Alternate strip-based substructuring algorithms for elliptic PDEs in two dimensions

^** Email: angela.mihai{at}strath.ac.uk^*** Email: alan.craig{at}durham.ac.uk The alternate strip-based substructuring algorithms are efficientpreconditioning techniques for the discrete systems which arisefrom the finite-element approximation of symmetric ellipticboundary-value problems in 2D Euclidean spaces. The new approachis based on alternate decomposition of the given domain intoa finite number of strips. Each strip is a union of non-overlappingsubdomains and the global interface between subdomains is partitionedas a union of edges between strips and edges between subdomainsthat belong to the same strip. Both scalability and efficiencyare achieved by alternating the direction of the strips. Thisapproach generates algorithms in two stages and allows the useof a two-grid V cycle. Numerical estimates illustrate the behaviourof the new domain decomposition techniques.     

The Z-transform and linear multistep stability

^** Email: mapjjc{at}maths.bath.ac.uk^*** Corresponding author. Email: ath{at}maths.bath.ac.uk^**** Email: hl{at}maths.bath.ac.uk This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods.     

A unified framework for the numerical solution of general quadratic matrix equations

^** Email: vassilios.tsachouridis{at}ieee.org^*** Email: N.karcanias{at}city.ac.uk^**** Email: ixp{at}le.ac.uk Algebraic quadratic equations are special cases of a singlegeneralized algebraic quadratic matrix equation (GQME). Thispaper focuses on the numerical solution of the GQME using probability-1homotopy methods. A synoptic review of these methods and theirapplication to algebraic matrix equations is provided as background.A large variety of analysis and design problems in systems andcontrol are reported as special cases of the presented frameworkand some of them are illustrated via numerical examples fromthe literature.     

An explicit expression for the surface-impedance tensor of a compressible monoclinic material in a state of plane strain

^** Email: y.fu{at}keele.ac.uk^*** Email: d.w.brookes{at}keele.ac.uk We present an explicit expression for the surface-impedancetensor associated with a compressible monoclinic elastic materialin a state of plane strain. Among a wide range of applications,such an explicit expression can, for instance, be used to writedown an explicit secular equation for the surface or interfacialwave speed, and an explicit bifurcation condition for surfaceor interfacial wrinkling. A previously known quartic secularequation for the surface-wave speed is recovered as a by-product.     

Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem

Email: ain{at}mcs.le.ac.uk Email: D.Kelly{at}unsw.edu.au^* Email: I.Sloan{at}unsw.edu.au^** Email: swang{at}cs.curtin.edu.au It is shown how the finite element approximation of a nonlinearheat conduction problem may be post-processed to yield enhancedapproximations to the solution and the flux at any point inthe domain. Sharp computable bounds on the accuracy of the post-processedapproximations are derived. A criterion is identified for guidingadaptive refinements of the finite element discretization. Anumerical example is given illustrating the theoretical results.     

On the numerical solution of involutive ordinary differential systems: enhanced linear algebra

^** Email: jukka.tuomela{at}joensuu.fi^*** Corresponding author. Email: arponen{at}maths.warwick.ac.uk^**** Email: villesamuli.normi{at}joensuu.fi We analyse some Runge–Kutta type methods for computing1D integral manifolds, i.e. solutions to ordin-ary differentialequations and differential-algebraic equations. We show thatwe can compute the solutions which respect all the constraintsof the problem reliably and reasonably quickly. Moreover, weshow that the so-called impasse points are regular points inour approach and hence require no special attention.     

A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems

^** Email: emmanuil.georgoulis{at}mcs.le.ac.uk^*** Email: al{at}maths.strath.ac.uk We consider a variant of the hp-version interior penalty discontinuousGalerkin finite element method (IP-DGFEM) for second-order problemsof degenerate type. We do not assume uniform ellipticity ofthe diffusion tensor. Moreover, diffusion tensors of arbitraryform are covered in the theory presented. A new, refined recipefor the choice of the discontinuity-penalization parameter (thatis present in the formulation of the IP-DGFEM) is given. Makinguse of the recently introduced augmented Sobolev space framework,we prove an hp-optimal error bound in the energy norm and anh-optimal and slightly p-suboptimal (by only half an order ofp) bound in the L² norm (the latter, for the symmetric versionof the IP-DGFEM), provided that the solution belongs to an augmentedSobolev space.     

