Boundary particle method: Difference between revisions

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Revision as of 12:35, 3 April 2016

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The boundary particle method (BPM) is a boundary-only discretization of an inhomogeneous partial differential equation by combining the RC-MRM with strong-form meshless boundary collocation discretization schemes, such as the [[method of fundamental solution]] (MFS), [[boundary knot method]] (BKM), [[regularized meshless method]] (RMM), [[singular boundary method]] (SBM), and [[Trefftz method]] (TM). The BPM has been applied to problems such as nonhomogeneous [[Helmholtz]] and [[convection-diffusion equation]]. The BPM interpolation representation is of a [[wavelet]] series.

For the application of the BPM to [[Helmholtz]],<ref name="Chena" /> [[Siméon Denis Poisson|Poisson]]<ref name="Chenb" /> and [[plate bending]] problems,<ref>Fu ZJ, Chen W, Yang W, Winkler plate bending problems by a truly boundary-only boundary particle method. Computational Mechanics 2009,44(6): 757–563</ref> the high-order [[fundamental solution]] or general solution, harmonic function<ref>Hon YC, Wu ZM, A numerical computation for inverse boundary determination problem. Engineering Analysis with Boundary Elements 2000,24(7–8): 599–606</ref> or [[Trefftz]] function (T-complete functions)<ref>Chen W, Fu ZJ, Qin QH, Boundary particle method with high-order Trefftz functions. CMC: Computers, Materials & Continua 2010,13(3): 201–217</ref> are often used, for instance, those of [[Marcel Berger|Berger]]{{Disambiguation needed|date=January 2016}}, [[Peter Winkler|Winkler]]{{dn|date=August 2014}}, and vibrational thin plate equations.<ref>Chen W, Shen ZJ, Shen LJ, Yuan GW, General solutions and fundamental solutions of varied orders to the vibrational thin, the Berger, and the Winkler plates. Engineering Analysis with Boundary Elements 2005,29(7): 699–702</ref> The method has been applied to inverse Cauchy problem associated with [[Siméon Denis Poisson|Poisson]]<ref>Fu ZJ, Chen W, Zhang CZ, Boundary particle method for Cauchy inhomogeneous potential problems. Inverse Problems in Science and Engineering 2012,20(2): 189–207</ref> and nonhomogeneous [[Helmholtz]] equations.<ref>Chen W, Fu ZJ, Boundary particle method for inverse Cauchy problems of inhomogeneous Helmholtz equations. Journal of Marine Science and Technology–Taiwan 2009,17(3): 157–163</ref>

==Further comments==