ORCID Profile
0000-0003-1642-613X
Current Organisation
Macquarie University
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Numerical Analysis | Numerical and Computational Mathematics | Stochastic Analysis and Modelling | Numerical Computation
Publisher: World Scientific Pub Co Pte Lt
Date: 12-2005
DOI: 10.1142/S0219691305001044
Abstract: An operator splitting type preconditioner is presented for fast solution of linear systems obtained by Galerkin discretization of the Burton and Miller formulation for the Helmholtz equation. Our approach differs from usual boundary element treatments of the three-dimensional scattering problem because we use a basis of biorthogonal wavelets. Such wavelets result in a sparse linear system and that facilitates preconditioning and makes matrix vector products cheap to form. In this Part I of our work, we implement a biorthogonal wavelet transform on a closed surface in three dimensions. Numerical results demonstrate the gains in efficiency that are already achievable with this convenient but non-optimal implementation.
Publisher: IEEE
Date: 09-2010
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 27-10-2008
Publisher: Springer Science and Business Media LLC
Date: 30-10-2008
Publisher: Association for Computing Machinery (ACM)
Date: 19-05-2020
DOI: 10.1145/3381537
Abstract: MieSolver provides an efficient solver for the problem of wave propagation through a heterogeneous configuration of nonidentical circular cylinders. MieSolver allows great flexibility in the physical properties of each cylinder, and the cylinders may have opaque or penetrable cores, as well as an arbitrary number of penetrable layers. The wave propagation is governed by the two-dimensional Helmholtz equation and models electromagnetic, acoustic, and elastic waves. The solver is based on the Mie series solution for scattering by a single circular cylinder and hence is numerically stable and highly accurate. We demonstrate the accuracy of our software with extensive numerical experiments over a wide range of frequencies (about five orders of magnitude) and up to 60 cylinders.
Publisher: Rocky Mountain Mathematics Consortium
Date: 03-2020
Publisher: Springer Science and Business Media LLC
Date: 20-05-2014
Publisher: Informa UK Limited
Date: 03-2004
Publisher: Springer Science and Business Media LLC
Date: 15-11-2006
Publisher: Elsevier BV
Date: 07-2010
Publisher: Elsevier BV
Date: 07-2013
Publisher: Elsevier BV
Date: 12-2019
Publisher: Elsevier BV
Date: 03-2024
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 03-02-2016
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 12-05-2010
Publisher: Elsevier BV
Date: 04-2014
Publisher: Association for Computing Machinery (ACM)
Date: 14-07-2017
DOI: 10.1145/3054945
Abstract: The T-matrix (TMAT) of a scatterer fully describes the way the scatterer interacts with incident fields and scatters waves, and is therefore used extensively in several science and engineering applications. The T-matrix is independent of several input parameters in a wave propagation model and hence the offline computation of the T-matrix provides an efficient reduced order model (ROM) framework for performing online scattering simulations for various choices of the input parameters. The authors developed and mathematically analyzed a numerically stable formulation for computing the T-matrix (J. Comput. Appl. Math. 234 (2010), 1702--1709). The TMATROM software package provides an object-oriented implementation of the numerically stable formulation and can be used in conjunction with the user’s preferred forward solver for the two-dimensional Helmholtz model. We compare TMATROM with standard methods to compute the T-matrix for a range of two-dimensional test scatterers with large aspect ratios and acoustic sizes. Our numerical results demonstrate the robust numerical stability of the TMATROM implementation, even with scatterers for which the standard methods are numerically unstable. The efficiency and flexibility of the TMATROM software package to handle a wide range of two-dimensional scatterers with various shapes and material properties are also demonstrated.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 16-05-2011
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 07-09-2008
Publisher: Elsevier BV
Date: 02-2022
Publisher: Acoustical Society of America (ASA)
Date: 04-2021
DOI: 10.1121/10.0003958
Abstract: Regarding wave scattering on a three-dimensional nonspherical obstacle, the Rayleigh hypothesis states that the scattered field can be expanded everywhere outside the obstacle using only outgoing eigensolutions of the underlying Helmholtz equation. However, the correctness of this assumption has not yet been finally clarified, although it is important for the near-field analysis of scattering processes and for multiple scattering. To circumvent this uncertainty, Waterman introduced the extended boundary condition to develop his T-matrix method. This approach leads to the restriction that, when modeling multiple scattering processes using this T-matrix, the smallest circumscribing spheres of the in idual obstacles must not overlap. The purpose of this paper is to provide a justification of the correctness of Rayleigh's hypothesis and clarify its implications for modeling multiple scattering. We show that Waterman's T-matrix can in fact be used inside the critical region between the surface of the obstacle and its smallest circumscribing sphere to represent the near-field and that one does not necessarily have to exclude an overlap of these spheres in the multiple scattering modeling. The theoretical considerations in the first part of this paper are supplemented by a numerical study of a benchmark configuration for multiple scattering in the last part.
