Spectral properties of radiation for the Helmholtz equation with a random coefficient

Mirza Karamehmedovic; Kristoffer Linder-Steinlein

Spectral properties of radiation for the Helmholtz equation with a random coefficient

Mirza Karamehmedovic
, Kristoffer Linder-Steinlein

Research output: Contribution to conference › Conference abstract for conference › Research › peer-review

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Abstract

For the Helmholtz equation with a Gaussian random field coefficient, we approximate and characterize spectrally the source-to-measurement map. To this end, we first analyze the case with a deterministic coefficient, and here discover and quantify a ’spectral leakage’ effect. We compare the theoretically predicted forward operator spectrum with a Finite Element Method computation. Our results are applicable in the analysis of the robustness of solution of inverse source problems in the presence of deterministic and random media.

Original language	English
Publication date	2023
Publication status	Published - 2023
Event	11^th Applied Inverse Problems Conference - Georg-August-Universität, Göttingen, Germany Duration: 4 Sept 2023 → 8 Sept 2023

Conference

Conference	11^th Applied Inverse Problems Conference
Location	Georg-August-Universität
Country/Territory	Germany
City	Göttingen
Period	04/09/2023 → 08/09/2023

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title = "Spectral properties of radiation for the Helmholtz equation with a random coefficient",

abstract = "For the Helmholtz equation with a Gaussian random field coefficient, we approximate and characterize spectrally the source-to-measurement map. To this end, we first analyze the case with a deterministic coefficient, and here discover and quantify a {\textquoteright}spectral leakage{\textquoteright} effect. We compare the theoretically predicted forward operator spectrum with a Finite Element Method computation. Our results are applicable in the analysis of the robustness of solution of inverse source problems in the presence of deterministic and random media.",

author = "Mirza Karamehmedovic and Kristoffer Linder-Steinlein",

year = "2023",

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T1 - Spectral properties of radiation for the Helmholtz equation with a random coefficient

AU - Karamehmedovic, Mirza

AU - Linder-Steinlein, Kristoffer

PY - 2023

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N2 - For the Helmholtz equation with a Gaussian random field coefficient, we approximate and characterize spectrally the source-to-measurement map. To this end, we first analyze the case with a deterministic coefficient, and here discover and quantify a ’spectral leakage’ effect. We compare the theoretically predicted forward operator spectrum with a Finite Element Method computation. Our results are applicable in the analysis of the robustness of solution of inverse source problems in the presence of deterministic and random media.

AB - For the Helmholtz equation with a Gaussian random field coefficient, we approximate and characterize spectrally the source-to-measurement map. To this end, we first analyze the case with a deterministic coefficient, and here discover and quantify a ’spectral leakage’ effect. We compare the theoretically predicted forward operator spectrum with a Finite Element Method computation. Our results are applicable in the analysis of the robustness of solution of inverse source problems in the presence of deterministic and random media.

M3 - Conference abstract for conference

SP - 126

EP - 126

T2 - 11<sup>th</sup> Applied Inverse Problems Conference

Y2 - 4 September 2023 through 8 September 2023

ER -

Spectral properties of radiation for the Helmholtz equation with a random coefficient

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