An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation

By Liviu Marin, Lionel Elliott, Peter J. Heggs, Derek B. Ingham, Daniel Lesnic, X. Wen. 2003

121 citations recorded by the source corpus.

Subfields: Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/72bc698a6c19742a60857250be598566e2a2dba2

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In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

A meshless method for some inverse problems associated with the Helmholtz equation (2006, unknown): “However, a preliminary comparison with the results of Marin et al. [7] shows that the results presented here seem to be more accurate for both exact and noisy data.”
BOUNDARY PARTICLE METHOD FOR INVERSE CAUCHY PROBLEMS OF INHOMOGENEOUS HELMHOLTZ EQUATIONS (2009, methodology): “And the boundary element method (BEM) with iterative or regularization techniques has been applied for the Cauchy problems in the literature [24, 25].”
An alternating iterative procedure for the Cauchy problem for the Helmholtz equation (2014, methodology): “[16] implemented the alternating iterative algorithm formulated in [17] for a purely imaginary number k and in that case, they solved the Cauchy problem for the modified Helmholtz equation, i.”
Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation (2004, methodology): “A detailed numerical implementation of this algorithm can be found in Reference [14] where it was shown that the iterative algorithm produces a convergent and stable numerical solution for the Cauchy problem considered, provided that a regularizing stopping criterion is used.”
Two regularization methods for the Cauchy problems of the Helmholtz equation (2010, methodology): “Several numerical methods have been proposed to solve this problem, such as the boundary element method (BEM) [14], the conjugate gradient method [4,16], the Landweber method [15], the singular value decomposition (SVD) method [16], the method of fundamental solutions (MFS) [13,17,18], the boundary ”
BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method (2004, methodology): “A BEM with constant boundary elements [15,16] is used in order to discretise the problem given by Eqs.”
The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations (2005, unknown): “[32,33] have solved the Cauchy problem for Helmholtztype equations by employing the BEM in conjunction with an alternating iterative algorithm and the conjugate gradient method, respectively.”
Application of the Generalized Finite-Difference Method to Inverse Biharmonic Boundary-Value Problems (2014, methodology): “[8] analyzed the Cauchy problems governed by the Helmholtz equation.”