ORCID Profile
0000-0002-9184-8941
Current Organisation
The University of Newcastle
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Publisher: Oxford University Press (OUP)
Date: 02-04-2008
Publisher: Elsevier BV
Date: 02-2021
Publisher: EDP Sciences
Date: 2004
DOI: 10.1051/M2AN:2004004
Publisher: Cambridge University Press (CUP)
Date: 2019
DOI: 10.1017/S1446181118000391
Abstract: The Douglas–Rachford method has been employed successfully to solve many kinds of nonconvex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections of hypersurfaces. Motivated by these discoveries, we reformulate a second order boundary value problem (BVP) as a feasibility problem where the sets are hypersurfaces. We show that such a problem may always be reformulated as a feasibility problem on no more than three sets and is well suited to parallelization. We explore the stability of the method by applying it to several BVPs, including cases where the traditional Newton’s method fails.
Publisher: Springer Science and Business Media LLC
Date: 03-07-2015
Publisher: Elsevier BV
Date: 09-2014
Publisher: Wiley
Date: 21-12-2020
DOI: 10.1002/NUM.22722
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 12-05-2013
Publisher: Springer Science and Business Media LLC
Date: 17-02-2023
DOI: 10.1007/S40789-023-00570-Z
Abstract: One factor that limits development of fundamental research on the influence of coke microstructure on its strength is the difficulty in quantifying the way that microstructure is both classified and distributed in three dimensions. To support such fundamental studies, this study evaluated a novel volumetric approach for classifying small (approx. 450 μm 3 ) blocks of coke microstructure from 3D computed tomography scans. An automated process for classifying microstructure blocks was described. It is based on Landmark Multi-Dimensional Scaling and uses the Bhattacharyya metric and k-means clustering. The approach was evaluated using 27 coke s les across a range of coke with different properties and reliably identified 6 ordered class of coke microstructure based on the distribution of voxel intensities associated with structural density. The lower class (1–2) subblocks tend to be dominated by pores and thin walls. Typically, there is an increase in wall thickness and reduced pore sizes in the higher classes. Inert features are also likely to be seen in higher classes (5–6). In general, this approach provides an efficient automated means for identifying the 3D spatial distribution of microstructure in CT scans of coke.
Publisher: Springer Science and Business Media LLC
Date: 12-06-2015
Publisher: Cambridge University Press (CUP)
Date: 07-2022
DOI: 10.1017/S1446181123000019
Abstract: We consider a local projection stabilization based on biorthogonal systems for convection–diffusion–reaction differential equations with mixed boundary conditions. The approach based on biorthogonal systems is numerically more efficient than other existing approaches to obtain a uniform approximation for convection dominated problems. We prove optimal a priori error estimates for the proposed numerical technique. Numerical ex les are presented to demonstrate the performance of the approach.
Publisher: Elsevier BV
Date: 04-2014
Publisher: Elsevier BV
Date: 05-2013
Publisher: Wiley
Date: 11-10-2014
DOI: 10.1002/FLD.3848
Publisher: MDPI AG
Date: 06-09-2022
DOI: 10.3390/MATH10183227
Abstract: The goal of this research article is to introduce a sequence of α–Stancu–Schurer–Kantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of modulus of continuity. A Voronovskaja-type approximation result is also proven. Next, error analysis and convergence of the operators for certain functions are presented numerically and graphically. Furthermore, two-dimensional α–Stancu–Schurer–Kantorovich operators are constructed and their rate of convergence, graphical representation of approximation and numerical error estimates are presented.
Publisher: Public Library of Science (PLoS)
Date: 07-07-2021
DOI: 10.1371/JOURNAL.PCBI.1008353
Abstract: Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are: solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues. However, these swarms are usually preceded by the aggregation of juvenile wingless locust nymphs. In this paper we attempt to understand how the distribution of food resources affect the group formation process. We do this by introducing a multi-population partial differential equation model that includes non-local locust interactions, local locust and food interactions, and gregarisation. Our results suggest that, food acts to increase the maximum density of locust groups, lowers the percentage of the population that needs to be gregarious for group formation, and decreases both the required density of locusts and time for group formation around an optimal food width. Finally, by looking at foraging efficiency within the numerical experiments we find that there exists a foraging advantage to being gregarious.