Differentiated service delivery in cooperative IP-based broadcast and mobile telecommunications networks

Email: angelo.centonza{at}brunel.ac.uk Corresponding author. Email: thomas.owens{at}brunel.ac.uk Email: john.cosmas{at}brunel.ac.uk^¶ Email: y.h.song{at}brunel.ac.uk Received on 26 November 2005. Accepted on 20 March 2007. The evolution of wireless systems has led recently to the deploymentof cooperative network infrastructures where networks basedon different technologies cooperate together to offer innovativeservices which the networks individually could not offer. Cooperativenetwork infrastructures are hybrid systems. Examples of hybridsystems are already in use in areas as diverse power systemsand locomotion systems. It is very important to apply efficientsystem management techniques to hybrid systems that produceadvantageous business case scenarios for each participatingsystem and efficient use of the available resources. In thispaper, scenarios are investigated where cooperation betweenan integrated project (IP)-based broadcast network and an IP-basedmobile telecommunications network has the potential to allowservices to be provided to mobile users which would not be economicalto offer over either an IP-based broadcast network or an IP-basedmobile telecommunications network alone. The paper presentsa novel technique for determining which network to use to deliversuch services at a given point in time. The application of thistechnique in appropriate scenarios has the potential to generateadditional income for both the IP-based broadcast network operatorand the IP-based mobile telecommunications network operatorin an infrastructure where the operators cooperate to offerinnovative services. The paper explains the construction ofutility functions for cooperative IP-based broadcast and mobiletelecommunications networks. These utility functions are thenused to provide results that enable the efficiency of the managementof the network to be assessed in terms of the utility volumegenerated by the innovative services provided.     

An a posteriori error indicator for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

^** Email: paul.houston{at}nottingham.ac.uk^*** Corresponding author. Email: ilaria.perugia{at}unipv.it^**** Email: schoetzau{at}math.ubc.ca We introduce a residual-based a posteriori error indicator fordiscontinuous Galerkin discretizations of H(curl; )-ellipticboundary value problems that arise in eddy current models. Weshow that the indicator is both reliable and efficient withrespect to the approximation error measured in terms of a naturalenergy norm. We validate the performance of the indicator withinan adaptive mesh refinement procedure and show its asymptoticexactness for a range of test problems.     

Diffusion and convection of gaseous and fine particulate from a chimney

^** Email: ajm{at}maths.strath.ac.uk Particle dispersion from a high chimney is considered and anexpression for the subsequent concentration of the particulatedeposited on the ground is derived. We consider the generalcase wherein the effects of both diffusion and convection onthe steady state ground concentration of particulate are incorporated.Two key parameters emerge from this analysis: the ratio of diffusionto convection and the nondimensionalised surface mass transferrate. We also solve the inverse problem of recovering thesetwo parameters given the boundary concentration profile andprovide an estimate of the concentration flux above the chimneystack.     

A finite-element analysis of critical-state models for type-II superconductivity in 3D

^** Email: c.m.elliott{at}sussex.ac.uk^*** Corresponding author. Email: y.kashima{at}sussex.ac.uk We consider the numerical analysis of evolution variationalinequalities which are derived from Maxwell's equations coupledwith a nonlinear constitutive relation between the electricfield and the current density and governing the magnetic fieldaround a type-II bulk superconductor located in 3D space. Thenonlinear Ohm's law is formulated using the subdifferentialof a convex energy so the theory is applied to the Bean critical-statemodel, a power law model and an extended Bean critical-statemodel. The magnetic field in the nonconducting region is expressedas a gradient of a magnetic scalar potential in order to handlethe curl-free constraint. The variational inequalities are discretizedin time implicitly and in space by Nédélec's curl-conformingfinite element of lowest order. The nonsmooth energies are smoothedwith a regularization parameter so that the fully discrete problemis a system of nonlinear algebraic equations at each time step.We prove various convergence results. Some numerical simulationsunder a uniform external magnetic field are presented.     

On a modified version of ILDM approach: asymptotic analysis based on integral manifolds

^** Email: vbykov{at}cs.bgu.ac.il^*** Email: goldfarb{at}cs.bgu.ac.il^**** Email: vladimir{at}bgumail.bgu.ac.il^***** Email: umaas{at}itt.mach.uni-karlsruhe.de Using the method of integral (invariant) manifolds, the intrinsiclow-dimensional manifolds (ILDM) method is analysed. This isa method for identifying invariant manifolds of a system's slowdynamics and has proven to be an efficient tool in modellingof laminar and turbulent combustion. It allows treating multi-scalesystems by revealing their hidden hierarchy and decomposingthe system dynamics into fast and slow motions. The performedanalysis shows that the original ILDM technique can be interpretedas one of the many possible realizations of the general framework,which is based on a special transformation of the original coordinatesin the state space. A modification of the ILDM is proposed basedon a new definition of the transformation matrix. The proposednumerical procedure is demonstrated on linear examples and highlynon-linear test problems of mathematical theory of combustionand demonstrates in some cases better performance with respectto the existing one.     

