Judith Bunder

Dr Judith Bunder

Research Associate

School of Mathematical Sciences

Faculty of Engineering, Computer and Mathematical Sciences

Eligible to supervise Masters and PhD - email supervisor to discuss availability.


Many systems of interest in science and engineering exist over multiple scales, and the disparate scales of these systems are a significant challenge in numerical simulations. The fine-scale detail is essential to the accurate modelling of a multiscale system, but simulating at the finest scale is not only prohibitively inefficient and severely constrained by memory limitations, it is also an arduous task to analyse simulation data generated at a scale which may be significantly smaller than the scale of interest.

My research investigates different ways of managing the complexities of multiscale systems. For example, patch dynamics is an 'on the fly' numerical scheme which aims to quickly and accurately simulate a multiscale system at the desired scale of interest. I also look at analytic methods for extracting the slow evolution of multiscale models, thus providing a simplified model for more efficient simulation.

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  • Journals

    Year Citation
    2021 Bunder, J. E., & Roberts, A. J. (2021). Nonlinear emergent macroscale PDEs, with error bound, for nonlinear microscale systems. SN Applied Sciences, 3(7), 703-1-703-28.
    DOI
    2021 Bunder, J. E., Divahar, J., Kevrekidis, I. G., Mattner, T. W., & Roberts, A. J. (2021). Large‐scale simulation of shallow water waves via computation only on small staggered patches. International Journal for Numerical Methods in Fluids, 93(4), 953-977.
    DOI Scopus1 WoS2
    2021 Maclean, J., Bunder, J. E., & Roberts, A. J. (2021). A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation. Numerical Algorithms, 87(4), 1729-1748.
    DOI Scopus1 WoS1
    2021 Bunder, J. E., Kevrekidis, I. G., & Roberts, A. J. (2021). Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling. Numerische Mathematik, 149(2), 229-272.
    DOI
    2021 MacLean, J., Bunder, J. E., Kevrekidis, I. G., & Roberts, A. J. (2021). An Equation Free Algorithm Accurately Simulates Macroscale Shocks Arising from Heterogeneous Microscale Systems. IEEE Journal on Multiscale and Multiphysics Computational Techniques, 6, 8-15.
    DOI Scopus1
    2020 Arbabi, H., Bunder, J. E., Samaey, G., Roberts, A. J., & Kevrekidis, I. G. (2020). Linking machine learning with multiscale numerics: data-driven discovery of homogenized equations. JOM, 72(12), 4444-4457.
    DOI Scopus5 WoS6
    2019 Edson, R. A., Bunder, J. E., Mattner, T. W., & Roberts, A. J. (2019). Lyapunov exponents of the Kuramoto-Sivashinksy PDE. The ANZIAM Journal, 61(3), 270-285.
    DOI Scopus5 WoS5
    2018 Chen, C., Roberts, A., & Bunder, J. (2018). Boundary conditions for macroscale waves in an elastic system with microscale heterogeneity. IMA Journal of Applied Mathematics, 83(3), 347-379.
    DOI Scopus2 WoS2
    2017 Roberts, A., & Bunder, J. (2017). Slowly varying, macroscale models emerge from microscale dynamics over multiscale domains. IMA Journal of Applied Mathematics, 82(5), 971-1012.
    DOI Scopus2 WoS2
    2017 Bunder, J., Roberts, A., & Kevrekidis, I. (2017). Good coupling for the multiscale patch scheme on systems with microscale heterogeneity. Journal of Computational Physics, 337, 154-174.
    DOI Scopus8 WoS8
    2017 Bunder, J., & Roberts, A. (2017). Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations. Applied Mathematics and Computation, 304, 164-179.
    DOI Scopus4 WoS4
    2016 Bunder, J., Roberts, A., & Kevrekidis, I. (2016). Accuracy of patch dynamics with mesoscale temporal coupling for efficient massively parallel simulations. SIAM Journal on Scientific Computing, 38(4), C335-C371.
    DOI Scopus4 WoS4
    2015 Bunder, J., & Hill, J. (2015). General model for diffusive growth of nanostructures. IMA Journal of Applied Mathematics, 80(2), 235-254.
    DOI
    2015 Bunder, J., & Roberts, A. (2015). Numerical integration of ordinary differential equations with rapidly oscillatory factors. Journal of Computational and Applied Mathematics, 282, 54-70.
    DOI Scopus1 WoS1
    2014 Roberts, A., MacKenzie, T., & Bunder, J. (2014). A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions. Journal of Engineering Mathematics, 86(1), 175-207.