Publisher: Wiley
Date: 14-07-2016
DOI: 10.1002/NUM.22082
Publisher: Cambridge University Press (CUP)
Date: 05-04-2017
DOI: 10.1017/S1446181116000365
Abstract: An initial-boundary value problem for a time-fractional diffusion equation is discretized in space, using continuous piecewise-linear finite elements on a domain with a re-entrant corner. Known error bounds for the case of a convex domain break down, because the associated Poisson equation is no longer $H^{2}$ -regular. In particular, the method is no longer second-order accurate if quasi-uniform triangulations are used. We prove that a suitable local mesh refinement about the re-entrant corner restores second-order convergence. In this way, we generalize known results for the classical heat equation.
Publisher: Elsevier BV
Date: 07-2018
Publisher: Cold Spring Harbor Laboratory
Date: 21-09-2020
DOI: 10.1101/2020.09.21.305896
Abstract: Locust swarms are a major threat to agriculture, affecting every continent except Antarctica and impacting the lives of 1 in 10 people. Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues. However, these swarms are usually preceded by the formation of hopper bands by the juvenile wingless locust nymphs. It is thus important to understand the hopper band formation process to control locust outbreaks. On longer time-scales, environmental conditions such as rain events synchronize locust lifecycles and can lead to repeated outbreaks. On shorter time-scales, changes in resource distributions at both small and large spatial scales have an effect on locust gregarisation. It is these short time-scale locust-resource relationships and their effect on hopper band formation that are of interest. In this paper we investigate not only the effect of food on both the formation and characteristics of locust hopper bands but also a possible evolutionary explanation for gregarisation in this context. We do this by deriving a multi-population aggregation equation that includes non-local inter-in idual interactions and local inter-in idual and food interactions. By performing a series of numerical experiments we find that there exists an optimal food width for locust hopper band formation, and by looking at foraging efficiency within the model framework we uncover a possible evolutionary reason for gregarisation. Locusts are short horned grass hoppers that live in two diametrically opposed behavioural states. In the first, solitarious, they will actively avoid other locusts, whereas the second, gregarious, they will actively seek them out. It is in this gregarious state that locusts form the recognisable and destructive flying adult swarms. However, prior to swarm formation juvenile flightless locusts will form marching hopper bands and make their way from food source to food source. Predicting where these hopper bands might form is key to controlling locust outbreaks. Research has shown that changes in food distributions can affect the transition from solitarious to gregarious. In this paper we construct a mathematical model of locust-locust and locust-food interactions to investigate how and why isolated food distributions affect hopper band formation. Our findings suggest that there is an optimal food width for hopper band formation and that being gregarious increases a locusts ability to forage when food width decreases.
