2011
DOI: 10.1016/j.apm.2010.07.030
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A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems

Abstract: a b s t r a c t This paper presents a meshless method, which replaces the inhomogeneous biharmonic equation by two Poisson equations in terms of an intermediate function. The solution of the Poisson equation with the intermediate function as the right-hand term may be written as a sum of a particular solution and a homogeneous solution of a Laplace equation. The intermediate function is approximated by a series of radial basis functions.Then the particular solution is obtained via employing Kansa's method, whi… Show more

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Cited by 20 publications
(4 citation statements)
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References 35 publications
(37 reference statements)
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“…(15). Furthermore, to estimate the computational accuracy appropriately, the maximum absolute error (E MA ), the root-mean-squared error (E RMS ), and the relative error (E Rel ) are respectively introduced as [20,25,38]                             …”
Section: Verification Of the Present Methods And The Determination Of mentioning
confidence: 99%
“…(15). Furthermore, to estimate the computational accuracy appropriately, the maximum absolute error (E MA ), the root-mean-squared error (E RMS ), and the relative error (E Rel ) are respectively introduced as [20,25,38]                             …”
Section: Verification Of the Present Methods And The Determination Of mentioning
confidence: 99%
“…In the following tests, we obtained the solution of ( 1) by means of DRM, FDRM, CDNN and FCDNN, respectively. Their network size is (120, 60, 50, 50, 40), (60, 60, 50, 50, 40), (100, 50,30,30,20) and (50,50,30,30,20), respectively. It is easy to know that the number of parameters for the methods is 14100, 10800, 14000 and 10000, respectively.…”
Section: Numerical Examplesmentioning
confidence: 99%
“…Based on this coupled scheme, the finite difference technique [9,18,19], finite element technique and mixed element technique [20][21][22][23][24] are naturally used to solve the two second-order equations. In addition, the collocation method [25][26][27] and radial basis functions (RBF) method [28][29][30] are also approaches considered to solve (1).…”
Section: Introductionmentioning
confidence: 99%
“…From 1990, RBFs have been used as meshless (or meshfree) methods [14][15][16][17] to approximate the solutions of partial differential equations (PDEs). [18][19][20][21][22] The so-called Kansa's method is one of the collocation methods, [18] in which the approximate solution is obtained by collocation with RBFs on nodes.…”
Section: Introductionmentioning
confidence: 99%