a reconstruction based chebyshev collocation method for the poisson equation an accurate treatment of the gibbs wilbraham phenomenon on irregular interfaces abstract an accurate numerical solution of the laplace equation and poisson equation is desirable in physical problems related to fluid flows and spectral methods are well suited towards this goal however in the presence of an interface the solution is discontinuous owing to the interface jump conditions and thus the numerical approximation is susceptible to the gibbs wilbraham phenomenon leading to a reduced solution accuracy in order to resolve the discontinuity at the interface we propose a reconstruction technique wherein the approximate solution is expressed as the sum of an infinitely differentiable smooth function and a modified heaviside function the smooth function is composed of chebyshev polynomials while the modified heaviside function is expressed in a weak form using the jump conditions across the interface the reconstruction framework allows us to impose the interfacial conditions exactly to motivate further application of the technique we first present the underlying rationale by revisiting the work of wilbraham 1848 13 followed by the numerical implementation we present numerical solution of four equations to illustrate the application of the proposed technique i an ordinary differential equation ode ii the euler bernoulli equation iii the laplace equation and iv the poisson equation the laplace and poisson equation are solved on a square domain embedded with complex interfacial geometries in two dimensions and on a cube with a spherical interface in three dimensions the method achieves error in the maximum norm o 10 14 using approximately 30 modes in each direction and requires a computational time of less than a second for all the problems we also conduct a sensitivity analysis to demonstrate the robustness of the algorithm under sub grid scale perturbations to interface location an alternate derivation for the modified heaviside function is proposed that is distinct from the taylor series expansion used to treat interface conditions in difference methods the pointwise error plots are subsequently presented to demonstrate that the gibbs wilbraham phenomenon is accurately resolved finally we present concluding thoughts on the potential applications of the reconstruction technique

a fast numerical method for solving the three dimensional stokes equations in the presence of suspended particles abstract a new fast numerical method for solving the three dimensional stokes equations in the presence of suspended particles is presented the fluid dynamics equations are solved on a lattice a particle is represented by a set of points each of which moves at the local fluid velocity and is not constrained to lie on the lattice these points are coupled by forces which resist deformation of the particle these forces contribute to the force density in the stokes equations as a result a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries particle size shape and deformability may be prescribed computational work increases only linearly with the number of particles so large numbers 500 1000 of particles may be studied efficiently the numerical method involves implicit calculation of the particle forces by minimizing an energy function and solution of a finite difference approximation to the stokes equations using the fourier toeplitz method the numerical method has been implemented to run on all cray computers the implementation exploits the cray s vectorized arithmetic and on machines with insufficient central memory it performs efficient disk 1 o while storing most of the data on disk applications of the method to sedimentation of one two and many particle systems are described trajectories and settling speeds for two particle sedimentation and settling speed for multiparticle sedimentation from initial distributions on a cubic lattice or at random give good quantitative agreement with existing theories

an nth step set invariance approach to the analysis and design of discrete time linear systems subject to actuator saturation abstract for a discrete time linear system subject to actuator saturation an analysis and design approach based on n th step set invariance is proposed an n th step invariant set is a set from which all trajectories will enter a contractively invariant set in n steps and thus can be used as an estimate of the domain of attraction such an estimate is less conservative than an estimate obtained on the basis of contractive invariance of ellipsoids which excludes initial conditions from which the trajectories overshoot outside the ellipsoid before converging to the origin in comparison with the existing approach based on conventional set invariance the proposed approach results in a larger domain of attraction and better performance both in the analysis of the closed loop system under a given feedback gain and in the design of feedback gain in comparison with the saturated and nonsaturated sns invariant set approach which is an analysis approach the proposed approach can be used for control design even in the presence of plant uncertainties

brief an analysis and design method for linear systems subject to actuator saturation and disturbance we present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant this condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis this condition is then extended to determine the invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements the effectiveness of the developed methods is illustrated with examples