Publisher: Springer Science and Business Media LLC
Date: 11-07-2006
Publisher: SAGE Publications
Date: 2021
DOI: 10.1177/17483026211008405
Abstract: We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares functional. The penalties are based on partial differential operators, and are integrated using the finite element method. We compare three methods to two problems: to remove the mixture of Gaussian and impulsive noise from an image, and to recover a continuous function from a set of noisy observations.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 10-08-2017
Publisher: Hindawi Limited
Date: 11-04-2013
DOI: 10.1155/2013/189045
Abstract: We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagrange multiplier space forming biorthogonal and quasi-biorthogonal systems, respectively. We also establish an optimal a priori error estimate for both finite element approximations.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 05-09-2017
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 16-07-2018
Publisher: Elsevier BV
Date: 07-2006
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 11-08-2020
DOI: 10.21914/ANZIAMJ.V61I0.15176
Abstract: We present a mixed finite element method for the elasticity problem. We expand the standard Hu–Washizu formulation to include a pressure unknown and its Lagrange multiplier. By doing so, we derive a five-field formulation. We apply a biorthogonal system that leads to an efficient numerical formulation. We address the coercivity problem by adding a stabilisation term with a parameter. We also present an analysis of the optimal choices of parameter approximation. References I. Babuska and T. Strouboulis. The finite element method and its reliability. Oxford University Press, New York, 2001. cademic roduct/the-finite-element-method-and-its-reliability-9780198502760?cc=au& lang=en& . D. Braess. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, Cambridge, UK, 3rd edition edition, 2007. doi:10.1017/CBO9780511618635. J. K. Djoko and B. D. Reddy. An extended Hu–Washizu formulation for elasticity. Comput. Meth. Appl. Mech.Eng. 195(44):6330–6346, 2006. doi:10.1016/j.cma.2005.12.013. J. Droniou, M. Ilyas, B. P. Lamichhane, and G. E. Wheeler. A mixed finite element method for a sixth-order elliptic problem. IMA J. Numer. Anal. 39(1):374–397, 2017. doi:10.1093/imanum/drx066. M. Ilyas. Finite element methods and multi-field applications. PhD thesis, University of Newcastle, 2019. 959.13/1403421. M. Ilyas and B. P. Lamichhane. A stabilised mixed finite element method for the Poisson problem based on a three-field formulation. In Proceedings of the 12th Biennial Engineering Mathematics and Applications Conference, EMAC-2015, volume 57 of ANZIAM J. pages C177–C192, 2016. doi:10.21914/anziamj.v57i0.10356. M. Ilyas and B. P. Lamichhane. A three-field formulation of the Poisson problem with Nitsche approach. In Proceedings of the 13th Biennial Engineering Mathematics and Applications Conference, EMAC-2017, volume 59 of ANZIAM J. pages C128–C142, 2018. doi:10.21914/anziamj.v59i0.12645. B. P. Lamichhane. Two simple finite element methods for Reissner–Mindlin plates with cl ed boundary condition. Appl. Numer. Math. 72:91–98, 2013. doi:10.1016/j.apnum.2013.04.005. B. P. Lamichhane and E. P. Stephan. A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems. Numer. Meth. Part. Diff. Eq. 28(4):1336–1353, 2011. doi:10.1002/num.20683. B. P. Lamichhane, A. T. McBride, and B. D. Reddy. A finite element method for a three-field formulation of linear elasticity based on biorthogonal systems. Comput. Meth. Appl. Mech. Eng. 258:109–117, 2013. doi:10.1016/j.cma.2013.02.008. J. C. Simo and F. Armero. Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int. J. Numer. Meth. Eng. 33(7):1413–1449, may 1992. doi:10.1002/nme.1620330705. A. Zdunek, W. Rachowicz, and T. Eriksson. A five-field finite element formulation for nearly inextensible and nearly incompressible finite hyperelasticity. Comput. Math. Appl. 72(1):25–47, 2016. doi:10.1016/j.camwa.2016.04.022.
