reduction of parametrized nonlinear PD

From playlist Data-driven Physical Simulations (DDPS) Seminar Series

Martin Vohralík: Adaptive inexact Newton methods and their application to multi-phase flows

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Numerical Analysis and Scientific Computing

Tzanio Kolev - Meso and Macroscale Modeling 1 - IPAM at UCLA

Recorded 15 March 2023. Tzanio Kolev of Lawrence Livermore National Laboratory presents "Meso and Macroscale Modeling 1" at IPAM's New Mathematics for the Exascale: Applications to Materials Science Tutorials. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/new-mathematic

From playlist 2023 New Mathematics for the Exascale: Applications to Materials Science Tutorials

Martin Vohralik: A posteriori error estimates and solver adaptivity in numerical simulations

Abstract: We review how to bound the error between the unknown weak solution of a PDE and its numerical approximation via a fully computable a posteriori estimate. We focus on approximations obtained at an arbitrary step of a linearization (Newton-Raphson, fixed point, ...) and algebraic s

From playlist Numerical Analysis and Scientific Computing

MFEM Workshop 2021 | The State of MFEM

The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s first community workshop was held virtually on October 20, 2021, with participants around the world. Learn more about MFEM at https

From playlist MFEM Community Workshop 2021

Numerical Homogenization by Localized Orthogonal Decomposition (Lecture 3) by Daniel Peterseim

DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño

From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)

MFEM Workshop 2022 | High-Order Solvers + GPU Acceleration

The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s second community workshop was held on October 25, 2022, with participants around the world. Learn more about MFEM at https://mfem.o

From playlist MFEM Community Workshop 2022

What is Curve Fitting Toolbox? - Curve Fitting Toolbox Overview

Get a Free Trial: https://goo.gl/C2Y9A5 Get Pricing Info: https://goo.gl/kDvGHt Ready to Buy: https://goo.gl/vsIeA5 Fit curves and surfaces to data using regression, interpolation, and smoothing using Curve Fitting Toolbox. For more videos, visit http://www.mathworks.com/products/curvefi

From playlist Math, Statistics, and Optimization

FEM@LLNL | Computing Meets Cardiology: Making Heart Simulations Fast and Accurate

Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community. On September 13, 2022, Dennis Ogiermann of the University of Bochum presented "Computing Meets Cardiology: Making Heart Simulations Fast

From playlist FEM@LLNL Seminar Series

Stanford Seminar - Rethinking Memory System Design for Data-Intensive Computing

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From playlist Engineering

Wolfram Physics Project: Solving the Einstein Equations & Other PDEs Tuesday, Mar. 9, 2021

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From playlist Wolfram Physics Project Livestream Archive