Unique Continuation on a Sphere for Helmholtz Equation and Its Numerical Treatments

2021 ◽  
pp. 133-144
Author(s):  
Yu Chen ◽  
Jin Cheng
Keyword(s):  
Helmholtz Equation ◽  
Unique Continuation ◽  
Numerical Treatments

Unique continuation on a line for the Helmholtz equation

2012 ◽  
Vol 91 (9) ◽  
pp. 1761-1771 ◽  
Author(s):  
Shuai Lu ◽  
Boxi Xu ◽  
Xiang Xu
Keyword(s):  
Helmholtz Equation ◽  
Unique Continuation

scholarly journals Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
María Ángeles García-Ferrero ◽  
Angkana Rüland ◽  
Wiktoria Zatoń
Keyword(s):  
Helmholtz Equation ◽  
Frequency Dependence ◽  
High Frequency ◽  
Convex Sets ◽  
Unique Continuation ◽  
Approximation Properties ◽  
Frequency Limit ◽  
Partial Data ◽  
Calderón Problem ◽  
Quantitative Unique Continuation

<p style='text-indent:20px;'>In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on [<xref ref-type="bibr" rid="b3">3</xref>,<xref ref-type="bibr" rid="b35">35</xref>]. The results rely on quantitative unique continuation estimates in suitable function spaces with explicit frequency dependence. We contrast the frequency dependence of interior Runge approximation results from non-convex and convex sets.</p>

A preconditioned method for the solution of the Robbins problem for the Helmholtz equation

2011 ◽  
Vol 51 ◽  
pp. 87
Author(s):  
Jiang Le ◽  
Huang Jin ◽  
Xiao-Guang Lv ◽  
Qing-Song Cheng
Keyword(s):  
Helmholtz Equation
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