Publisher: Elsevier BV
Date: 11-2009
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 07-03-2022
DOI: 10.21914/ANZIAMJ.V62.16056
Abstract: Aggregations abound in nature, from cell formations to locust swarms. One method of modelling these aggregations is the non-local aggregation equation with the addition of degenerate diffusion. In this article we develop a finite volume based numerical scheme for this style of equation and perform an error, computation time, and convergence analysis. In addition we investigate two methods for approximating the non-local component. References A. J. Bernoff and C. M. Topaz. Nonlocal aggregation models: A primer of swarm equilibria. SIAM Rev. 55.4 (2013), pp. 709–747. doi: 10.1137/130925669 R. Bürger, D. Inzunza, P. Mulet, and L. M. Villada. Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour. Appl. Numer. Math. 144 (2019), pp. 234–252. doi: 10.1016/j.apnum.2019.04.018 J. A. Carrillo, A. Chertock, and Y. Huang. A finite-volume method for nonlinear nonlocal equations with a gradient flow structure. In: Commun. Comput. Phys. 17.1 (2015), pp. 233–258. doi: 10.4208/cicp.160214.010814a J. R. Dormand and P. J. Prince. A family of embedded Runge–Kutta formulae. J. Comput. Appl. Math. 6.1 (1980), pp. 19–26. doi: 10.1016/0771-050X(80)90013-3 J. von zur Gathen and J. Gerhard. Modern computer algebra. 3rd ed. Cambridge University Press, 2013. doi: 10.1017/CBO9781139856065 F. Georgiou, J. Buhl, J. E. F. Green, B. Lamichhane, and N. Thamwattana. Modelling locust foraging: How and why food affects group formation. PLOS Comput. Biol. 17.7 (2021), e1008353. doi: 10.1371/journal.pcbi.1008353 F. Georgiou, B. P. Lamichhane, and N. Thamwattana. An adaptive numerical scheme for a partial integro-differential equation. Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2018. Ed. by B. Lamichhane, T. Tran, and J. Bunder. Vol. 60. ANZIAM J. 2019, pp. C187–C200. doi: 10.21914/anziamj.v60i0.14066 F. Georgiou, N. Thamwattana, and B. P. Lamichhane. Modelling cell aggregation using a modified swarm model. Proceedings of the 23rd International Congress on Modelling and Simulation, MODSIM2019. Vol. 6. 2019, pp. 22–27. doi: 10.36334/modsim.2019.a1.georgiou J. E. F. Green, S. L. Waters, J. P. Whiteley, L. Edelstein-Keshet, K. M. Shakesheff, and H. M. Byrne. Non-local models for the formation of hepatocyte–stellate cell aggregates. J. Theor. Bio. 267.1 (2010), pp. 106–120. doi: 10.1016/j.jtbi.2010.08.013 R. J. LeVeque. Finite-volume methods for hyperbolic Pproblems. Cambridge Texts in Applied Mathematics. Cambridge University Press, 2002. doi: 10.1017/CBO9780511791253 C. F. Van Loan. Introduction to Scientific Computing: A Matrix Vector Approach Using MATLAB. 1997. url: s/higher-education rogram/Van- Loan-Introduction-to-Scientific-Computing-A-Matrix-Vector- Approach-Using-MATLAB-2nd-Edition/PGM215520.html A. Mogilner and L. Edelstein-Keshet. A non-local model for a swarm. J. Math. Bio. 38.6 (1999), pp. 534–570. doi: 10.1007/s002850050158 C. M. Topaz, A. L. Bertozzi, and M. A. Lewis. A nonlocal continuum model for biological aggregation. Bull. Math. Biol. 68 (2006), p. 1601. doi: 10.1007/s11538-006-9088-6 C. M. Topaz, M. R. D’Orsogna, L. Edelstein-Keshet, and A. J. Bernoff. Locust dynamics: Behavioral phase change and swarming. PLOS Comput. Bio. 8.8 (2012), e1002642. doi: 10.1371/journal.pcbi.1002642
Publisher: Springer Science and Business Media LLC
Date: 03-08-2011
Publisher: American Mathematical Society (AMS)
Date: 2007
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 19-03-2023
DOI: 10.21914/ANZIAMJ.V64.17543
Abstract: We consider a local projection stabilization based on biorthogonal systems for convection–diffusion–reaction differential equations with mixed boundary conditions. The approach based on biorthogonal systems is numerically more efficient than other existing approaches to obtain a uniform approximation for convection dominated problems. We prove optimal a priori error estimates for the proposed numerical technique. Numerical ex les are presented to demonstrate the performance of the approach. doi: 10.1017/S1446181123000019
Publisher: MDPI AG
Date: 03-01-2021
DOI: 10.3390/APP11010391
Abstract: The main objective of the current work is to determine meshless methods using the radial basis function (rbf) approach to estimate the elastic strain field from energy-resolved neutron imaging. To this end, we first discretize the longitudinal ray transformation with rbf methods to give us an unconstrained optimization problem. This discretization is then transformed into a constrained optimization problem by adding equilibrium conditions to ensure uniqueness. The efficiency and accuracy of this approach are investigated for the situation of 2d plane stress. In addition, comparisons are made between the results obtained with rbf collocation, finite-element (fem) and analytical solution methods for test problems. The method is then applied to experimentally measured continuous and discontinuous strain fields using steel s les for an offset ring-and-plug and crushed ring, respectively.