stability analysis for the immersed fiber problem a linear stability analysis is performed on a two dimensional version of the immersed fiber problem formulated by c peskin to model the flow of fluid in the presence of a mesh of moving elastic fibers the purpose of the analysis is to isolate the modes in the solution which are associated with the fiber and thereby determine the effect of the presence of a fiber on the fluid the results are used not only to make conclusions about the stability of the problem but also to suggest guidelines for developing numerical methods for flows with immersed fibers

cubic hypersurfaces admitting an embedding with gauss map of rank 0 abstract we give a characterization of fermat cubic hypersurfaces of dimension greater than 2 in characteristic 2 in terms of the property called gmrz that a projective variety admits an embedding whose gauss map is of rank 0 in contrast to the higher dimensional case for cubic surfaces the above characterization is no longer true moreover we prove that the process of blowing up at points preserves the property gmrz and that every smooth rational surface in fact satisfies gmrz in the characteristic 2 case

guaranteed cost synchronization of chaotic cellular neural networks with time varying delay synchronization of cellular neural networks with time varying delay is discussed in this letter based on razumikhin theorem a guaranteed cost synchronous controller is given unlike lyapunov krasovskii analysis process there is no constraint on the change rate of time delay the saturated terms emerging in the razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by lipschitz condition and vector inequality which will bring more conservatism then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form with the help of a sufficient and necessary transformation condition the minimization of the guaranteed cost is studied and a further criterion for getting the controller is presented finally the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time varying delay cellular neural networks

absolute stability with a generalized sector condition this paper generalizes the linear sector in the classical absolute stability theory to a sector bounded by concave convex functions this generalization allows more flexible or more specific description of the nonlinearity and will thus reduce the conservatism in the estimation of the domain of attraction we introduce the notions of generalized sector and absolute contractive invariance for estimating the domain of attraction of the origin necessary and sufficient conditions are identified under which an ellipsoid is absolutely contractively invariant in the case that the sector is bounded by piecewise linear concave convex functions these conditions can be exactly stated as linear matrix inequalities moreover if we have a set of absolutely contractively invariant aci ellipsoids then their convex hull is also aci and inside the domain of attraction we also present optimization technique to maximize the absolutely contractively invariant ellipsoids for the purpose of estimating the domain of attraction the effectiveness of the proposed method is illustrated with examples

on finite gain stabilizability of linear systems subject to input saturation this paper deals with global finite gain input output stabilization of linear systems with saturated controls for neutrally stable systems it is shown that the linear feedback law suggested by the passivity approach indeed provides stability with respect to every l p norm explicit bounds on closed loop gains are obtained and they are related to the norms for the respective systems without saturation these results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple size 1 jordan blocks contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state space sense this is shown in particular for the double integrator

on the order of accuracy of the immersed boundary method higher order convergence rates for sufficiently smooth problems the immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a visco elastic structure in m c lai simulations of the flow past an array of circular cylinders as a test of the immersed boundary method ph d thesis courant institute of mathematical sciences new york university 1998 m c lai c s peskin an immersed boundary method with formal second order accuracy and reduced numerical viscosity j comput phys 160 2000 705 719 lai and peskin introduced a formally second order accurate immersed boundary method but the convergence properties of their algorithm have only been examined computationally for problems with nonsmooth solutions consequently in practice only first order convergence rates have been observed in the present work we describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid structure interaction problem involving an immersed viscoelastic shell of finite thickness studied over a broad range of reynolds numbers we consider two sets of material properties for the viscoelastic structure including a case where the material properties of the coupled system are discontinuous at the fluid structure interface for both sets of material properties the true solutions appear to possess sufficient smoothness for the method to converge at a second order rate for fully resolved computations

immersed finite element method abstract in this paper the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models in ifem a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain hence the mesh generation is greatly simplified moreover both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method rkpm delta function in comparison with the immersed boundary ib method the higher ordered rkpm delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions the use of such kernel functions may eventually open doors to multi scale and multi resolution modelings of complex fluid structure interaction problems rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method the results compare well with the experimental data to the authors knowledge these are the first solutions that deal with particulate flows with very flexible solids