    DOI Scopus11 WoS12
    2012 Bunder, J., & Hill, J. (2012). Modelling the diffusive growth of carbon fullerenes. Materials Science Forum, 700, 100-103.
    DOI Scopus1 WoS1
    2012 Bunder, J., & Hill, J. (2012). Geometric influence on Ruderman-Kittel-Kasuya-Yosida interactions in zigzag carbon nanotubes. Journal of Chemical Physics, 136(15), 154504-1-154504-6.
    DOI Scopus6 WoS5
    2010 Bunder, J., & Hill, J. (2010). Electronic properties of carbon nanotubes with distinct bond lengths. Journal of Applied Physics, 107(2), 023511-1-023511-5.
    DOI Scopus2 WoS3
    2009 Bunder, J., & Lin, H. (2009). Ruderman-Kittel-Kasuya-Yosida interactions on a bipartite lattice. Physical Review B (Condensed Matter and Materials Physics), 80(15), 1-4.
    DOI Scopus45 WoS44
    2009 Bunder, J., & Lin, H. (2009). Generic short-range interactions in two-leg ladders. Physical Review B (Condensed Matter and Materials Physics), 79(4), 1-11.
    DOI Scopus4 WoS3
    2009 Yeo, S., Bunder, J., Lin, H., Jung, M., & Lee, S. (2009). Concurrent magnetic and metal-insulator transitions in Eu₁₋ₓSmₓB₆ single crystals. Applied Physics Letters, 94(4), 042509-1-042509-3.
    DOI Scopus2 WoS2
    2009 Bunder, J., & Hill, J. (2009). Diffusive growth of fullerenes and carbon nanotubes. Journal of Chemical Physics, 131(24), 244703-1-244703-5.
    DOI Scopus3 WoS3
    2009 Bunder, J., & Hill, J. (2009). Zigzag carbon nanotubes with generic electron-electron interactions. Physical Review B (Condensed Matter and Materials Physics), 80(15), 1-4.
    DOI Scopus6 WoS4
    2009 Bunder, J., & Hill, J. (2009). Electronic properties of silicon nanotubes with distinct bond lengths. Physical Review B (Condensed Matter and Materials Physics), 79(23), online (4 pages).
    DOI Scopus12 WoS12
    2008 Bunder, J., & Lin, H. (2008). Phase diagrams of the metallic zigzag carbon nanotube. Physical Review B (Condensed Matter and Materials Physics), 78(3), 1-15.
    DOI Scopus9 WoS9
    2007 Bunder, J., & Lin, H. (2007). Dynamical symmetry enlargement in metallic zigzag carbon nanotubes. Physical Review B (Condensed Matter and Materials Physics), 75(7), 1-7.
    DOI Scopus6 WoS6
    2007 Bunder, J. (2007). Spin-polarized transport in dilute magnetic semiconductor tunnel junctions. Applied Physics Letters, 91(9), 1-3.
    DOI Scopus3 WoS2
    2007 Bunder, J., Efetov, K., Kravtsov, V., Yevtushenko, O., & Zirnbauer, M. (2007). Superbosonization formula and its application to random matrix theory. Journal of Statistical Physics, 129(5-6), 809-832.
    DOI Scopus21 WoS20
    2006 Bunder, J., Sun, S., & Lin, H. (2006). Spin-wave relaxation in diluted magnetic semiconductors within the self-consistent Green's function approach. Applied Physics Letters, 89(7), 1-3.
    DOI Scopus6 WoS6
    2004 Bunder, J., & Efetov, K. (2004). Nonlinear σ model for odd-frequency triplet superconductivity in superconductor/ferromagnet structures. Physical Review B (Condensed Matter and Materials Physics), 70(13), 1-7.
    DOI Scopus1 WoS1
    2001 Bunder, J. E., & McKenzie, R. H. (2001). Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry. Nuclear Physics B, 592(3), 445-478.
    DOI Scopus7 WoS6
    1999 Bunder, J. E., & Mc Kenzie, R. H. (1999). Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field. Physical Review B - Condensed Matter and Materials Physics, 60(1), 344-358.
    DOI Scopus81 WoS83
    Bunder, J. E., Roberts, A. J., & Kevrekidis, I. G. (n.d.). Better buffers for patches in macroscale simulation of systems with
    microscale randomness.
    Bunder, J. E., & Lin, H. -H. (n.d.). Magnetism, spin-wave relaxation and spiral exchange in a trilayer
    magnetic junction.
    Roberts, A. J., MacKenzie, T., & Bunder, J. E. (n.d.). Accurate macroscale modelling of spatial dynamics in multiple dimensions.
    Tisdell, C. C., Jovanoski, Z., Guo, W., & Bunder, J. (n.d.). Proceedings of the 14th Engineering Mathematics and Applications Conference. ANZIAM Journal, 61.
    DOI
    Maclean, J., Bunder, J. E., Roberts, A. J., & Kevrekidis, I. G. (n.d.). A multiscale scheme accurately simulates macroscale shocks in an
    equation-free framework.
    Maclean, J., Bunder, J. E., Kevrekidis, I. G., & Roberts, A. J. (n.d.). Adaptively detect and accurately resolve macro-scale shocks in an
    efficient Equation-Free multiscale simulation.
  • Books

