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The Modified Collocation Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm for the Inverse Boundary Determination Problem for the Biharmonic Equation

Published online by Cambridge University Press:  29 January 2013

H.-F. Chan  and
C.-M. Fan
H.-F. Chan
Affiliation:
Department of Harbor and River Engineering & Computation and Simulation Center, National Taiwan Ocean University, Keelung, Taiwan 20224, R.O.C.
C.-M. Fan*
Affiliation:
Department of Harbor and River Engineering & Computation and Simulation Center, National Taiwan Ocean University, Keelung, Taiwan 20224, R.O.C.
*
*Corresponding author (, [email protected])
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Abstract

In this paper, the modified collocation Trefftz method (MCTM) and the exponentially convergent scalar homotopy algorithm (ECSHA) are adopted to analyze the inverse boundary determination problem governed by the biharmonic equation. The position for part of the boundary with given boundary condition is unknown and the position for the rest of the boundary with overspecified Cauchy boundary conditions is given a priori. Since the spatial position for portion of boundary is not given a priori, it is extremely difficult to solve such a boundary determination problem by any numerical scheme. In order to stably solve the boundary determination problem, the MCTM will be adopted in this study owing to that it can avoid the generation of mesh grid and numerical integration. When this problem is modeled by MCTM, a system of nonlinear algebraic equations will be formed and then be solved by ECSHA. Some numerical examples will be provided to demonstrate the ability and accuracy of the proposed scheme. In addition, the stability of the proposed meshless method will be tested by adding some noise into the prescribed boundary conditions and then to see how does that affect the numerical results.

Keywords

Boundary determination problemModified collocation Trefftz methodExponentially convergent scalar homotopy algorithmBoundary-type meshless methodBiharmonic equation
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 363 - 372
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

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