Publisher: Elsevier BV
Date: 12-2016
Publisher: Acoustical Society of America (ASA)
Date: 06-2020
DOI: 10.1121/10.0001472
Abstract: Recently Janus particles have become important in several technological fields because they have interesting properties compared with homogeneous particles. The interaction of Janus particles with sound waves is of particular interest for diagnostic purposes, and also in applications in micro- and nanotechnology. In this paper the authors demonstrate that a method of fundamental solution combined with a T-matrix that is computed from far-field information can be applied with benefit to analyse the scattering of sound waves by a particular type of Janus sphere. Moreover, it is shown that this method converges faster than the conventional T-matrix method introduced by Waterman [(1969). J. Acoust. Soc. Am. 45, 1417–1429]. This is of special importance if orientation averaged scattering quantities are required, or if multiple scattering processes on Janus spheres are considered. This method is used to demonstrate the interesting phenomenon of an enhanced side scattering intensity that is larger than the forward scattering intensity, and that this effect can be strengthened using a particular configuration of two identical Janus spheres. Finally, the authors discuss a useful approximation that can be readily applied for two or more Janus spheres.
Publisher: Walter de Gruyter GmbH
Date: 2022
Abstract: Dynamic compartmentalized data (DCD) and compartmentalized differential equations (CDEs) are key instruments for modeling transmission of pathogens such as the SARS-CoV-2 virus. We describe an effi-cient nowcasting algorithm for modeling transmission of SARS-CoV-2 with uncertainty quantification for the COVID-19 impact. A key concern for transmission of SARS-CoV-2 is under-reporting of cases, and this is addressed in our data-driven model by providing an estimate for the detection rate. Our novel top-down model is based on CDEs with stochastic constitutive parameters obtained from the DCD using Bayesian inference. We demonstrate the robustness of our algorithm for simulation studies using synthetic DCD, and nowcasting COVID-19 using real DCD from several regions across five continents.
Publisher: Wiley
Date: 12-2007
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2005
Publisher: World Scientific Pub Co Pte Lt
Date: 03-2011
DOI: 10.1142/S0218396X11004304
Abstract: In this article we present an algorithm for the three-dimensional numerical simulation of the sound spectrum and the propagation of acoustic radiation inside and around long slender hollow objects. The fluid inside and close to the object is meshed by Lagrangian tetrahedral finite elements. To obtain results in the far field of the object, complex conjugated Astley-Leis infinite elements are used. To apply these infinite elements the finite element domain is meshed either in a spherical or an ellipsoidal shape. Advantages and disadvantages of both shapes regarding the form of the object are discussed in this article. The formulation leads to a quadratic eigenvalue problem with real, large and nonsymmetric matrices. An eigenvalue search algorithm is implemented to concentrate on the computation of the interior eigenmodes. This algorithm is based on a linearization of the quadratic problem in a state space formulation. The search algorithm uses a complex shift to efficiently extract the relevant eigenvalues only.
Publisher: Elsevier BV
Date: 04-2008
Publisher: Springer International Publishing
Date: 2020
Publisher: Begell House
Date: 2023
DOI: 10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2023045687
Abstract: Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires computational modeling of the PDE in bounded/unbounded regions. Uncertainty in the computational model manifests through lack of precise knowledge of the input field or configuration. Uncertainty quantification (UQ) in the output physical process is typically carried out by modeling the uncertainty using a random field, governed by an appropriate covariance function. This leads to solving high-dimensional stochastic counterparts of the PDE computational models. Such UQ-PDE models require a large number of simulations of the PDE in conjunction with s les in the high-dimensional probability space, with probability distribution associated with the covariance function. Those UQ computational models having explicit knowledge of the covariance function are known as aleatoric UQ (AUQ) models. The lack of such explicit knowledge leads to epistemic UQ (EUQ) models, which typically require solution of a large number of AUQ models. In this article, using a surrogate, post-processing, and domain decomposition framework with coarse stochastic solution adaptation, we develop an offline/online algorithm for efficiently simulating a class of EUQ-PDE models. We demonstrate the algorithm for celebrated bounded and unbounded spatial region models, with high-dimensional uncertainties.