disturbance attenuation for systems with input saturation an lmi approach a new design technique is proposed to improve disturbance attenuation for systems with input saturation the main results rely on a multiobjective approach which combines the quadratic stabilization technique with constraints on inputs for the full state feedback problem the sufficient conditions for the feasibility of a high gain controller are expressed in terms of linear matrix inequalities lmi for output feedback design the controllers are assumed to have an observer based structure the sufficient conditions for the output feedback controller to recover the full state properties are also given in terms of lmi

h sub spl infin almost disturbance decoupling with internal stability for linear systems subject to input saturation for a linear system subject to input saturation and input additive disturbances we show that 1 the h sub spl infin almost disturbance decoupling problem with local asymptotic stability is always solvable via state feedback as long as the system in the absence of saturation is stabilizable no matter where the open loop poles are and 2 the h sub spl infin almost disturbance decoupling problem with semiglobal asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open loop poles located in the closed left half plane the results generalize those in lin et al 1996 by not requiring the disturbance to be bounded by a known bound or even bounded

brief paper disturbance tolerance and rejection of linear systems with imprecise knowledge of actuator input output characteristics we study the robustness of linear systems with respect to the disturbances and the uncertainties in the actuator input output characteristics disturbances either bounded in energy or bounded in magnitude are considered the actuator input output characteristics are assumed to reside in a so called generalized sector bounded by piecewise linear curves robust bounded state stability of the closed loop system is first defined and characterized in terms of linear matrix inequalities lmis based on this characterization the evaluation of the disturbance tolerance and disturbance rejection capabilities of the closed loop system under a given feedback law is formulated into and solved as optimization problems with lmi constraints

brief paper l2 gain analysis for a class of switched systems this paper considers the problem of disturbance tolerance rejection for a family of linear systems subject to actuator saturation and l 2 disturbances for a given set of linear feedback gains a given switching scheme and a given bound on the l 2 norm of the disturbances conditions are established in terms of linear or bilinear matrix inequalities under which the resulting switched system is bounded state stable that is trajectories starting from a bounded set will remain inside the set or a larger bounded set with these conditions both the problem of assessing the disturbance tolerance rejection capability of the closed loop system and the design of feedback gain and switching scheme can be formulated and solved as constrained optimization problems disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories from a given set remain bounded disturbance rejection is measured by the restricted l 2 gain over the set of tolerable disturbances in the event that all systems in the family are identical the switched system reduces to a single system under a switching feedback law it will be shown that such a single system under a switching feedback law has stronger disturbance tolerance rejection capability than a single linear feedback law can achieve

the almost disturbance decoupling problem with internal stability for linear systems subject to input saturation state feedback case abstract we consider the almost disturbance decoupling problem addp and or almost d bounded disturbance decoupling problem addp d with internal stability for linear systems subject to input saturation and input additive disturbance via linear static state feedback we show that the almost d bounded disturbance decoupling problem with local asymptotic stability addp las d is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable no matter where the poles of the open loop system are and the locations of these poles play a role only in the solution of addp gas d addp sgas d or addp gas where semi global or global asymptotic stability is required

the immersed structural potential method for haemodynamic applications in this paper a new fluid structure interaction immersed computational methodology based upon the original immersed boundary method ibm 1 is outlined with the final aim of modelling cardiovascular phenomena specifically heart valve related problems the principal characteristic of such immersed techniques is the representation of any deformable or rigid body immersed within an incompressible viscous flow field as a momentum forcing source in the navier stokes equations a number of shortcomings within the immersed formulation still require further investigation and improvement including the excessive numerical diffusion caused by the interpolation spreading process the need to include realistic viscoelastic composite constitutive models describing more accurately the nature of cardiovascular tissues and also the need to capture more effectively stresses developed at the fluid structure interface by following the same philosophy as the original ibm a more sophisticated formulation is derived in this paper the immersed structural potential method ispm the method introduced presents an alternative approach to compute the equivalent fluid structure interaction forces at the fluid mesh accounts for a sophisticated viscoelastic fibre reinforced constitutive model to better describe the mechanics of cardiovascular tissues and utilises a novel time integration methodology for the computation of the deformation gradient tensor which ensures compliance with the incompressibility constraint a series of numerical examples will be presented in order to demonstrate the robustness and applicability of this new methodology

