Numerical analysis | Numerical differential equations
The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem. It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they are a single source. The FMM has also been applied in accelerating the iterative solver in the method of moments (MOM) as applied to computational electromagnetics problems. The FMM was first introduced in this manner by Leslie Greengard and Vladimir Rokhlin Jr. and is based on the multipole expansion of the vector Helmholtz equation. By treating the interactions between far-away basis functions using the FMM, the corresponding matrix elements do not need to be explicitly stored, resulting in a significant reduction in required memory. If the FMM is then applied in a hierarchical manner, it can improve the complexity of matrix-vector products in an iterative solver from to in finite arithmetic, i.e., given a tolerance , the matrix-vector product is guaranteed to be within a tolerance The dependence of the complexity on the tolerance is , i.e., the complexity of FMM is . This has expanded the area of applicability of the MOM to far greater problems than were previously possible. The FMM, introduced by Rokhlin Jr. and Greengard has been said to be one of the top ten algorithms of the 20th century. The FMM algorithm reduces the complexity of matrix-vector multiplication involving a certain type of dense matrix which can arise out of many physical systems. The FMM has also been applied for efficiently treating the Coulomb interaction in the Hartree–Fock method and density functional theory calculations in quantum chemistry. (Wikipedia).
Multimeter Review / DMM Review / buyers guide / tutorial
A list of my multimeters can be purchased here: http://astore.amazon.com/m0711-20?_encoding=UTF8&node=5 In this video I do a review of several digital multimeters. I compare features and functionality. I explain safety features, number of digits, display count, accuracy and resolution. Th
From playlist Multimeter reviews, buyers guide and comparisons.
How to use a Multimeter for beginners: Part 1 - Voltage measurement / Multimeter tutorial
Visit my website for more Tips, Videos, DIY projects and more: http://www.mjlorton.com/ --------------------- Click "Show more" ------------------------------- Multimeter tutorial - This series of videos is a tutorial on how to use a digital multimeter for beginners. It will also explain
From playlist How to use a multimeter for beginners
How to use a Multimeter for beginners: Part 3 - Resistance and Continuity
Visit my website for more Tips, Videos, DIY projects and more: http://www.mjlorton.com/ --------------------- Click "Show more" ------------------------------- Multimeter tutorial - This series of videos is a tutorial on how to use a digital multimeter for beginners. It will also explain
From playlist How to use a multimeter for beginners
Solving an equation with variables on both side and one solution
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist Solve Multi-Step Equations......Help!
Solve an equation for x by clearing fractions with multiple steps
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
Self-force and radiation reaction in general relativity by Adam Pound ( Lecture 4 )
PROGRAM SUMMER SCHOOL ON GRAVITATIONAL WAVE ASTRONOMY ORGANIZERS : Parameswaran Ajith, K. G. Arun and Bala R. Iyer DATE : 15 July 2019 to 26 July 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore This school is part of the annual ICTS summer schools on gravitational-wave (GW) astronomy.
From playlist Summer School on Gravitational Wave Astronomy -2019
Benjamin Stamm: An embedded corrector problem for stochastic homogenization
The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Numerical Inverse and Stochastic Homogenization. (14.02.2017) A very efficient algorithm has recently been introduced in [1] in order to approximate the solution of implicit solva
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Lecture 24 (CEM) -- Introduction to Variational Methods
This lecture introduces to the student to variational methods including finite element method, method of moments, boundary element method, and spectral domain method. It describes the Galerkin method for transforming a linear equation into matrix form as well as populating the global matr
From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering
David Keyes : To compute, to breathe: computing in the 21st century university
David Keyes, founding dean of the King Abdullah University of Science and Technology's (KAUST) division of Computer, Electrical, and Mathematical Sciences and Engineering, delivers the opening keynote address at the IEEE Cluster 2013 Conference, September 24, 2013, in Indianapolis. This c
From playlist 2013 IEEE Cluster Conference plenary presentations
François Alouges : The sparse cardinal sine decomposition and applications
Abstract : When solving wave scattering problems with the Boundary Element Method (BEM), one usually faces the problem of storing a dense matrix of huge size which size is proportional to the (square of) the number N of unknowns on the boundary of the scattering object. Several methods, am
From playlist Numerical Analysis and Scientific Computing
FFT based spectral Ewald methods as an alternative to multipole methods – A.-K. Tornberg – ICM2018
Numerical Analysis and Scientific Computing Invited Lecture 15.5 FFT based spectral Ewald methods as an alternative to fast multipole methods Anna-Karin Tornberg Abstract: In this paper, we review a set of fast and spectrally accurate methods for rapid evaluation of three dimensional ele
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Live CEOing Ep 41: n-Body Problem in the Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about n-Body Problem in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
New Architectures for a New Biology
October 11, 2006 lecture by David E. Shaw for the Stanford University Computer Systems Colloquium (EE 380). This talk describes the current state of the art in biomolecular simulation and explore the potential role of high-performance computing technologies in extending current capabili
From playlist Course | Computer Systems Laboratory Colloquium (2006-2007)
Solving a multi-step equation by multiplying by the denominator
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
With a variable on both sides solving a multi step equation two ways
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
Solve an equation with a variable on both sides of the equation
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
How to use a Multimeter for beginners: Part 2a - Current measurement
Visit my website for more Tips, Videos, DIY projects and more: http://www.mjlorton.com/ --------------------- Click "Show more" ------------------------------- Multimeter tutorial - This series of videos is a tutorial on how to use a digital multimeter for beginners. It will also explain
From playlist How to use a multimeter for beginners
Gravitational radiation from post-Newtonian sources.... by Luc Blanchet (Lecture - 5)
PROGRAM SUMMER SCHOOL ON GRAVITATIONAL WAVE ASTRONOMY ORGANIZERS : Parameswaran Ajith, K. G. Arun and Bala R. Iyer DATE : 15 July 2019 to 26 July 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore This school is part of the annual ICTS summer schools on gravitational-wave (GW) astronomy.
From playlist Summer School on Gravitational Wave Astronomy -2019
Solving an equation with fraction where your variable is on both sides
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides