Pub Date : 2023-11-27DOI: 10.21914/anziamj.v64.17965
M. Ganesh, S. C. Hawkins, N. Kordzakhia, Linda Stals
We present an efficient data-driven offline/online Bayesian algorithm for uncertainty quantification (UQ) in the induced scattered field when a time-harmonic incident wave interacts with an uncertain heterogeneous medium. The incident wave of interest need not be known in advance, and the uncertainty is informed by noisy scattering data obtained from other incident waves impinging on the medium. Our UQ algorithm is accelerated by a novel stochastic reduced order model (ROM) based on the T-matrix, and the ROM is independent of both the incident wave, and other incident waves used to generate the data. This important property allows the model to be set up offline. References M. Bachmayr and A. Djurdjevac. Multilevel representations of isotropic Gaussian random fields on the sphere. IMA J. Numer. Anal. 43.4 (2023), pp. 1970–2000. doi: 10.1093/imanum/drac034 C. Borges and G. Biros. Reconstruction of a compactly supported sound profile in the presence of a random background medium. Inv. Prob. 34, 115007 (2018). doi: 10.1088/1361-6420/aadbc5 on p. C101). Y. Chen. Inv. Prob. 13 (1997), pp. 253–282. doi: 10.1088/0266-5611/13/2/005 D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. 4th. Springer, 2019. doi: 10.1007/978-3-030-30351-8 M. Ganesh and S. C. Hawkins. A far-field based T-matrix method for two dimensional obstacle scattering. Proceedings of the 9th Biennial Engineering Mathematics and Applications Conference, EMAC-2009. Ed. by P. Howlett, M. Nelson, and A. J. Roberts. Vol. 51. ANZIAM J. 2010, pp. C215–C230. doi: 10.21914/anziamj.v51i0.2581 M. Ganesh and S. C. Hawkins. A numerically stable T-matrix method for acoustic scattering by nonspherical particles with large aspect ratios and size parameters. J. Acoust. Soc. Am. 151 (2022), pp. 1978–1988. doi: 10.1121/10.0009679 M. Ganesh and S. C. Hawkins. Algorithm 975: TMATROM–A T-matrix reduced order model software. ACM Trans. Math. Softw. 44, 9 (2017), pp. 1–8. doi: 10.1145/3054945 M. Ganesh, S. C. Hawkins, and R. Hiptmair. Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. IMA J. Numer. Anal. 32 (2012), pp. 1348–1374. doi: 10.1093/imanum/drr041 M. Ganesh, S. C. Hawkins, A. M. Tartakovsky, and R. Tipireddy. A stochastic domain decomposition and post-processing algorithm for epistemic uncertainty quantification. Int. J. Uncertain. Quant. 13 (2023), pp. 1–22. doi: 10.1615/Int.J.UncertaintyQuantification.2023045687 S. C. Hawkins. Algorithm 1009: MieSolver–An object-oriented Mie series software for wave scattering by cylinders. ACM Trans. Math. Softw. 46, 19 (2020), pp. 1–28. doi: 10.1145/3381537 on p. C109). S. C. Hawkins. Noisy far-field data. Published online 12th August 2023. doi: 10.5281/zenodo.8240111 T. Hohage. On the numerical solution of a three-dimensional inverse medium scattering problem. Inv. Prob. 17 (2001), pp. 1743–1763. doi: 10.1088/0266-5611/17/6/314 A. Kirsch and P. Monk. An analysis of the coupling of fini
我们提出了一种高效的数据驱动离线/在线贝叶斯算法，用于时谐入射波与不确定的异质介质相互作用时的诱导散射场不确定性量化（UQ）。相关入射波不需要事先知道，不确定性可以从其他入射波撞击介质时获得的噪声散射数据中获得。我们的 UQ 算法通过基于 T 矩阵的新型随机减阶模型 (ROM) 进行加速，该 ROM 与入射波和用于生成数据的其他入射波无关。这一重要特性允许离线设置模型。参考文献 M. Bachmayr 和 A. Djurdjevac.球面上各向同性高斯随机场的多级表示。IMA J. Numer.Anal.43.4 (2023)，pp. 1970-2000。doi: 10.1093/imanum/drac034 C. Borges and G. Biros.存在随机背景介质时紧凑支撑声音轮廓的重建.Inv. Prob. 34, 115007 (2018). doi: 10.1088/1361-6420/aadbc5 on p. C101).Y. Chen.Inv. Prob. 13 (1997), pp.Colton and R. Kress.反声学和电磁散射理论》。第 4 版。DOI: 10.1007/978-3-030-30351-8 M. Ganesh and S. C. Hawkins.基于远场的二维障碍物散射 T 矩阵方法》。第 9 届双年工程数学与应用会议论文集，EMAC-2009。由 P. Howlett、M. Nelson 和 A. J. Roberts 编辑。第 51 卷。C215-C230. doi: 10.21914/anziamj.v51i0.2581 M. Ganesh and S. C. Hawkins.大长径比和尺寸参数非球形颗粒声散射的数值稳定 T 矩阵方法.J. Acoust.151 (2022), pp.算法 975：TMATROM-A T 矩阵降阶模型软件。ACM Trans.Math.Softw.44, 9 (2017), pp.减基声学散射 T 矩阵方法的收敛分析与参数估计。IMA J. Numer.Anal.doi: 10.1093/imanum/drr041 M. Ganesh, S. C. Hawkins, A. M. Tartakovsky, and R. Tipireddy.用于认识不确定性量化的随机领域分解和后处理算法.Int. J. Uncertain.J. Uncertain.Quant.doi: 10.1615/Int.J.UncertaintyQuantification.2023045687 S. C. Hawkins.算法 1009：MieSolver-An object-oriented Mie series software for wave scattering by cylinders.ACM Trans.Math. Softw.Softw.46, 19 (2020), pp.）S. C. Hawkins.噪声远场数据。doi: 10.5281/zenodo.8240111 T. Hohage.关于三维反向介质散射问题的数值解。Inv. Prob. 17 (2001), pp.Kirsch and P. Monk.声散射中有限元与 Nyström 方法耦合分析.IMA J. Numer.doi: 10.1093/imanum/14.4.523 on p. C101).M. Löhndorf and J. M. Melenk.论薄板样条插值。Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016.由 M. Bittencourt、N. Dumont 和 J. Hesthaven 编辑。第 119 卷。计算科学与工程讲义》。Springer 出版社，2017 年，第 451-466 页。DOI：10.1007/978-3-319-65870-4_32 T. D. Mast.人体软组织声学参数之间的经验关系。Acoust.Res.Lett.doi: 10.1121/1.1336896 L. Stals.有限元薄板样条公式的高效求解技术。J. Sci.63 (2015), pp.超声波缺陷表征中的二维反玻恩近似。J. Nondestruct.Eval.5 (1985), pp.改进的米氏散射算法。19 (1980), pp.
