Applied Mathematics
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Applied Mathematics at the University of Adelaide is one of the leading groups in teaching and research in Australia. Members conduct internationally recognized research into a wide range of Applied Mathematics. The research within Applied Mathematics can be loosely grouped into the following areas.
- Biomedical Engineering
- Fluid Dynamics
- Optimisation
- Stochastic Modelling
- Teletraffic Research
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Item Metadata only A 3-D non-hydrostatic pressure model for small amplitude free surface flows(John Wiley & Sons Ltd, 2006) Lee, J.; Teubner, M.; Nixon, J.; Gill, P.A three-dimensional, non-hydrostatic pressure, numerical model with k- equations for small amplitude free surface flows is presented. By decomposing the pressure into hydrostatic and non-hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step the momentum equations are solved without the non-hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure-Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the central processing unit (CPU) time dramatically. In order to prevent pressure oscillations which may arise in collocated grid arrangements, transformed velocities are defined at cell faces by interpolating velocities at grid nodes. After the new pressure field is obtained, the intermediate velocities, which are calculated from the previous fractional step, are updated. The newly developed model is verified against analytical solutions, published results, and experimental data, with excellent agreement.Item Metadata only A boundary element method for a second order elliptic partial differential equation with variable coefficients(ELSEVIER SCI LTD, 1997) Ang, W.; Kusuma, J.; Clements, D.A boundary element method is derived for solving a class of boundary value problems governed by an elliptic second order linear partial differential equation with variable coefficients. Numerical results are given for a specific test problem.Item Metadata only A boundary element method for anisotropic inhomogeneous elasticity(Pergamon-Elsevier Science Ltd, 2001) Azis, M.; Clements, D.This paper is concerned with obtaining boundary integral equations for the numerical solution of the partial differential equations governing static deformations of inhomogeneous anisotropic elastic materials. The elastic parameters for the inhomogeneous materials are assumed to vary continuously with the spatial variables.Item Metadata only A boundary element method for generalized plane thermoelastic deformations of anistropic elastic media(SAGE PUBLICATIONS INC, 1999) Ang, W.; Clements, D.; Cooke, T.A boundary element method is derived for solving a class of boundary value problems governing generalized plane thermoelastic deformations of anisotropic elastic materials. The method involves boundary integrals only and provides a simple boundary element procedure for a wide class of problems which do not involve inertia or coupling effects. Numerical results are given for some specific problems in order to assess the effectiveness of the method.Item Metadata only A boundary element method for steady infiltration from periodic channels(Australian Mathematical Society, 2003) Azis, M.; Clements, D.; Lobo, M.The matric flux potential and horizontal and vertical flux distributions are obtained for periodic irrigation channels by using boundary integral equation techniques. Numerical results are given for the special cases of semicircular and rectangular channels and the results compared with those of Batu [Soil Science Society of America Journal, 42:545--549, 1978] and Warrick and Lomen [Soil Science Society of America Journal, 40:639--643, 1976] for a flat strip. The results show that the matric flux potential associated with the flat strip and semicircular channel are similar; whereas for the particular rectangular channel considered the matric flux potential is subtantially increased in the region adjacent to the channel.Item Metadata only A boundary element method for the numerical solution of a class of elliptic boundary value problems for anisotropic inhomogeneous media(Australian Mathematical Society, 2003) Azis, M.; Clements, D.; Budhi, W.A boundary element method is obtained for a class of two dimensional elliptic boundary value problems for inhomogeneous media. The method can be applied to variety of problems in such areas as antiplane strain in elastostatics, plane thermostatic problems for inhomogeneous anisotropic materials and flow through porous media.Item Metadata only A boundary element method for the solution of a class of steady-state problems for anisotropic media(American Society of Mechanical Engineers, 1999) Clements, D.; Budhi, W.Item Metadata only A boundary integral formulation for the indentation of an anisotropic bi-layered elastic slab(Springer, 2006) Ang, W.; Sridhar, I.; Clements, D.; First International Conference on Computational Methods. (2004 : Singapore); Liu, G.This conference proceedings contains some 290 papers from more than 30 countries/regions. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Computational methods for geomechanics, machine learning, vibration, shock, impact, health monitoring, material modeling, fracture and damage mechanics, multi-physics and multi-scales simulation, sports and environments are also included. All the papers are pre-reviewed before they are accepted for publication in this proceedings. The proceedings will provide an informative, timely and invaluable resource for engineers and scientists working in the important areas of computational methods.Item Metadata only A characterization of suprathreshold stochastic resonance in an array of comparators by correlation coefficient(World Scientific Publishing Co. Pty. Ltd., 2002) McDonnell, M.; Abbott, D.; Pearce, C.Suprathreshold Stochastic Resonance (SSR), as described recently by Stocks, is a new form of Stochastic Resonance (SR) which occurs in arrays of nonlinear elements subject to aperiodic input signals and noise. These array elements can be threshold devices or FitzHugh-Nagumo neuron models for example. The distinguishing feature of SSR is that the output measure of interest is not maximized simply for nonzero values of input noise, but is maximized for nonzero values of the input noise to signal intensity ratio, and the effect occurs for signals of arbitrary magnitude and not just subthreshold signals. The original papers described SSR in terms of information theory. Previous work on SR has used correlation based measures to quantify SR for aperiodic input signals. Here, we argue the validity of correlation based measures and derive exact expressions for the cross-correlation coefficient in the same system as the original work, and show that the SSR effect also occurs in this alternative measure. If the output signal is thought of as a digital estimate of the input signal, then the output noise can be considered simply as quantization noise. We therefore derive an expression for the output signal to quantization noise ratio, and show that SSR also occurs in this measure.Item Metadata only A comparison of models for catchment runoff(The Institution of Engineers, Australia, 2002) Metcalfe, A.; Heneker, T.; Lambert, M.; Kuczera, G.; Atan, I.; Hydrology and Water Resources Symposium (27th : 2002 : Melbourne, Vic.); David Sheehan,Item Open Access A comparison of Poisson and uniform sampling for active measurements(IEEE-Inst Electrical Electronics Engineers Inc, 2006) Roughan, M.Active probes of network performance represent samples of the underlying performance of a system. Some effort has gone into considering appropriate sampling patterns for such probes, i.e., there has been significant discussion of the importance of sampling using a Poisson process to avoid biases introduced by synchronization of system and measurements. However, there are unanswered questions about whether Poisson probing has costs in terms of sampling efficiency, and there is some misinformation about what types of inferences are possible with different probe patterns. This paper provides a quantitative comparison of two different sampling methods. This paper also shows that the irregularity in probing patterns is useful not just in avoiding synchronization, but also in determining frequency-domain properties of a system. This paper provides a firm basis for practitioners or researchers for making decisions about the type of sampling they should use in a particular applications, along with methods for the analysis of their outputs.Item Metadata only A complete yield curve description of a Markov interest rate model(World Scientific Publishing Co Pte Ltd, 2003) Elliott, R.; Mamon, R.This paper aims to present a complete term structure characterisation of a Markov interest rate model. To attain this objective, we first give a proof that establishes the Unbiased Expectation Hypothesis (UEH) via the forward measure. The UEH result is then employed, which considerably facilitates the calculation of an explicit analytic expression for the forward rate f(t, T). The specification of the bond price P(t, T), yield rate Y(t, T) and f(t, T) gives a complete set of yield curve descriptions for an interest rate market where the short rate r is a function of a continuous time Markov chain.Item Metadata only A complex variable boundary element method for a class of boundary value problems in anisotropic thermoelasticity(Gordon and Breach, 1999) Ang, W.; Clements, D.; Cooke, T.A boundary element method based on the Cauchy's integral formulae, called the complex variable boundary element method (CVBEM), is proposed for the numerical solution of boundary value problems governing plane thermoelastic deformations of anisotropic elastic bodies. The method is applicable for a wide class of problems which do not involve inertia or coupling effects and can be easily and efficiently implemented on the computer. It is applied to solve specific test problems.Item Metadata only A corrected quadrature formula and applications(Australian Mathematical Society, 2004) Ujevic, N.; Roberts, A.A straightforward three-point quadrature formula of closed type is derived that improves on Simpson’s rule. Just using the additional information