    Year Citation
    2015 Nelson, M., Mallet, D., Pincombe, B., & Bunder, J. (Eds.) (2015). Proceedings of the 12th Engineering Mathematics and Applications Conference, (EMAC2015), Adelaide, December 2015 (Vol. 57). Australian Mathematical Society.
    DOI
    2015 Nelson, M., Mallet, D., Pincombe, B., & Bunder, J. (Eds.) (2015). Proceedings of the 12th Engineering Mathematics and Applications Conference, (EMAC2015), Adelaide, December 2015 (Vol. 57). Australian Mathematical Society.
    DOI
    2014 Sharples, J., & Bunder, J. (Eds.) (2014). Proceedings of 17th Computational Techniques and Applications Conference (CTAC2014), Canberra, 1-3 December, 2014. Australian Mathematical Society.
    2013 Nelson, M., Bunder, J., Hamilton, T., & Jennings, M. (Eds.) (2013). Proceedings of the 11th Engineering Mathematics and Applications Conference, (EMAC2013), Brisbane, December 2013. Australian Mathematical Society.
    2013 McCue, S., Moroney, T., Mallett, D., & Bunder, J. (Eds.) (2013). Proceedings of 16th Computational Techniques and Applications Conference, ANZIAM J. (CTAC2012), Queensland, 23-26 September, 2012 (Vol. 54). Australian Mathematical Society.
  • Conference Papers

    Year Citation
    2015 Chen, C., Roberts, A., & Bunder, J. (2015). Macroscale boundary conditions for a non-linear heat exchanger. In Proceedings of 17th Computational Techniques and Applications Conference (CTAC2014), as published in ANZIAM Journal Vol. 56 (pp. C16-C31). Canberra, A.C.T.: Cambridge University Press.
    DOI
    2014 Chen, C., Roberts, A., & Bunder, J. (2014). The macroscale boundary conditions for diffusion in a material with microscale varying diffusivities. In A. Roberts, A. Bassom, G. Hocking, M. Nelson, T. Popiel, J. Bunder, . . . AustMS (Eds.), Proceedings of 11th Engineering Mathematics and Applications Conference (EMAC2013), as published in ANZIAM Journal Vol. 55 (pp. C218-C234). Brisbane, Qld.: Cambridge University Press.
    DOI
    2012 Bunder, J., & Roberts, A. (2012). Patch dynamics for macroscale modelling in one dimension. In ANZIAM Journal Vol. 53 (pp. 280-295). Australia: Cambridge University Press.
    DOI Scopus3 WoS3
    1996 Dytlewski, N., Evans, P. J., Noorman, J. T., Wielunski, L. S., & Bunder, J. (1996). Heavy ion time-of-flight ERDA of high dose metal implanted germanium. In Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms Vol. 118 (pp. 278-282). ARIZONA STATE UNIV CAMPUS, TEMPE, AZ: ELSEVIER.
    DOI Scopus4 WoS3

2018  Australian Research Council Discovery Project, DP180100050 with Prof. Tony Roberts (Adelaide) and Prof. Yannis Kevrekidis (Johns Hopkins).

  • Position: Research Associate
  • Phone: 83134846
  • Email: judith.bunder@adelaide.edu.au
  • Fax: 8313 3696
  • Campus: North Terrace
  • Building: Ingkarni Wardli, floor 6
  • Room: 6 62
  • Org Unit: Mathematical Sciences

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