Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations
By Liviu Marin, Lionel Elliott, Peter J. Heggs, Derek B. Ingham, Daniel Lesnic, X. Wen. 2003
132 citations recorded by the source corpus.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/33b4fec245f764bef110e908f193dddadf76249e
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In Computational Mechanics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- 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.”
- Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation (2004, methodology): “[14, 15] have solved the Cauchy problem associated to the Helmholtz equation using the BEM in conjunction with an alternating iterative procedure consisting of obtaining successive solutions to well-posed mixed boundary value problems and with the conjugate gradient method (CGM), respectively.”
- 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.”