Numerical analysis | Numerical differential equations

Boundary knot method

In numerical mathematics, the boundary knot method (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme. Recent decades have witnessed a research boom on the meshfree numerical PDE techniques since the construction of a mesh in the standard finite element method and boundary element method is not trivial especially for moving boundary, and higher-dimensional problems. The boundary knot method is different from the other methods based on the , such as boundary element method, method of fundamental solutions and singular boundary method in that the former does not require special techniques to cure the singularity. The BKM is truly meshfree, spectral convergent (numerical observations), symmetric (self-adjoint PDEs), integration-free, and easy to learn and implement. The method has successfully been tested to the Helmholtz, diffusion, convection-diffusion, and Possion equations with very irregular 2D and 3D domains. (Wikipedia).

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The Best Guide to Rope Skills

This step by step guide demonstrates tying 15 types: 00:36 Overhand 01:22 Square 02:36 Figure Eight 03:40 Bowline, 05:29 Running 06:19 Half, 07:45 Timber, 09:42 Rolling, 10:43 Clove Hitches 11:30 Cat's Paw 12:58 Single, 14:40 Double Sheet or Becket Bends 15:30 Fisherman's, 17:09 Doubl

From playlist How To Tutorials

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How to Tie a Taut Line Knot

This knot is very useful for adjusting tie downs quickly and easily. For example, a tarp could be held down by a series of these knots and be made very tight so the wind cannot make it rise, and easily be removed simply by sliding the knots later. A taut line knot is also used to keep larg

From playlist Practical Projects & Skills

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Knots and surfaces II | Algebraic Topology | NJ Wildberger

In the 1930's H. Siefert showed that any knot can be viewed as the boundary of an orientable surface with boundary, and gave a relatively simple procedure for explicitly constructing such `Seifert surfaces'. We show the algorithm, exhibit it for the trefoil and the square knot, and then di

From playlist Algebraic Topology

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Fast Necktie Knot

I saw that one day on Korean TV. With little practice, it takes about half the time than the normal method. Actually, I'm rather slow on this video. I can do it in around 7 seconds.

From playlist Other...

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Gluing a Torus

Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus. Often the fundamental group of the glued object can be calculated from the pieces (here a rectangles) and the glue (here two intersecting circles). Th

From playlist Algebraic Topology

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How to Tie the Most Useful Knot in the World (Bowline)

This is a short video to help those who have seen many of my past videos where I use a bowline knot. This is the most useful knot you will ever learn. It will not slip when in use, and comes undone easily even after being tightened under thousands of pounds. #NightHawkInLight -~-~~-~~~-~~

From playlist Practical Projects & Skills

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Make A Combination Lock - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

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Untangling the beautiful math of KNOTS

Visit ► https://brilliant.org/TreforBazett/ to help you learn STEM topics for free, and the first 200 people will get 20% off an annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Suppose yo

From playlist Cool Math Series

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Cut The Knot Action 12!

Link: https://www.geogebra.org/m/a72HSgzU

From playlist Geometry: Challenge Problems

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Knotty Problems - Marc Lackenby

Knots are a familiar part of everyday life, for example tying your tie or doing up your shoe laces. They play a role in numerous physical and biological phenomena, such as the untangling of DNA when it replicates. However, knot theory is also a well-developed branch of pure mathematics.

From playlist Oxford Mathematics Public Lectures

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Joel Hass - Lecture 1 - Algorithms and complexity in the theory of knots and manifolds - 18/06/18

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From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects

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Marc Lackenby - Using machine learning to formulate mathematical conjectures - IPAM at UCLA

Recorded 14 February 2023. Marc Lackenby of the University of Oxford presents "Using machine learning to formulate mathematical conjectures" at IPAM's Machine Assisted Proofs Workshop. Abstract: I will describe how machine learning can be used as a tool for pure mathematicians to formulate

From playlist 2023 Machine Assisted Proofs Workshop

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Kai Smith: Character Varieties of Tangles and Singular Instanton Homology

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From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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Ed Witten -- From Gauge Theory to Khovanov Homology Via Floer Theory

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From playlist Research Lectures

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Jessica Purcell - Lecture 3 - Knots in infinite volume 3-manifolds

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From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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Knot contact homology and partially wrapped Floer homology - Lenhard Ng

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From playlist Workshop on Homological Mirror Symmetry: Methods and Structures

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Algebraic topology: Fundamental group of a knot

This lecture is part of an online course on algebraic topology. We calculate the fundamental group of (the complement of) a knot, and give a couple of examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52yxQGxQoxwOtjIEtxE2BWx

From playlist Algebraic topology

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The Computational Complexity of Geometric Topology Problems - Greg Kuperberg

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From playlist Mathematics

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Differential Equations: Separation of Variables

This video provides several examples of how to solve a DE using the technique of separation of variables. website: http://mathispower4u.com blog: http://mathispower4u.wordpress.com

From playlist First Order Differential Equations: Separation of Variables

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Results on abundance of global surfaces of section - Umberto Hryniewicz

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From playlist Mathematics

Related pages

Finite volume method | Boundary element method | Finite element method | Method of fundamental solutions | Singular boundary method | Boundary particle method