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 fundamental solutions, 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.
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In numerical mathematics, the boundaryknotmethod (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme. Recent...
numerical methods, called boundary-type RBF collocation method, such as the method of fundamental solution, boundaryknotmethod, singular boundarymethod, boundary...
singular boundarymethod, and regularized meshless method. Radial basis function Boundary element methodBoundaryknotmethodBoundary particle method Singular...
Meshfree method Radial basis function Boundary element method Trefftz methodMethod of fundamental solution Boundaryknotmethod Singular boundarymethod Partridge...
of fundamental solutions (MFS), boundaryknotmethod (BKM), regularized meshless method (RMM), boundary particle method (BPM), modified MFS, and so on...
element methodMethod of fundamental solutions BoundaryknotmethodBoundary particle method Singular boundarymethod A.K. G. Fairweather, The method of fundamental...
methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar diagram called a knot...
Ross–Fahroo pseudospectral methods. According to Ross and Fahroo a pseudospectral (PS) knot is a double Lobatto point; i.e. two boundary points on top of one...
properties. In geometric topology a basic type are embeddings, of which knot theory is a central example, and generalizations such as immersions, submersions...
Boundary layer control refers to methods of controlling the behaviour of fluid flow boundary layers. It may be desirable to reduce flow separation on fast...
a knot, the direction of the wood (grain direction) is up to 90 degrees different from the grain direction of the regular wood. In the tree a knot is...
topology—for example in knot theory—the idea of isotopy is used to construct equivalence relations. For example, when should two knots be considered the same...
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whether or not a knot is trivial is known to be in the complexity classes NP as well as co-NP. The problem of determining the genus of a knot is known to have...
algorithm uses the theory of normal surfaces to find a disk whose boundary is the knot. Haken originally used this algorithm to show that unknotting is...
have a knot with a projecting looped cord between their breasts. Evans noticed that these are analogous to the sacral knot, his name for a knot with a...
i^{th}} knot, n {\displaystyle n} is the number of functions, p {\displaystyle p} refers to the basis functions order. A knot divides the knot span into...
Wilson. She was the creator of the "Gallardo Method," a method of acting where "there are no boundaries, there are no limits, there simply is The Art...
the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves,...
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