analysis of linear systems in the presence of actuator saturation and l2 disturbances this paper presents a method for the analysis and control design of linear systems in the presence of actuator saturation and l 2 disturbances a simple condition is derived under which trajectories starting from an ellipsoid will remain inside an outer ellipsoid the stability and disturbance tolerance rejection ability of the closed loop system under a given feedback law is measured by the size of these two ellipsoids and the difference between them based on the above mentioned condition the problem of estimating the largest inner ellipsoid and or the smallest difference between the two ellipsoid is then formulated as a constrained optimization problem all the constraints are shown to be equivalent to lmis in addition disturbance rejection ability in terms of l 2 gain is also determined by the solution of an lmi optimization problem by viewing the feedback gain as an additional free parameter the optimization problem can easily be adapted for controller design numerical examples show that the proposed analysis and design methods significantly improve recent results on the same problems

a spectral element formulation of the immersed boundary method for newtonian fluids a spectral element formulation of the immersed boundary method ibm is presented the spectral element formulation se ibm is a generalisation of the finite element immersed boundary method fe ibm based on high order approximations of the fluid variables several schemes for tracking the movement of the immersed boundary are considered and a semi implicit euler scheme is shown to offer advantages in terms of accuracy and efficiency high order spectral element approximations provide improved area conservation properties of the ibm due to the incompressibility constraint being more accurately satisfied superior orders of convergence are obtained for se ibm compared with fe ibm in both l2 and h1 norms the area conservation and convergence properties of the scheme are demonstrated on a series of benchmark problems

on computational issues of immersed finite element methods the objective of this paper is to provide a review of recent finite element formulations for immersed methods in these finite element formulations independent lagrangian solid meshes are introduced to move on top of a background eulerian fluid mesh this key feature allows the handling without excessive fluid mesh adaptation multiple deformable solids immersed in viscous fluid in particular pros and cons of both explicit and implicit approaches are illustrated along with subtle differences between incompressible and slightly compressible models

unconditionally stable discretizations of the immersed boundary equations the immersed boundary ib method is known to require small timesteps to maintain stability when solved with an explicit or approximately implicit method many implicit methods have been proposed to try to mitigate this timestep restriction but none are known to be unconditionally stable and the observed instability of even some of the fully implicit methods is not well understood in this paper we prove that particular backward euler and crank nicolson like discretizations of the nonlinear immersed boundary terms of the ib equations in conjunction with unsteady stokes flow can yield unconditionally stable methods we also show that the position at which the spreading and interpolation operators are evaluated is not relevant to stability so as long as both operators are evaluated at the same location in time and space we further demonstrate through computational tests that approximate projection methods which do not provide a discretely divergence free velocity field appear to have a stabilizing influence for these problems and that the implicit methods of this paper when used with the full navier stokes equations are no longer subject to such a strict timestep restriction and can be run up to the cfl constraint of the advection terms

chebyshev collocation method and multi domain decomposition for navier stokes equations in complex curved geometries a general multidomain decomposition is proposed for the numerical solution of the 2d incompressible stationary navier stokes equations the solution technique consists in a chebyshev orthogonal collocation method preconditioned by a standard galerkin finite element technique the preconditioned system is then solved through a richardson procedure the domain of interest is decomposed into quadrilaterals curved when needed a gordon transfinite interpolation performs the curvilinear grid generation of the obtained simply connected planar subdomains the interface conditions naturally incorporated into the finite element approach relate neighbour subdomains through the normal jump of appropriate fluxes across internal boundaries where an integral form ofc 1 continuity is consequently achieved at convergence of the iterative processes the study of model stokes problems demonstrates that the current method still behaves spectrally in distorted geometries for curvilinear distortion a loss of several orders of magnitude is observed in the solution accuracy even when the distortion is very limited finally some results of flow simulation in a constricted channel are proposed to illustrate the abilities of the present method to treat navier stokes problems