Publisher: The Optical Society
Date: 27-02-2015
DOI: 10.1364/OE.23.006228
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2015
DOI: 10.1137/140996069
Publisher: Elsevier BV
Date: 12-2019
Publisher: Springer International Publishing
Date: 2018
Publisher: Oxford University Press (OUP)
Date: 17-01-2012
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 12-01-2020
DOI: 10.21914/ANZIAMJ.V62.16110
Abstract: We present an efficient Bayesian algorithm for identifying the shape of an object from noisy far field data. The data is obtained by illuminating the object with one or more incident waves. Bayes' theorem provides a framework to find a posterior distribution of the parameters that determine the shape of the scatterer. We compute the distribution using the Markov Chain Monte Carlo (MCMC) method with a Gibbs s ler. The principal novelty of this work is to replace the forward far-field-ansatz wave model (in an unbounded region) in the MCMC s ling with a neural-network-based surrogate that is hundreds of times faster to evaluate. We demonstrate the accuracy and efficiency of our algorithm by constructing the distributions, medians and confidence intervals of non-convex shapes using a Gaussian random circle prior. References Y. Chen. Inverse scattering via Heisenberg’s uncertainty principle. 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 Edition. Vol. 93. Applied Mathematical Sciences. References C112 Springer, 2019. doi: 10.1007/978-3-030-30351-8 R. DeVore, B. Hanin, and G. Petrova. Neural Network Approximation. Acta Num. 30 (2021), pp. 327–444. doi: 10.1017/S0962492921000052 M. Ganesh and S. C. Hawkins. A reduced-order-model Bayesian obstacle detection algorithm. 2018 MATRIX Annals. Ed. by J. de Gier et al. Springer, 2020, pp. 17–27. doi: 10.1007/978-3-030-38230-8_2 M. Ganesh and S. C. Hawkins. Algorithm 975: TMATROM—A T-matrix reduced order model software. ACM Trans. Math. Softw. 44.9 (2017), pp. 1–18. doi: 10.1145/3054945 M. Ganesh and S. C. Hawkins. Scattering by stochastic boundaries: hybrid low- and high-order quantification algorithms. ANZIAM J. 56 (2016), pp. C312–C338. doi: 10.21914/anziamj.v56i0.9313 M. Ganesh, S. C. Hawkins, and D. Volkov. An efficient algorithm for a class of stochastic forward and inverse Maxwell models in R3. J. Comput. Phys. 398 (2019), p. 108881. doi: 10.1016/j.jcp.2019.108881 L. Lamberg, K. Muinonen, J. Ylönen, and K. Lumme. Spectral estimation of Gaussian random circles and spheres. J. Comput. Appl. Math. 136 (2001), pp. 109–121. doi: 10.1016/S0377-0427(00)00578-1 T. Nousiainen and G. M. McFarquhar. Light scattering by quasi-spherical ice crystals. J. Atmos. Sci. 61 (2004), pp. 2229–2248. doi: 10.1175/1520-0469(2004)061 :LSBQIC .0.CO A. Palafox, M. A. Capistrán, and J. A. Christen. Point cloud-based scatterer approximation and affine invariant s ling in the inverse scattering problem. Math. Meth. Appl. Sci. 40 (2017), pp. 3393–3403. doi: 10.1002/mma.4056 M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378 (2019), pp. 686–707. doi: 10.1016/j.jcp.2018.10.045 A. C. Stuart. Inverse problems: A Bayesian perspective. Acta Numer. 19 (2010), pp. 451–559. doi: 10.1017/S0962492910000061 B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande. Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry. J. Quant. Spectro. Rad. Trans. 100 (2006), pp. 393–405. doi: 10.1016/j.jqsrt.2005.11.053
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2007
DOI: 10.1137/060664859
Publisher: Elsevier BV
Date: 2011
Start Date: 12-2022
End Date: 11-2025
Amount: $420,000.00
Funder: Australian Research Council
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