Publisher: Springer Science and Business Media LLC
Date: 29-08-2019
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 07-2009
Publisher: Springer Science and Business Media LLC
Date: 22-09-2005
Publisher: IOP Publishing
Date: 17-11-2017
Publisher: Cambridge University Press (CUP)
Date: 10-2017
DOI: 10.1017/S144618111700030X
Abstract: A new minimization principle for the Poisson equation using two variables – the solution and the gradient of the solution – is introduced. This principle allows us to use any conforming finite element spaces for both variables, where the finite element spaces do not need to satisfy the so-called inf–sup condition. A numerical ex le demonstrates the superiority of this approach.
Publisher: Elsevier BV
Date: 07-2014
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 28-10-2015
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 31-12-2021
DOI: 10.21914/ANZIAMJ.V63.15944
Abstract: Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement. doi:10.1017/S1446181121000353
Publisher: Wiley
Date: 31-05-2011
DOI: 10.1002/NUM.20683
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 15-09-2016
Publisher: Wiley
Date: 13-08-2009
DOI: 10.1002/NME.2594
Publisher: MDPI AG
Date: 22-03-2020
Abstract: A novel pulsed neutron imaging technique based on the finite element method is used to reconstruct the residual strain within a polycrystalline material from Bragg edge strain images. This technique offers the possibility of a nondestructive analysis of strain fields with a high spatial resolution. The finite element approach used to reconstruct the strain uses the least square method constrained by the conditions of equilibrium. This inclusion of equilibrium makes the problem well-posed. The procedure is developed and verified by validating for a cantilevered beam problem. It is subsequently demonstrated by reconstructing the strain from experimental data for a ring-and-plug s le, measured at the spallation neutron source RADEN at J-PARC in Japan. The reconstruction is validated by comparison with conventional constant wavelength strain measurements on the KOWARI diffractometer at ANSTO in Australia. It is also shown that the addition of a Tikhonov regularisation scheme further improves the reconstruction.
Publisher: Elsevier BV
Date: 09-2007
Publisher: Springer Science and Business Media LLC
Date: 12-2002
Publisher: Walter de Gruyter GmbH
Date: 21-06-2018
Abstract: We consider a mixed finite element method for an obstacle problem with the p -Laplace differential operator for p ∈ ( 1 , ∞ ) {p\\in(1,\\infty)} , where the obstacle condition is imposed by using a Lagrange multiplier. In the discrete setting the Lagrange multiplier basis forms a biorthogonal system with the standard finite element basis so that the variational inequality can be realized in the point-wise form. We provide a general a posteriori error estimate for adaptivity and prove an a priori error estimate. We present numerical results for the adaptive scheme (mesh-size adaptivity with and without polynomial degree adaptation) for the singular case p = 1.5 {p=1.5} and the degenerated case p = 3 {p=3} . We also present numerical results on the mesh independency and on the polynomial degree scaling of the discrete inf-sup constant when using biorthogonal basis functions for the dual variable defined on the same mesh with the same polynomial degree distribution.