analysis and design of singular linear systems under actuator saturation and l2 l disturbances abstract this paper carries out an analysis of the l 2 gain and l performance for singular linear systems under actuator saturation the notion of bounded state stability bss with respect to the influence of l 2 or l disturbances is introduced and conditions under which a system is bounded state stable are established in terms of linear matrix inequalities lmis the disturbance tolerance capability of the system is then measured as the bound on the l 2 or l norm of the disturbances under which the system remains bounded state stable and the disturbance rejection capability is measured by the restricted l 2 gain from the disturbance to the system output or l norm of the system output based on the bss conditions assessment of the disturbance tolerance and rejection capabilities of the system under a given state feedback law is formulated and solved as lmi constrained optimization problems by viewing the feedback gain as an additional variable these optimization problems can be readily adapted for control design our analysis and design reduce to the existing results for regular linear systems in the degenerate case where the singular linear system reduces to a regular system and to the existing results for singular systems in the absence of actuator saturation or when the disturbance is weak enough to not cause saturation

modeling and parallel computation of the non linear interaction of rigid bodies with incompressible multi phase flow a computational tool is developed to capture the interaction of solid object with two phase flow the full two dimensional navier stokes equations are solved on a regular structured grid to resolve the flow field the level set and the immersed boundary methods are used to capture the free surface of a fluid and a solid object respectively a two step projection method along with multi processing openmp is employed to solve the flow equations the computational tool is verified based on numerical and experimental data with three scenarios a cylinder falling into a rectangular domain due to gravity transient vertical oscillation of a cylinder by releasing above its equilibrium position and a dam breaking in the presence of a fixed obstacle in the first two validation simulations the accuracy of the immersed boundary method is verified however the accuracy of the level set method while the computational tool can model the high density ratio is confirmed in the dam breaking simulation the results obtained from the current method are in good agreement with experimental data and other numerical studies the applicability of the current computational tool for the interaction of a buoy in a water wave tank with two types of waves symmetrical and asymmetrical waves has also been studied

a computational model of the cochlea using the immersed boundary method this thesis describes a two dimensional computational model of the cochlea inner ear solved using a modified form of peskin s immersed boundary method this method is an extension of peskin s method that was originally applied to solving a model of the heart 1972 this method solves the time dependent incompressible navier stokes equations in the presence of immersed boundaries the fluid equations are specified on a fixed eulerian grid while the immersed boundaries are specified on a moving lagrangian grid the immersed boundaries are used to represent the structures of the cochlea the rigid bone the actively moving stapes and the flexible membranes the immersed boundaries exert forces locally on the fluid these local forces are seen by the fluid as external forces that are added to the other forces pressure and viscous acting on the fluid the computational method divides into three separate parts first the forces exerted by the points of the immersed boundary are calculated and extended to the fluid grid second the fluid equations are solved and the velocities are restricted to the immersed boundary points finally the immersed boundary points are moved to their new locations at the new local velocities the immersed boundary forces are either specified such that the boundary moves at a given velocity zero or non zero or they are specified such that the forces obey some given force law for example hooke s law these forces can be calculated either explicitly or implicitly or a combination of both for the fluid the navier stokes equations are solved on a doubly periodic rectangular grid in a second order accurate manner using a projection method developed by bell colella and glaz 1988 the extension and restriction of the boundary forces and fluid velocities to and from the fluid grid are also done in a second order accurate manner the cochlea is modelled as two fluid chambers separated by a flexible partition whose stiffness varies exponentially along its length the stapes is represented by a moving piston and the bony outer walls are allowed to be either straight or tapered a travelling wave propagates along the flexible partition under the influence of the moving piston and the dependence of this wave on cochlea geometry and partition stiffness is studied also included are studies of bone conduction and transient signal analysis finally comparisons of the model results are made to experimental data and asymptotic results

