Boundary control for inverse Cauchy problems of the Laplace equations
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Bibliographic record
Abstract
Abstract: The method of fundamental solu-tions is coupled with the boundary control tech-nique to solve the Cauchy problems of theLaplaceEquations. Themainideaoftheproposedmethod is to solve a sequence of direct problemsinsteadofsolvingtheinverse problemdirectly. Inparticular,weusea boundarycontroltechniquetoobtain an approximation of the missing Dirichletboundary data; the Tikhonov regularization tech-nique and the L-curve method are employed toachieve such goal stably. Once the boundarydataon the whole boundary are known, the numericalsolution to the Cauchy problem can be obtainedby solving a direct problem. Numerical exam-plesare providedfor verificationsoftheproposedmethod on the steady-state heat conductionprob-lems. Keyword: Method of fundamental solution,methodofparticularsolution,collocationmethod,Tikhonovregularization,L-curve. 1 Introduction The Cauchy problem for an elliptic equation isa typical ill-posed problem whose solution doesnot depend continuously on the boundary data.That is, a small error in the specified data mayresult in an enormous error in the numerical so-lution. This problem appears in many applica-tions for example in the cardiography, the non-destructive testing, and etc. Stable and efficientnumerical methods are of highimportance. How-ever, it is well-known that the Cauchy problemfor an elliptic equation is ill-posed without any
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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