A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations

^** Corresponding author. Email: l.elalaoui{at}imperial.ac.uk^*** Email: ern{at}cermics.enpc.fr^**** Email: erik.burman{at}epfl.ch We analyse a non-conforming finite-element method to approximateadvection–diffusion–reaction equations. The methodis stabilized by penalizing the jumps of the solution and thoseof its advective derivative across mesh interfaces. The a priorierror analysis leads to (quasi-)optimal estimates in the meshsize (sub-optimal by order in the L²-norm and optimal in thebroken graph norm for quasi-uniform meshes) keeping the Pécletnumber fixed. Then, we investigate a residual a posteriori errorestimator for the method. The estimator is semi-robust in thesense that it yields lower and upper bounds of the error whichdiffer by a factor equal at most to the square root of the Pécletnumber. Finally, to illustrate the theory we present numericalresults including adaptively generated meshes.     

Parallel variable neighbourhood search algorithms for job shop scheduling problems

^** Email: msevkli{at}fatih.edu.tr^*** Corresponding author. Email: mehmetaydin{at}acm.org, mehmet.aydin{at}beds.ac.uk Variable neighbourhood search (VNS) is one of the most recentmetaheuristics used for solving combinatorial optimization problemsin which a systematic change of neighbourhood with a local searchis carried out. However, as happens with other metaheuristics,it takes a long time to reach some useful solutions while solvingsome sort of hard combinatorial problems such as job shop scheduling(JSS). Parallelization is one of the most considerable policiesto overcome this matter. In this paper, firstly, a number ofVNS algorithms are examined for JSS problems and then four differentparallelization policies are taken into account to determineefficient parallelization for VNS algorithms. The experimentationreveals the performance of various VNS algorithms and the efficiencyof policies to follow in parallelization. In the end, the unilateral-ringtopology, a noncentral parallelization method, is found as themost efficient policy.     

Robust constrained linear regulator problem

^** Email: mesquine{at}ucam.ac.ma^*** Email: a.benlamkadem{at}ucam.ac.ma The robust constrained state and control regulator problem isconsidered. Necessary and sufficient conditions of positiveinvariance are established. A linear programming approach ispresented in order to construct, for an uncertain constrainedlinear system, a stabilizing linear state feedback control.The control law transfers asymptotically to the origin any initialstate belonging to a given set, while constraints on the stateand the control vectors are respected.     

Explicit stability conditions for time-discrete vector Lur'e-type systems

^** Email: gilmi{at}cs.bgu.ac.il^*** Email: rmedina{at}ulagos.cl Non-linear discrete-time Lur'e-type systems are considered.Explicit stability conditions are suggested. They are formulatedin terms of the determinants of characteristic polynomials.Moreover, an estimate for the region of attraction of the zerosolution is derived.     

Boundary feedback stabilization of coupled sine-Gordon equations

^** Email: koba{at}cntl.kyutech.ac.jp^*** Email: sakamoto{at}cntl.kyutech.ac.jp This paper is concerned with global stabilization of the systemgoverned by coupled sine-Gordon equations without damping. Astabilizer is constructed by boundary velocity feedback. Theclosed-loop system is shown to be well posed by the non-linearsemigroup approach. Moreover, using a multiplier method, globalexponential stabilization of the closed-loop system is proved.     

An adaptive boundary element method for the exterior Stokes problem in three dimensions

^** Email: vjervin{at}clemson.edu^*** Email: norbert.heuer{at}brunel.ac.uk We present an adaptive refinement strategy for the h-versionof the boundary element method with weakly singular operatorson surfaces. The model problem deals with the exterior Stokesproblem, and thus considers vector functions. Our error indicatorsare computed by local projections onto 1D subspaces definedby mesh refinement. These indicators measure the error separatelyfor the vector components and allow for component-independentadaption. Assuming a saturation condition, the indicators giverise to an efficient and reliable error estimator. Also we describehow to deal with meshes containing quadrilaterals which arenot shape regular. The theoretical results are underlined bynumerical experiments. To justify the saturation assumption,in the Appendix we prove optimal lower a priori error estimatesfor edge singularities on uniform and graded meshes.     

Regular linear systems governed by systems with state, input and output delays

^** Email: hadd{at}ucam.ac.ma^*** Email: idrissi{at}ucam.ac.ma In this paper, we give a new reformulation of linear systemswith delays in input, state and output. We show that these systemscan be written as a regular linear system without delays. Thetechnique used here is essentially based on the theory recentlydeveloped by Salamon and Weiss and the shift in semigroup properties.Our framework can be applied, in particular, when the delayoperators are given by Riemann–Stieltjes integrals.     

The dynamic control of risk in optimised portfolios

E-mail: c.j.adcock{at}sheffield.ac.uk or adcock{at}intonet.co.uk This paper presents a theoretical treatment of the statisticalproperties of optimal portfolios. The results demonstrate theway in which the statistical properties of forecast returnsaffect the performance of optimised portfolios. The paper thenindicates how these methods may be used in principle to controlthe performance of an optimised portfolio. This is exemplifiedby an optimal portfolio of foreign currencies.