of the integrand’s derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite formulas can be applied to integrands with lower order derivatives.Item Metadata only A coupled damage-plasticity model for concrete based on thermodynamic principles: Part 1: model formulation and parameter identification(John Wiley & Sons, 2008) Nguyen, G.; Houlsby, G.AbstractThe development of a coupled damage‐plasticity constitutive model for concrete is presented. Emphasis is put on thermodynamic admissibility, rigour and consistency both in the formulation of the model, and in the identification of model parameters based on experimental tests. The key feature of the thermodynamic framework used in this study is that all behaviour of the model can be derived from two specified energy potentials, following procedures established beforehand. Based on this framework, a constitutive model featuring full coupling between damage and plasticity in both tension and compression is developed. Tensile and compressive responses of the material are captured using two separate damage criteria, and a yield criterion with a multiple hardening rule. A crucial part of this study is the identification of model parameters, with these all being shown to be identifiable and computable based on standard tests on concrete. Behaviour of the model is assessed against experimental data on concrete. Copyright © 2007 John Wiley & Sons, Ltd.Item Metadata only A coupled damage-plasticity model for concrete based on thermodynamic principles: Part II: non-local regularization and numerical implementation(John Wiley & Sons, 2008) Nguyen, G.; Houlsby, G.AbstractNon‐local regularization is applied to a new coupled damage–plasticity model (Int. J. Numer. Anal. Meth. Geomech. 2007; DOI: 10.1002/nag.627), turning it into a non‐local model. This procedure resolves softening‐related problems encountered in local constitutive models when dealing with softening materials. The parameter identification of the new non‐local coupled damage–plasticity model is addressed, with all parameters being shown to be obtainable from the experimental data on concrete. Because of the appearance of non‐local spatial integrals in the constitutive equations, a new implementation scheme is developed for the integration of the non‐local incremental constitutive equations in nonlinear finite element analysis. The performance of the non‐local model is assessed against a range of two‐dimensional structural tests on concrete, illustrating the stability of the stress update procedure and the lack of mesh dependency of the model. Copyright © 2007 John Wiley & Sons, Ltd.Item Open Access A deterministic discretisation-step upper bound for state estimation via Clark transformations(North Atlantic Science Publishing Company, 2004) Malcolm, W.; Elliott, R.; Van Der Hoek, J.We consider the numerical stability of discretisation schemes for continuous-time state estimation filters. The dynamical systems we consider model the indirect observation of a continuous-time Markov chain. Two candidate observation models are studied. These models are (a) the observation of the state through a Brownian motion, and (b) the observation of the state through a Poisson process. It is shown that for robust filters (via Clark's transformation), one can ensure nonnegative estimated probabilities by choosing a maximum grid step to be no greater than a given bound. The importance of this result is that one can choose an a priori grid step maximum ensuring nonnegative estimated probabilities. In contrast, no such upper bound is available for the standard approximation schemes. Further, this upper bound also applies to the corresponding robust smoothing scheme, in turn ensuring stability for smoothed state estimates.Item Metadata only A dual-reciprocity boundary element method for a class of elliptic boundary value problems for non-homogenous anisotropic media(Elsevier Sci Ltd, 2003) Ang, W.; Clements, D.; Vahdati, N.A dual-reciprocity boundary element method is proposed for the numerical solution of a two-dimensional boundary value problem (BVP) governed by an elliptic partial differential equation with variable coefficients. The BVP under consideration has applications in a wide range of engineering problems of practical interest, such as in the calculation of antiplane stresses or temperature in non-homogeneous anisotropic media. The proposed numerical method is applied to solve specific test problems.Item Metadata only A Finite-Dimensional Filter for Hybrid Observations(Institute of Electrical and Electronics Engineers (IEEE), 1998) Elliott, R.; van der Hoek, J.Item Metadata only A fundamental solution for linear second-order elliptic systems with variable coefficients(Kluwer Academic Publ, 2004) Clements, D.A fundamental solution and a Green’s function are obtained for a system of second-order elliptic partial differential equations with variable coefficients. Both the fundamental solution and the Green’s function are suitable for facilitating the numerical solution of boundary-value problems in a number of practical areas. Some particular areas of application are outlined.