{"title":"Data-informed uncertainty quantification for wave scattering by heterogeneous media","authors":"M. Ganesh, S. C. Hawkins, N. Kordzakhia, Linda Stals","doi":"10.21914/anziamj.v64.17965","DOIUrl":"https://doi.org/10.21914/anziamj.v64.17965","url":null,"abstract":"We present an efficient data-driven offline/online Bayesian algorithm for uncertainty quantification (UQ) in the induced scattered field when a time-harmonic incident wave interacts with an uncertain heterogeneous medium. The incident wave of interest need not be known in advance, and the uncertainty is informed by noisy scattering data obtained from other incident waves impinging on the medium. Our UQ algorithm is accelerated by a novel stochastic reduced order model (ROM) based on the T-matrix, and the ROM is independent of both the incident wave, and other incident waves used to generate the data. This important property allows the model to be set up offline. References M. Bachmayr and A. Djurdjevac. Multilevel representations of isotropic Gaussian random fields on the sphere. IMA J. Numer. Anal. 43.4 (2023), pp. 1970–2000. doi: 10.1093/imanum/drac034 C. Borges and G. Biros. Reconstruction of a compactly supported sound profile in the presence of a random background medium. Inv. Prob. 34, 115007 (2018). doi: 10.1088/1361-6420/aadbc5 on p. C101). Y. Chen. Inv. Prob. 13 (1997), pp. 253–282. doi: 10.1088/0266-5611/13/2/005 D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. 4th. Springer, 2019. doi: 10.1007/978-3-030-30351-8 M. Ganesh and S. C. Hawkins. A far-field based T-matrix method for two dimensional obstacle scattering. Proceedings of the 9th Biennial Engineering Mathematics and Applications Conference, EMAC-2009. Ed. by P. Howlett, M. Nelson, and A. J. Roberts. Vol. 51. ANZIAM J. 2010, pp. C215–C230. doi: 10.21914/anziamj.v51i0.2581 M. Ganesh and S. C. Hawkins. A numerically stable T-matrix method for acoustic scattering by nonspherical particles with large aspect ratios and size parameters. J. Acoust. Soc. Am. 151 (2022), pp. 1978–1988. doi: 10.1121/10.0009679 M. Ganesh and S. C. Hawkins. Algorithm 975: TMATROM–A T-matrix reduced order model software. ACM Trans. Math. Softw. 44, 9 (2017), pp. 1–8. doi: 10.1145/3054945 M. Ganesh, S. C. Hawkins, and R. Hiptmair. Convergence analysis with parameter estimates for a reduced basis acoustic scattering T-matrix method. IMA J. Numer. Anal. 32 (2012), pp. 1348–1374. doi: 10.1093/imanum/drr041 M. Ganesh, S. C. Hawkins, A. M. Tartakovsky, and R. Tipireddy. A stochastic domain decomposition and post-processing algorithm for epistemic uncertainty quantification. Int. J. Uncertain. Quant. 13 (2023), pp. 1–22. doi: 10.1615/Int.J.UncertaintyQuantification.2023045687 S. C. Hawkins. Algorithm 1009: MieSolver–An object-oriented Mie series software for wave scattering by cylinders. ACM Trans. Math. Softw. 46, 19 (2020), pp. 1–28. doi: 10.1145/3381537 on p. C109). S. C. Hawkins. Noisy far-field data. Published online 12th August 2023. doi: 10.5281/zenodo.8240111 T. Hohage. On the numerical solution of a three-dimensional inverse medium scattering problem. Inv. Prob. 17 (2001), pp. 1743–1763. doi: 10.1088/0266-5611/17/6/314 A. Kirsch and P. Monk. An analysis of the coupling of fini","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":"82 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-23DOI: 10.1017/s1446181123000184
WEN-HUA WANG, ZHENG-LI CHEN, WEI LI
Abstract The Hamiltonian of a conventional quantum system is Hermitian, which ensures real spectra of the Hamiltonian and unitary evolution of the system. However, real spectra are just the necessary conditions for a Hamiltonian to be Hermitian. In this paper, we discuss the metric operators for pseudo-Hermitian Hamiltonian which is similar to its adjoint. We first present some properties of the metric operators for pseudo-Hermitian Hamiltonians and obtain a sufficient and necessary condition for an invertible operator to be a metric operator for a given pseudo-Hermitian Hamiltonian. When the pseudo-Hermitian Hamiltonian has real spectra, we provide a new method such that any given metric operator can be transformed into the same positive-definite one and the new inner product with respect to the positive-definite metric operator is well defined. Finally, we illustrate the results obtained with an example.
