Graphics processing unit accelerated Helmholtz equation solver in two dimensions using the traditional Born series formulation for linear and nonlinear media in biomedical ultrasound.
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| Title: | Graphics processing unit accelerated Helmholtz equation solver in two dimensions using the traditional Born series formulation for linear and nonlinear media in biomedical ultrasound. |
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| Authors: | Mandal, Ujjal1 (AUTHOR), Singh, Jagpreet2 (AUTHOR), Cox, Ben T.3 (AUTHOR), Saha, Ratan K.1 (AUTHOR) ratank.saha@iiita.ac.in |
| Source: | Journal of the Acoustical Society of America. Mar2026, Vol. 159 Issue 3, p1948-1962. 15p. |
| Subjects: | Helmholtz equation, Born approximation, Ultrasonic imaging, Numerical analysis, Acoustic wave propagation, Nonlinear acoustics |
| Abstract: | This study numerically solves inhomogeneous Helmholtz equations modeling acoustic wave propagation in homogeneous and lossless, absorbing and dispersive, and inhomogeneous and nonlinear media. The traditional Born series (TBS) method has been employed to solve such equations. Simulated pressure field patterns for a linear array of acoustic sources (a line source) estimated by the TBS procedure exhibit excellent agreement with that of a standard time domain approach (the k-wave toolbox). For instance, the maximum absolute error of normalized pressure amplitude made by the proposed technique for the homogeneous and lossless medium is ≈ 2 % with respect to the latter method. The TBS scheme, though iterative, is a very fast method. For example, the graphics processing unit (GPU)-enabled cuda c code implementing the TBS procedure for calculating the pressure field for the homogeneous and lossless medium is 102× faster than the k-wave module and also 4× faster than the corresponding central processing unit C code for the computational domain considered in this study (4096 × 4096). The findings of this study demonstrate the effectiveness of the TBS method for solving inhomogeneous Helmholtz equation, while the GPU-based implementation significantly reduces the computation time. In this work, the capability and performance of the method have been tested in two dimensions only. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192669263 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Graphics processing unit accelerated Helmholtz equation solver in two dimensions using the traditional Born series formulation for linear and nonlinear media in biomedical ultrasound. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mandal%2C+Ujjal%22">Mandal, Ujjal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Singh%2C+Jagpreet%22">Singh, Jagpreet</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Cox%2C+Ben+T%2E%22">Cox, Ben T.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Saha%2C+Ratan+K%2E%22">Saha, Ratan K.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ratank.saha@iiita.ac.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+the+Acoustical+Society+of+America%22">Journal of the Acoustical Society of America</searchLink>. Mar2026, Vol. 159 Issue 3, p1948-1962. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Helmholtz+equation%22">Helmholtz equation</searchLink><br /><searchLink fieldCode="DE" term="%22Born+approximation%22">Born approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Ultrasonic+imaging%22">Ultrasonic imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Acoustic+wave+propagation%22">Acoustic wave propagation</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+acoustics%22">Nonlinear acoustics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study numerically solves inhomogeneous Helmholtz equations modeling acoustic wave propagation in homogeneous and lossless, absorbing and dispersive, and inhomogeneous and nonlinear media. The traditional Born series (TBS) method has been employed to solve such equations. Simulated pressure field patterns for a linear array of acoustic sources (a line source) estimated by the TBS procedure exhibit excellent agreement with that of a standard time domain approach (the k-wave toolbox). For instance, the maximum absolute error of normalized pressure amplitude made by the proposed technique for the homogeneous and lossless medium is ≈ 2 % with respect to the latter method. The TBS scheme, though iterative, is a very fast method. For example, the graphics processing unit (GPU)-enabled cuda c code implementing the TBS procedure for calculating the pressure field for the homogeneous and lossless medium is 102× faster than the k-wave module and also 4× faster than the corresponding central processing unit C code for the computational domain considered in this study (4096 × 4096). The findings of this study demonstrate the effectiveness of the TBS method for solving inhomogeneous Helmholtz equation, while the GPU-based implementation significantly reduces the computation time. In this work, the capability and performance of the method have been tested in two dimensions only. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1121/10.0042817 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 1948 Subjects: – SubjectFull: Helmholtz equation Type: general – SubjectFull: Born approximation Type: general – SubjectFull: Ultrasonic imaging Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Acoustic wave propagation Type: general – SubjectFull: Nonlinear acoustics Type: general Titles: – TitleFull: Graphics processing unit accelerated Helmholtz equation solver in two dimensions using the traditional Born series formulation for linear and nonlinear media in biomedical ultrasound. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mandal, Ujjal – PersonEntity: Name: NameFull: Singh, Jagpreet – PersonEntity: Name: NameFull: Cox, Ben T. – PersonEntity: Name: NameFull: Saha, Ratan K. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00014966 Numbering: – Type: volume Value: 159 – Type: issue Value: 3 Titles: – TitleFull: Journal of the Acoustical Society of America Type: main |
| ResultId | 1 |
