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Congruences for sums of MacMahon's -Catalan polynomials
No full texthttp://dx.doi.org/10.1017/S000497271200033
An efficient algorithm for wave propagation in dynamic 3D configurations
No full textWe consider a model problem in which the motion of particles is examined using data carried by waves interacting with the particles. Such problems arise, for example, when tracer particles are carried by a fluid, and their position is detected using scattered light or sound waves. The time evolution of the model can be revealed by simulating the detected wave at a series of snapshots in time as their motion evolves, akin to a motion picture. In our model problem, for proof of concept, the motion of the particles is described by a simple second order ordinary differential equation, but the wave propagation simulation is extremely challenging because the governing partial differential equation must be solved in an unbounded region subject to boundary conditions on the particle boundaries, which change position as the motion of the particles evolves. The principal aim of this work is to demonstrate the use of a fast surrogate for the solution of the wave propagation partial differential equation, and we demonstrate both the accuracy of the surrogate and its efficiency. The efficiency is crucial to allow the simulation of the wave propagation to keep up with the frame rate of the simulation.
References
K. E. Atkinson. The Numerical Solution of Integral Equations of the Second Kind. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 1997. doi: 10.1017/CBO9780511626340
J. Bruning and Y. Lo. Multiple scattering of EM waves by spheres part I—Multipole expansion and ray-optical solutions. IEEE Trans. Ant. Prop. 19.3 (1971), pp. 378–390. doi: 10.1109/TAP.1971.1139944
O. P. Bruno, C. A. Geuzaine, J. A. Monro, and F. Reitich. Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: The convex case. Phil. Trans. A 362 (2004), pp. 629–645. doi: 10.1098/rsta.2003.1338
S. N. Chandler-Wilde, I. G. Graham, S. Langdon, and E. A. Spence. Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. Acta Numer. 21 (2012), pp. 89–305. doi: 10.1017/S0962492912000037
D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. 4th ed. Applied Mathematical Sciences, 93. Cham: Springer International Publishing, 2019. doi: 10.1007/978-3-030-30351-8
V. Domínguez, I. G. Graham, and V. P. Smyshlyaev. A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering. Numer. Math. 106.3 (2007), pp. 471–510. doi: 10.1007/s00211-007-0071-4.
T. Dufva, J. Sarvas, and J. Sten. Unified derivation of the translational addition theorems for the spherical scalar and vector wave functions. Prog. Electromagn. Res. B 4 (2008), pp. 79–99. doi: 10.2528/PIERB07121203
F. Ecevit and F. Reitich. Analysis of multiple scattering iterations for high-frequency scattering problems. I: the two-dimensional case. In: Numer. Math. 114.2 (2009), pp. 271–354. doi: 10.1007/s00211-009-0249-z.
M. Ganesh and I. G. Graham. A high-order algorithm for obstacle scattering in three dimensions. J. Comput. Phys. 198.1 (2004), pp. 211–242. doi: 10.1016/j.jcp.2004.01.007
M. Ganesh and S. C. Hawkins. A fully discrete Galerkin method for high frequency exterior acoustic scattering in three dimensions. J. Comput. Phys. 230.1 (2011), pp. 104–125. doi: 10.1016/j.jcp.2010.09.014.
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. 151.3 (2022), 1978–1988. doi: 10.1121/10.0009679
C. Geuzaine, O. Bruno, and F. Reitich. On the O(1) solution of multiple-scattering problems. IEEE Trans. Magnet. 41 (2005), pp. 1488–1491. doi: 10.1109/TMAG.2005.844567
O. P. Le Maître and O. M. Kino. Spectral Methods for Uncertainty Quantification. Springer, 2010. doi: 10.1007/978-90-481-3520-2
P. A. Martin. Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2006. doi: 10.1017/CBO9780511735110
P. C. Waterman. New formulation of acoustic scattering. J. Acoust. Soc. Am. 45.6 (1969), pp. 1417–1429. doi: 10.1121/1.191161
Proceedings of the 2024 Computational Techniques and Applications Conference
No full textMonash University, Melbourne, Australia
19–22 November, 2024
The 22nd Biennial Computational Techniques and Applications Conference (CTAC2024) was hosted by the School of Mathematics at Monash University in Melbourne, Australia.