Publisher: Springer Science and Business Media LLC
Date: 08-03-2004
Publisher: Elsevier BV
Date: 2015
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 28-07-2022
DOI: 10.21914/ANZIAMJ.V63.17187
Abstract: A vital input for steel manufacture is a coal-derived solid fuel called coke. Digital reconstructions and simulations of coke are valuable tools to analyse and test coke properties. We implement biased voxel iteration into a simulated annealing method via a kernel convolution to reduce the number of iterations required to generate a digital coke microstructure. We demonstrate that voxel connectivity assumptions impact the number of iterations and reduce the normalised computation time required to generate a digital microstructure by as much as 70%. References L. De Floriani, U. Fugacci, and F. Iuricich. Homological shape analysis through discrete morse theory. Perspectives in Shape Analysis. Ed. by M. Breuss, A. Bruckstein, P. Maragos, and S. Wuhrer. Springer, 2016, pp. 187–209. doi: 10.1007/978-3-319-24726-7_9 M. A. Diez, R. Alvarez, and C. Barriocanal. Coal for metallurgical coke production: predictions of coke quality and future requirements for cokemaking. Int. J. Coal Geol. 50.1–4 (2002), pp. 389–412. doi: 10.1016/S0166-5162(02)00123-4 D. T. Fullwood, S. R. Kalidindi, S. R. Niezgoda, A. Fast, and N. H son. Gradient-based microstructure reconstructions from distributions using fast Fourier transforms. Mat. Sci. Eng. A 494.1–2 (2008), pp. 68–72. doi: 10.1016/j.msea.2007.10.087 E.-Y. Guo, N. Chawla, T. Jing, S. Torquato, and Y. Jiao. Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation-erosion method. Mat. Character. 89 (2014), pp. 33–42. doi: 10.1016/j.matchar.2013.12.011 Y. Jiao, F. H. Stillinger, and S. Torquato. Modeling heterogeneous materials via two-point correlation functions: Basic principles. Phys. Rev. E 76.3, 031110 (2007). doi: 10.1103/PhysRevE.76.031110 H. Kumar, C. L. Briant, and W. A. Curtin. Using microstructure reconstruction to model mechanical behavior in complex microstructures. Mech. Mat. 38.8–10 (2006), pp. 818–832. doi: 10.1016/j.mechmat.2005.06.030 Z. Ma and S. Torquato. Generation and structural characterization of Debye random media. Phys. Rev. E 102.4, 043310 (2020). doi: 10.1103/PhysRevE.102.043310 F. Meng, S. Gupta, D. French, P. Koshy, C. Sorrell, and Y. Shen. Characterization of microstructure and strength of coke particles and their dependence on coal properties. Powder Tech. 320 (2017), pp. 249–256. doi: 10.1016/j.powtec.2017.07.046 M. G. Rozman and M. Utz. Uniqueness of reconstruction of multiphase morphologies from two-point correlation functions. Phys. Rev. Lett. 89.13, 135501 (2002). doi: 10.1103/PhysRevLett.89.135501 T. Tang, Q. Teng, X. He, and D. Luo. A pixel selection rule based on the number of different-phase neighbours for the simulated annealing reconstruction of sandstone microstructure. J. Microscopy 234.3 (2009), pp. 262–268. doi: 10.1111/j.1365-2818.2009.03173.x S. Torquato. Microstructure characterization and bulk properties of disordered two-phase media. J. Stat. Phys. 45.5 (1986), pp. 843–873. doi: 10.1007/BF01020577 S. Torquato and H. W. Haslach Jr. Random heterogeneous materials: microstructure and macroscopic properties. Appl. Mech. Rev. 55.4 (2002), B62–B63. doi: 10.1115/1.1483342 S. Torquato and C. L. Y. Yeong. Reconstructing random media.II: three-dimensional media from two-dimensional cuts. Phys. Rev. E 58.1 (1998), pp. 224–233. doi: 10.1103/PhysRevE.58.224 on p. C128). C. L. Y. Yeong and S. Torquato. Reconstructing random media. Phys. Rev. E 57.1, 495 (1998). doi: 10.1103/PhysRevE.57.495
Publisher: Elsevier BV
Date: 07-2011
Publisher: Springer Science and Business Media LLC
Date: 05-12-2014
Publisher: Wiley
Date: 26-07-2018
DOI: 10.1002/ACM2.12419
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 16-07-2017
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 29-07-2011
Publisher: Springer Science and Business Media LLC
Date: 06-2009
Publisher: Elsevier BV
Date: 08-2019
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 25-03-2019
Publisher: Elsevier BV
Date: 10-2018
Publisher: Cambridge University Press (CUP)
Date: 10-2021
DOI: 10.1017/S1446181121000353
Abstract: Dye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement.