{"title":"THE METRIC OPERATORS FOR PSEUDO-HERMITIAN HAMILTONIAN","authors":"WEN-HUA WANG, ZHENG-LI CHEN, WEI LI","doi":"10.1017/s1446181123000184","DOIUrl":"https://doi.org/10.1017/s1446181123000184","url":null,"abstract":"Abstract The Hamiltonian of a conventional quantum system is Hermitian, which ensures real spectra of the Hamiltonian and unitary evolution of the system. However, real spectra are just the necessary conditions for a Hamiltonian to be Hermitian. In this paper, we discuss the metric operators for pseudo-Hermitian Hamiltonian which is similar to its adjoint. We first present some properties of the metric operators for pseudo-Hermitian Hamiltonians and obtain a sufficient and necessary condition for an invertible operator to be a metric operator for a given pseudo-Hermitian Hamiltonian. When the pseudo-Hermitian Hamiltonian has real spectra, we provide a new method such that any given metric operator can be transformed into the same positive-definite one and the new inner product with respect to the positive-definite metric operator is well defined. Finally, we illustrate the results obtained with an example.","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":"14 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135406077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1017/s1446181123000135
H. ZHANG, D. A. BARRY, B. SEYMOUR, G. HOCKING
Abstract The effects of apparatus-induced dispersion on nonuniform, density-dependent flow in a cylindrical soil column were investigated using a finite-element model. To validate the model, the results with an analytical solution and laboratory column test data were analysed. The model simulations confirmed that flow nonuniformities induced by the apparatus are dissipated within the column when the distance to the apparatus outlet exceeds $3R/2$ , where R represents the radius of the cylindrical column. Furthermore, the simulations revealed that convergent flow in the vicinity of the outlet introduces additional hydrodynamic dispersion in the soil column apparatus. However, this effect is minimal in the region where the column height exceeds $3R/2$ . Additionally, it is found that an increase in the solution density gradient during the solute breakthrough period led to a decrease in flow velocity, which stabilized the flow and ultimately reduced dispersive mixing. Overall, this study provides insights into the behaviour of apparatus-induced dispersion in nonuniform, density-dependent flow within a cylindrical soil column, shedding light on the dynamics and mitigation of flow nonuniformities and dispersive mixing phenomena.
{"title":"NUMERICAL ANALYSIS OF APPARATUS-INDUCED DISPERSION FOR DENSITY-DEPENDENT SOLUTE TRANSPORT IN POROUS MEDIA","authors":"H. ZHANG, D. A. BARRY, B. SEYMOUR, G. HOCKING","doi":"10.1017/s1446181123000135","DOIUrl":"https://doi.org/10.1017/s1446181123000135","url":null,"abstract":"Abstract The effects of apparatus-induced dispersion on nonuniform, density-dependent flow in a cylindrical soil column were investigated using a finite-element model. To validate the model, the results with an analytical solution and laboratory column test data were analysed. The model simulations confirmed that flow nonuniformities induced by the apparatus are dissipated within the column when the distance to the apparatus outlet exceeds $3R/2$ , where R represents the radius of the cylindrical column. Furthermore, the simulations revealed that convergent flow in the vicinity of the outlet introduces additional hydrodynamic dispersion in the soil column apparatus. However, this effect is minimal in the region where the column height exceeds $3R/2$ . Additionally, it is found that an increase in the solution density gradient during the solute breakthrough period led to a decrease in flow velocity, which stabilized the flow and ultimately reduced dispersive mixing. Overall, this study provides insights into the behaviour of apparatus-induced dispersion in nonuniform, density-dependent flow within a cylindrical soil column, shedding light on the dynamics and mitigation of flow nonuniformities and dispersive mixing phenomena.","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135443190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1017/s1446181122000165
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
{"title":"ANZ VOLUME 65 ISSUE 1-2 COVER AND BACK MATTER","authors":"","doi":"10.1017/s1446181122000165","DOIUrl":"https://doi.org/10.1017/s1446181122000165","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135750275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1017/s1446181122000153
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
{"title":"ANZ VOLUME 65 ISSUE 1-2 COVER AND FRONT MATTER","authors":"","doi":"10.1017/s1446181122000153","DOIUrl":"https://doi.org/10.1017/s1446181122000153","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50745,"journal":{"name":"ANZIAM Journal","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135750627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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