CTAC is a flagship event of the ANZIAM Special Interest Group in Computational Mathematics. This biennial conference series, which began in 1981, offers an interactive forum for researchers developing and applying computational methods to solve engineering, scientific, and mathematical problems. Attendees are invited to submit papers based on their presentations for publication in the refereed Electronic Supplement of the ANZIAM Journal.
The editors, Ricardo Ruiz Baier, Bishnu Lamichhane, Quoc Thong Le Gia and Judy Bunder, thank all reviewers whose efforts helped ensure the quality of the proceedings.
This Special Section of the Proceedings of ANZIAM includes peer-reviewed papers from CTAC2024. The nine plenary speakers and one public lecture were as follows:
Santiago Badia, Monash UniversityFinite element interpolated neural networks
Fleurianne Bertrand, Technische Universität ChemnitzStress-based finite elements methods
Victor Calo, Curtin UniversityAdaptive stabilized finite element methods: A variational multiscale approach for robust and accurate flow simulations
Carsten Carstensen, Humboldt-Universität zu BerlinLower eigenvalue bounds for the harmonic and bi-harmonic operator
Vivien Challis, Queensland University of TechnologyComputational structural optimisation of piezoelectric materials
Nilima Nigam, Simon Fraser UniversitySkeletal muscles: modeling and simulation
Vijay Rajagopal, University of MelbourneWhat do we need a computational physiology framework to predict single cell biology?
Dingxuan Zhou, University of SydneyMathematical theory of structured deep neural networks
Terence O’Kane, CSIRO (Public Lecture)Mathematical methods and artificial intelligence in climate science
CTAC2024 attracted a vibrant mix of established and early-career researchers, including student contributors whose presentations were eligible for prizes sponsored by MoCaO and AMSI. In total, the program featured over 120 contributed talks across various themes, including numerical analysis, scientific computing, mathematical biology, hybrid and polytopal methods, and optimization.
CTAC2024 Organising Committee (Monash University)
Anne Boschman
Ngan Le
Janosch Rieger
Sergio Rojas Hernandez
Ricardo Ruiz Baier (Chair)
Jai Tushar
Segundo Villa-Fuentes
Jörn Wichmann
Mark Flegg
CTAC2024 Scientific Committee
Jennifer Flegg (University of Melbourne)
Frances Kuo (UNSW)
Bishnu Lamichhane (University of Newcastle)
Quoc Le Gia (UNSW)
Ricardo Ruiz Baier (Monash University)
Linda Stals (ANU)
Ian Turner (QUT)
AcknowledgementsMonash University acknowledges the Traditional Owners of the lands on which its campuses are located—the people of the Kulin Nations—and pays respects to their Elders past and present. We acknowledge that Indigenous Australians were this country’s first scientists.
CTAC2024 was made possible through generous support from:
School of Mathematics, Monash University
Australian Mathematical Sciences Institute (AMSI)
Mathematics of Computation and Optimisation (MoCaO) special interest group of AustMS
Society for Industrial and Applied Mathematics (SIAM)
ANZIAM Student Support Schem
Second Hankel determinant for logarithmic inverse coefficients of convex and starlike functions
No full texthttp://dx.doi.org/10.1017/S000497271200033
A class of symbols that induce bounded composition operators for Dirichlet-type spaces on the disc.: -
No full textIhttp://dx.doi.org/10.1017/S000497271200033
Some counting formulae for -quiddities over the rings
No full texthttp://dx.doi.org/10.1017/S000497271200033
Arithmetic properties for an analogue of -core partitions
No full texthttp://dx.doi.org/10.1017/S000497271200033
A conjecture on shifted primes with large prime factors, II
No full texthttp://dx.doi.org/10.1017/S000497271200033
Efficient inference for spatial and spatio-temporal statistical models using basis-function and deep-learning methods
No full texthttp://dx.doi.org/10.1017/S000497271200033