analysis of a one dimensional model for the immersed boundary method numerical methods are studied for the one dimensional heat equation with a singular forcing term u t u xx c t delta x alpha t the delta function delta x is replaced by a discrete approximation d h x and the resulting equation is solved by a crank nicolson method on a uniform grid the accuracy of this method is analyzed for various choices of d h the case where c t is specified and also the case where c is determined implicitly by a constraint on the solution at the point a are studied these problems serve as a model for the immersed boundary method of peskin for incompressible flow problems in irregular regions some insight is gained into the accuracy that can be achieved and the importance of choosing appropriate discrete delta functions

on the hyper elastic formulation of the immersed boundary method abstract the immersed boundary ib method is both a mathematical formulation and a numerical method for fluid structure interaction problems in which immersed incompressible visco elastic bodies or boundaries interact with an incompressible fluid previous formulations of the ib method were not able to treat appropriately immersed materials of finite nonzero thickness modeled by general hyper elastic constitutive laws because of the lack of appropriate transmission conditions between the immersed body and the surrounding fluid in the case of a nonzero jump in normal stress at the solid fluid interface such a jump does not arise when the solid is comprised of fibers that run parallel to the interface but typically does arise in other cases e g when the solid contains elastic fibers that terminate at the solid fluid interface we present a derivation of the ib method that takes into account in an appropriate way the missing term the derivation presented in this paper starts from a separation of the stress that appears in the principle of virtual work the stress is divided into its fluid like and solid like components and each of these two terms is treated in its natural framework i e the eulerian framework for the fluid like stress and the lagrangian framework for the solid like stress we describe how the ib method can be used in conjunction with standard formulations of continuum mechanics models for immersed incompressible elastic materials and present some illustrative numerical experiments

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

analysis of stiffness in the immersed boundary method and implications for time stepping schemes the immersed boundary method is known to exhibit a high degree of numerical stiffness associated with the interaction of immersed elastic fibres with the surrounding fluid we perform a linear analysis of the underlying equations of motion for immersed fibres and identify a discrete set of fibre modes which are associated solely with the presence of the fibre this work generalises our results in a previous paper 1995 siam j appl math 55 1577 by incorporating the effect of spreading the singular fibre force over a finite smoothing radius corresponding to the approximate delta function used in the immersed boundary method we investigate the stability of the fibre modes their stiffness and their dependence on the problem parameters focusing on the influence of smoothing we then extend the analytical results to include the effect of time discretisation and draw conclusions about the time step restrictions on various explicit schemes as well as the convergence rates for an iterative semi implicit method we draw comparisons with computations and show how the results can be applied to help in choosing alternate time stepping schemes that are specially tailored to handle the stiffness in immersed fibres in particular we present numerical results that show how fully explicit runge kutta schemes perform in comparison with the best of the semi implicit schemes currently in use

improved volume conservation in the computation of flows with immersed elastic boundaries this paper introduces a recipe for the construction of a finite difference divergence operator the coefficients of which are completely determined once an interpolation scheme has been chosen substitution of this divergence operator for the previously used divergence based on central differences makes a dramatic improvement in the overall volume conservation that is observed in an immersed boundary computation this improvement is particularly important for computations in which an elastic boundary separates chambers containing fluid at substantially different pressures a situation which is prominent in cardiac fluid dynamics during the contraction of the ventricles

a discontinuous galerkin based immersed boundary method a numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced the proposed method is conceptually simple and free of user defined parameters starting with a conforming finite element mesh the key ingredient is to switch those elements intersected by the dirichlet boundary to a discontinuous galerkin approximation and impose the dirichlet boundary conditions strongly by virtue of relaxing the continuity constraint at those elements boundary locking is avoided and optimal order convergence is achieved this is shown through numerical experiments in reaction diffusion problems copyright 2008 john wiley sons ltd