Publisher: Oxford University Press (OUP)
Date: 05-12-2019
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 11-01-2016
Publisher: Elsevier BV
Date: 2023
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 11-10-2019
DOI: 10.21914/ANZIAMJ.V60I0.14041
Abstract: The virtual element method is an extension of the finite element method on polygonal meshes. The virtual element basis functions are generally unknown inside an element and suitable projections of the basis functions onto polynomial spaces are used to construct the elemental stiffness and mass matrices. We present a gradient recovery method based on an oblique projection, where the gradient of the L2-polynomial projection of a solution is projected onto a virtual element space. This results in a computationally efficient numerical method. We present numerical results computing the gradients on different polygonal meshes to demonstrate the flexibility of the method. References B. Ahmad, A. Alsaedi, F. Brezzi, L. D. Marini, and A. Russo. Equivalent projectors for virtual element methods. Comput. Math. Appl., 66(3):376391, 2013. doi:10.1016/j.camwa.2013.05.015. L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, and A. Russo. Basic principles of virtual element methods. Math. Mod. Meth. Appl. Sci., 23(01): 199214, 2013. doi:10.1142/S0218202512500492. L. Beirao da Veiga, F. Brezzi, L. D. Marini, and A. Russo. The hitchhiker's guide to the virtual element method. Math. Mod. Meth. Appl. Sci., 24(08): 15411573, 2014. doi:10.1142/S021820251440003X. Ilyas, M. and Lamichhane, B. P. and Meylan, M. H. A gradient recovery method based on an oblique projection and boundary modification. In Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2016, volume 58 of ANZIAM J., pages C34C45, 2017. doi:10.21914/anziamj.v58i0.11730. B. P. Lamichhane. A gradient recovery operator based on an oblique projection. Electron. Trans. Numer. Anal., 37:166172, 2010. URL olumes/2001-2010/vol37/abstract.php?vol=37& ages=166-172. O. J. Sutton. Virtual element methods. PhD thesis, University of Leicester, Department of Mathematics, 2017. URL 381/39955. C. Talischi, G. H. Paulino, A. Pereira, and I. F. M. Menezes. Polymesher: a general-purpose mesh generator for polygonal elements written in matlab. Struct. Multidiscip. O., 45(3):309328, 2012. doi:10.1007/s00158-011-0706-z. G. Vacca and L. Beirao da Veiga. Virtual element methods for parabolic problems on polygonal meshes. Numer. Meth. Part. D. E., 31(6): 21102134, 2015. doi:10.1002/num.21982. J. Xu and Z. Zhang. Analysis of recovery type a posteriori error estimators for mildly structured grids. Math. Comput., 73:11391152, 2004. doi:10.1090/S0025-5718-03-01600-4.
Publisher: Hindawi Limited
Date: 03-02-2015
DOI: 10.1155/2015/187604
Abstract: A gradient recovery operator based on projecting the discrete gradient onto the standard finite element space is considered. We use an oblique projection, where the test and trial spaces are different, and the bases of these two spaces form a biorthogonal system. Biorthogonality allows efficient computation of the recovery operator. We analyze the approximation properties of the gradient recovery operator. Numerical results are presented in the two-dimensional case.
Publisher: Elsevier BV
Date: 10-2013
Publisher: Hindawi Limited
Date: 24-11-2013
DOI: 10.1155/2013/798059
Abstract: We present a new finite element method for Darcy-Stokes-Brinkman equations using primal and dual meshes for the velocity and the pressure, respectively. Using an orthogonal basis for the discrete space for the pressure, we use an efficiently computable stabilization to obtain a uniform convergence of the finite element approximation for both limiting cases.
No related grants have been discovered for Bishnu Lamichhane.